Arc Flash Hazard (IEEE 1584-2018) — help

Overview

Calculates the arc-flash hazard at one bus of a three-phase AC system from 208 V to 15 kV using the empirical model of IEEE 1584-2018: arcing current, incident energy at the working distance and the arc-flash boundary. PPE guidance follows NFPA 70E-2024 Table 130.5(G) for an incident-energy analysis. Use it for arc-flash risk assessments, PPE selection and equipment labelling.

The calculation follows the procedure of the standard step by step:

Intermediate average arcing currents at the three reference voltages 600 V, 2700 V and 14 300 V (Eq 1).
The final arcing current: interpolated to the system voltage above 600 V (Eq 16–18), or from Eq 25 at or below 600 V.
The arcing-current variation correction factor and the reduced arcing current (Eq 2).
The enclosure size correction factor (Eq 11–15).
Incident energy for the full and the reduced arcing current, each with its own clearing time (Eq 3–6, interpolated with Eq 19–21 above 600 V).
Arc-flash boundary for both cases (Eq 7–10, interpolated with Eq 22–24 above 600 V).
The higher incident energy governs; PPE per NFPA 70E-2024 Table 130.5(G).

The engine is verified against both worked examples of IEEE 1584-2018 Annex D and against cases exported from the official IEEE 1584-2018 calculator spreadsheet (see Testing).

Input Parameters

System Parameters

Parameter	Type	Default	Range	Description
`voltage`	Number	480 V	208 – 15 000 V	Nominal line-to-line voltage (three-phase). Any value in the range is accepted; common values are 208, 240, 380, 400, 415, 480, 600, 690, 1000, 2400, 3300, 4160, 6600, 11 000, 13 800 and 15 000 V. Values outside the range are rejected with the reason. At or below 600 V the low-voltage form of the model is used.
`fault_current`	Number	35 000 A	500 A – 106 kA (≤ 600 V) 200 A – 65 kA (> 600 V)	Three-phase symmetrical rms bolted fault current at the bus
`arcing_time`	Number	100 ms	> 0 ms	Arc duration (protective device clearing time) at the full arcing current \(I_{arc}\)
`arcing_time_min`	Number	= `arcing_time`	> 0 ms	Arc duration at the reduced arcing current \(I_{arc,min}\). With inverse-time protection this is usually longer; read it from the device characteristic at \(I_{arc,min}\).

Equipment Configuration

Parameter	Type	Default	Range	Description
`equipment_type`	Enum	LV_Switchgear	—	Equipment class from IEEE 1584-2018 Tables 8 and 10 (see below). Its typical conductor gap, working distance and enclosure size fill any of those inputs left blank; values you enter always take precedence. `Custom` has no class defaults.
`electrode_config`	Enum	VCB	—	VCB vertical conductors in a metal box; VCBB vertical conductors terminated in an insulating barrier in a box; HCB horizontal conductors in a box; VOA vertical conductors in open air; HOA horizontal conductors in open air.
`conductor_gap`	Number	32 mm	6.35 – 76.2 mm (≤ 600 V) 19.05 – 254 mm (> 600 V)	Gap between phase conductors
`working_distance`	Number	609.6 mm	≥ 305 mm	Distance from the arc to the worker’s face and chest

Enclosure Dimensions

Parameter	Type	Default	Range	Description
`enclosure_height`	Number	508 mm	> 0 mm	Height of the enclosure opening. Above 1244.6 mm (49 in) it is treated as 1244.6 mm.
`enclosure_width`	Number	508 mm	> 0 mm	Width of the enclosure opening. Above 1244.6 mm it is treated as 1244.6 mm.
`enclosure_depth`	Number	508 mm	> 0 mm	Enclosure depth. Below 600 V, a box with height and width < 508 mm and depth ≤ 203.2 mm is shallow.

Enclosure dimensions are required for the enclosed configurations (VCB, VCBB, HCB) and are not used for open air (VOA, HOA).

Equipment Classes (IEEE 1584-2018 Tables 8 and 10)

Equipment class (`equipment_type`; MCP `equipment_class`)	Gap (mm)	Working distance (mm)	H × W × D (mm)
15 kV switchgear (`15kV_Switchgear`; MCP `15kv_switchgear`)	152	914.4	1143 × 762 × 762
15 kV MCC (`15kV_MCC`; MCP `15kv_mcc`)	152	914.4	914.4 × 914.4 × 914.4
5 kV switchgear (`5kV_Switchgear`; MCP `5kv_switchgear`)	104	914.4	914.4 × 914.4 × 914.4
5 kV MCC (`5kV_MCC`; MCP `5kv_mcc`)	104	914.4	660.4 × 660.4 × 660.4
Low-voltage switchgear (`LV_Switchgear`; MCP `lv_switchgear`)	32	609.6	508 × 508 × 508
Shallow LV MCC or panelboard, depth ≤ 203.2 mm (`LV_MCC_Panel_Shallow`; MCP `lv_mcc_panel_shallow`)	25	457.2	355.6 × 304.8 × 203.2
Deep LV MCC or panelboard, depth > 203.2 mm (`LV_MCC_Panel_Deep`; MCP `lv_mcc_panel_deep`)	25	457.2	355.6 × 304.8 × 254
Shallow cable junction box, depth ≤ 203.2 mm (`Cable_Junction_Box_Shallow`; MCP `cable_junction_box_shallow`)	13	457.2	355.6 × 304.8 × 203.2
Deep cable junction box, depth > 203.2 mm (`Cable_Junction_Box_Deep`; MCP `cable_junction_box_deep`)	13	457.2	355.6 × 304.8 × 254

The class values are typical values. Use measured gaps and enclosure sizes where they are known.

Output Results

Output	Unit	Description
`iarc_600`, `iarc_2700`, `iarc_14300`	A	Intermediate arcing currents at the reference voltages (Eq 1). Only `iarc_600` is used (and reported) at or below 600 V.
`iarc`	A	Final arcing current at the system voltage (Eq 16–18 or Eq 25)
`var_cf`	—	Arcing-current variation correction factor (Eq 2)
`iarc_min` (and `iarc_600_min` … `iarc_14300_min` above 600 V)	A	Reduced arcing current \(I_{arc}(1 - 0.5\,VarC_f)\)
`enclosure_type`	—	`typical`, `shallow`, or none for open air
`equivalent_width_in`, `equivalent_height_in`, `ees_in`	in	Equivalent enclosure width, height and size (Eq 11–13)
`correction_factor`	—	Enclosure size correction factor CF (Eq 14 or 15; 1 for open air)
`ie_600` … `ie_14300_min`, `afb_600` … `afb_14300_min`	J/cm², mm	Incident energy and boundary at each reference voltage, for both cases (above 600 V only)
`ie_full_j` / `ie_cal`	J/cm² / cal/cm²	Incident energy at the working distance, full arcing current
`ie_min_j` / `ie_cal_min`	J/cm² / cal/cm²	Incident energy at the working distance, reduced arcing current
`afb_full`, `afb_min`	mm	Arc-flash boundary for each case
`governing_case`	—	`full` or `reduced`: the case with the higher incident energy
`incident_energy` / `incident_energy_j`	cal/cm² / J/cm²	Governing incident energy
`arc_flash_boundary` (`_inches`, `_meters`)	mm (in, m)	Larger of the two boundaries
`ppe_required`, `ppe_tier`, `ppe_min_arc_rating`, `ppe_description`	—, cal/cm²	PPE per NFPA 70E-2024 Table 130.5(G); the minimum arc rating is the incident energy rounded up to 0.1 cal/cm²
`ppe_category`, `ppe_category_rating`	—, cal/cm²	Equivalent PPE category (0–4), informational only (see PPE); empty above 40 cal/cm², which is beyond category 4
`exceeds_40_cal_cm2`	—	True when the incident energy is above 40 cal/cm²
`warnings`	—	Notes on the limits of the model (see Tips & Limitations)

Formulas

Units follow the standard: \(V_{oc}\) in kV, currents in kA, gap \(G\), working distance \(D\) and enclosure sizes in mm, arc duration \(T\) in ms, incident energy \(E\) in J/cm² (1 cal/cm² = 4.184 J/cm²), \(\lg = \log_{10}\). The coefficients \(k_1 \ldots k_{13}\) and \(b_1 \ldots b_3\) are those of IEEE 1584-2018 Tables 1–7 for the electrode configuration and reference voltage; they are not reproduced here.

Step 1: Intermediate Arcing Current (Eq 1)

\[ I_{arc,V_{oc}} = 10^{\,k_1 + k_2 \lg I_{bf} + k_3 \lg G}\;P_I(I_{bf}) \qquad P_I(I_{bf}) = k_4 I_{bf}^6 + k_5 I_{bf}^5 + k_6 I_{bf}^4 + k_7 I_{bf}^3 + k_8 I_{bf}^2 + k_9 I_{bf} + k_{10} \]

Evaluated at \(V_{oc}\) = 0.6, 2.7 and 14.3 kV with the Table 1 coefficients, giving \(I_{arc,600}\), \(I_{arc,2700}\) and \(I_{arc,14300}\). \(P_I\) is the degree-6 current polynomial; do not confuse it with \(P_E\), the degree-7 energy denominator of Step 5.

Step 2: Final Arcing Current

Above 600 V — interpolation (Eq 16–18)

\[ I_{arc,1} = \frac{I_{arc,2700} - I_{arc,600}}{2.1}\,(V_{oc} - 2.7) + I_{arc,2700} \qquad I_{arc,2} = \frac{I_{arc,14300} - I_{arc,2700}}{11.6}\,(V_{oc} - 14.3) + I_{arc,14300} \] \[ I_{arc,3} = \frac{I_{arc,1}\,(2.7 - V_{oc})}{2.1} + \frac{I_{arc,2}\,(V_{oc} - 0.6)}{2.1} \]

For \(0.6 < V_{oc} \le 2.7\) the final current is \(I_{arc,3}\); for \(V_{oc} > 2.7\) it is \(I_{arc,2}\). The two branches meet at 2.7 kV. The same three-step interpolation is applied to the incident energy (Eq 19–21) and the arc-flash boundary (Eq 22–24).

At or below 600 V (Eq 25)

\[ I_{arc} = \frac{1}{\sqrt{\left(\frac{0.6}{V_{oc}}\right)^2 \left[\frac{1}{I_{arc,600}^2} - \frac{0.6^2 - V_{oc}^2}{0.6^2\,I_{bf}^2}\right]}} \]

At exactly 600 V this returns \(I_{arc,600}\).

Step 3: Arcing-Current Variation and Reduced Arcing Current (Eq 2)

\[ VarC_f = k_1 V_{oc}^6 + k_2 V_{oc}^5 + k_3 V_{oc}^4 + k_4 V_{oc}^3 + k_5 V_{oc}^2 + k_6 V_{oc} + k_7 \qquad I_{arc,min} = I_{arc}\left(1 - 0.5\,VarC_f\right) \]

The arcing current varies about its average value. A lower current can take a protective device longer to clear, so a second calculation is made at \(I_{arc,min}\) with its own clearing time \(T_{min}\). Above 600 V the reduction is applied to each reference-voltage current, which are then interpolated with Eq 16–18. \(VarC_f\) depends on the voltage and the electrode configuration (Table 2) — it is not a fixed percentage.

Step 4: Enclosure Size Correction Factor (Eq 11–15)

Box type. Below 600 V an enclosure with height and width both < 508 mm and depth ≤ 203.2 mm is shallow; every other enclosure is typical.

Equivalent width and height (Eq 11–12, Table 6 constants A, B):

\[ W_1 = \left[660.4 + (W - 660.4)\,\frac{V_{oc} + A}{B}\right]\frac{1}{25.4} \qquad H_1 = \left[660.4 + (H - 660.4)\,\frac{V_{oc} + A}{B}\right]\frac{1}{25.4} \]

Below 508 mm: 20 in for a typical box; the actual size for a shallow box.
508 to 660.4 mm: the actual size (mm / 25.4).
660.4 to 1244.6 mm: Eq 11/12 — except the height of a VCB box, which stays the actual size.
Above 1244.6 mm: calculated as 1244.6 mm (49 in).

\[ EES = \frac{H_1 + W_1}{2} \quad\text{(Eq 13)} \qquad CF = b_1 EES^2 + b_2 EES + b_3 \quad\text{(typical, Eq 14)} \qquad CF = \frac{1}{b_1 EES^2 + b_2 EES + b_3} \quad\text{(shallow, Eq 15)} \]

Open-air configurations (VOA, HOA) have \(CF = 1\).

Step 5: Incident Energy (Eq 3–6)

\[ E = \frac{12.552}{50}\,T \times 10^{\,k_1 + k_2 \lg G + \frac{k_3 I^{*}}{P_E(I_{bf})} + k_{11} \lg I_{bf} + k_{12} \lg D + k_{13} \lg I_{arc} + \lg\frac{1}{CF}} \] \[ P_E(I_{bf}) = k_4 I_{bf}^7 + k_5 I_{bf}^6 + k_6 I_{bf}^5 + k_7 I_{bf}^4 + k_8 I_{bf}^3 + k_9 I_{bf}^2 + k_{10} I_{bf} \]

\(P_E\) uses the Tables 3–5 coefficients, has degree 7 and no constant term — a different polynomial from \(P_I\) in Eq 1, although the coefficient names \(k_4 \ldots k_{10}\) repeat.

Above 600 V (Eq 3, 4, 5): evaluated at each reference voltage with Tables 3–5, using that voltage’s intermediate current for both \(I^{*}\) and \(I_{arc}\); the three energies are then interpolated with Eq 19–21.
At or below 600 V (Eq 6): the 600 V coefficients, with \(I^{*} = I_{arc,600}\) and \(I_{arc}\) the final current of the case (full or reduced).

The reduced case is not symmetric across 600 V. At or below 600 V the \(k_3\) term keeps the full \(I_{arc,600}\) from Eq 1 even for the \(I_{arc,min}\) energy (only the \(k_{13}\) term uses \(I_{arc,min}\)); above 600 V each reduced reference current replaces \(I^{*}\) as well. Both follow the standard and the official IEEE calculator, but the reduced-current energy steps down between 600 V and 601 V while the full-current energy is continuous: for 20 kA bolted, VCB, \(G\) = 32 mm, a 610 mm cube, \(D\) = 609.6 mm and 100 ms, the reduced-current energy is 8.90 J/cm² at 600 V and 6.24 J/cm² at 601 V (full current 10.03 at both). Worked examples 29 and 30 pin both sides of the step.

Both cases are evaluated: \(I_{arc}\) with \(T\) and \(I_{arc,min}\) with \(T_{min}\). The higher energy governs.

Step 6: Arc-Flash Boundary (Eq 7–10)

\[ AFB = 10^{\left(k_1 + k_2 \lg G + \frac{k_3 I^{*}}{k_4 I_{bf}^7 + \cdots + k_{10} I_{bf}} + k_{11} \lg I_{bf} + k_{13} \lg I_{arc} + \lg\frac{1}{CF} - \lg\frac{20}{T}\right) / (-k_{12})} \]

The boundary is the distance at which the incident energy falls to 1.2 cal/cm² (5.0208 J/cm², the onset of a second-degree burn). Because \(E \propto D^{k_{12}}\), this is evaluated equivalently from the energy already found at the working distance:

\[ AFB = D\left(\frac{5.0208}{E}\right)^{1/k_{12}} \]

Above 600 V the boundary is found at each reference voltage and interpolated with Eq 22–24. The reported boundary is the larger of the two cases.

Step 7: PPE (NFPA 70E-2024 Table 130.5(G))

Incident energy	`ppe_tier`	PPE
≤ 1.2 cal/cm²	`none`	Arc-rated PPE not required — but non-melting or untreated natural-fibre clothing is still required, with safety glasses, hearing protection, leather gloves where there is a shock hazard
> 1.2 to 12 cal/cm²	`arc_rated_clothing`	Arc-rated clothing and equipment with an arc rating at or above the incident energy; arc-rated face shield with balaclava, or an arc-rated hood
> 12 cal/cm²	`arc_flash_suit`	Arc-rated clothing with an arc rating at or above the incident energy and an arc-rated arc-flash suit hood

The minimum arc rating of the PPE is the incident energy (rounded up to 0.1 cal/cm²). Above 40 cal/cm² the result is beyond category 4, the highest PPE category rating: the calculator flags it as a practical de-energise threshold. This is industry practice, not an NFPA 70E prohibition — NFPA 70E does not ban energised work above 40 cal/cm²; it requires the hierarchy of risk controls (eliminate the hazard, then reduce it) before any energised work.

How the checks are reported. Exceeding 1.2 cal/cm² is not a failed calculation — almost every real study point exceeds it. It is reported as informational (arc-rated PPE required or not required). Only two checks pass or fail: the 40 cal/cm² de-energise threshold and the 2 s arc duration. The governing check is the pass/fail check with the highest utilisation (value ÷ limit), a failing check taking precedence. When an arc lasts longer than 2 s the energy is reported for the full time entered, and the energy with both clearing times capped at 2 s is given as a sensitivity, since many other tools report the capped figure.

Why no PPE category method. NFPA 70E offers two alternative ways to select arc-flash PPE: an incident-energy analysis (Table 130.5(G)) or the PPE category method (Tables 130.7(C)(15)(a)/(b) and 130.7(C)(15)(c)). The category method has its own equipment tables, fault-current and clearing-time limits and does not use a calculated energy; NFPA 70E does not permit the two to be mixed. This calculator performs an incident-energy analysis, so PPE is specified by its arc rating. The equivalent category (0–4, by the 4/8/25/40 cal/cm² ratings) is reported only as a familiar scale and must not be used to select PPE.

Worked Examples

The 31 examples below are the validation cases for this calculation. Each one was produced by the calculation engine from the inputs shown, every figure was checked against the independent reference quoted at the end of the example, and the same cases are run against every engine build (see validation scorecard, tool fe_calc_arc_flash; worked examples for every calculation).

#	Case	System	I_arc / I_arc,min (kA)	E (cal/cm²)	AFB (mm)	PPE	Result
1	IEEE 1584-2018 Annex D.1: 4.16 kV switchgear (VCB)	4.16 kV VCB, 15 kA	12.979 / 12.675	3.19 (reduced)	1,704	arc-rated clothing	PASS
2	IEEE 1584-2018 Annex D.2: 480 V switchgear (VCB)	480 V VCB, 45 kA	28.793 / 25.244	12.71 (reduced)	2,669	arc-flash suit	PASS
3	208 V lighting panel, 0.5 kA: shallow box, minimum gap and distance	208 V VCB, 0.5 kA	0.229 / 0.197	<0.01 (full)	7	arc-rated PPE not required	PASS
4	400 V VCBB panel, 20 kA, 10 ms current-limiting clearing	400 V VCBB, 20 kA	15.337 / 13.412	0.12 (full)	252	arc-rated PPE not required	PASS
5	400 V busway tap-off box, 106 kA (HCB, shallow box)	400 V HCB, 106 kA	42.175 / 36.130	2.21 (full)	1,234	arc-rated clothing	PASS
6	400 V main switchboard, 106 kA, 1 s clearing: above 40 cal/cm²	400 V VCB, 106 kA	36.112 / 31.505	46.94 (full)	6,046	arc-flash suit; beyond category 4 — de-energise	FAIL
7	400 V open-air vertical bus, 106 kA, 1 s (VOA)	400 V VOA, 106 kA	32.639 / 28.496	29.65 (full)	4,536	arc-flash suit	PASS
8	400 V open-air horizontal bus, 76.2 mm gap (maximum LV gap)	400 V HOA, 106 kA	21.511 / 18.418	3.11 (full)	1,476	arc-rated clothing	PASS
9	415 V MCC bucket, 25 kA (shallow LV MCC preset, VCBB)	415 V VCBB, 25 kA	19.336 / 16.936	8.09 (reduced)	1,313	arc-rated clothing	PASS
10	415 V LV switchgear, 40 kA, ACB short-time delay (LV switchgear preset)	415 V VCB, 40 kA	24.489 / 21.385	14.55 (reduced)	2,906	arc-flash suit	PASS
11	600 V VCBB switchboard: top of the LV range (Eq 25 = Iarc,600)	600 V VCBB, 20 kA	17.465 / 15.571	27.56 (full)	3,447	arc-flash suit	PASS
12	1 kV VOA open-air bus, 20 kA, 10 ms	1 kV VOA, 20 kA	16.200 / 14.865	0.07 (full)	146	arc-rated PPE not required	PASS
13	10 kV HCB, 20 kA, narrow 600 × 200 mm box	10 kV HCB, 20 kA	18.658 / 18.390	8.79 (full)	1,998	arc-rated clothing	PASS
14	10 kV HOA open-air bus, 20 kA	10 kV HOA, 20 kA	18.220 / 17.624	6.07 (full)	1,637	arc-rated clothing	PASS
15	10 kV VCBB, 254 mm gap (maximum HV gap): reduced current governs	10 kV VCBB, 20 kA	18.450 / 18.085	7.54 (reduced)	1,798	arc-rated clothing	PASS
16	11 kV switchgear, 1 kA weak source, 2.5 s backup clearing: beyond the 2 s cap	11 kV VCB, 1 kA	0.914 / 0.902	1.05 (reduced)	1,657	arc-rated PPE not required	FAIL
17	15 kV, 0.2 kA: minimum HV fault current, 1 s clearing	15 kV VCB, 0.2 kA	0.182 / 0.180	0.79 (reduced)	349	arc-rated PPE not required	PASS
18	15 kV outdoor open-air vertical bus (15 kV switchgear preset gap and distance)	15 kV VOA, 20 kA	16.855 / 16.541	1.90 (reduced)	1,233	arc-rated clothing	PASS
19	15 kV open-air horizontal bus (15 kV MCC preset gap and distance)	15 kV HOA, 20 kA	17.766 / 17.190	4.51 (full)	2,059	arc-rated clothing	PASS
20	15 kV switchgear, 65 kA, 1 s clearing: extreme hazard (>120 cal/cm²)	15 kV VCB, 65 kA	59.721 / 59.073	130.56 (reduced)	12,134	arc-flash suit; beyond category 4 — de-energise	FAIL
21	690 V switchboard, VCB, 30 kA: the 0.6–2.7 kV blend inside a box	690 V VCB, 30 kA	23.815 / 21.135	3.55 (full)	1,201	arc-rated clothing	PASS
22	1 kV mine distribution board, VCBB, 25 kA: blend band with a barrier	1 kV VCBB, 25 kA	21.705 / 19.944	12.97 (reduced)	2,298	arc-flash suit	PASS
23	2700 V exactly, VCB, 20 kA: the top of the blend band	2.7 kV VCB, 20 kA	16.982 / 16.219	2.99 (full)	1,635	arc-rated clothing	PASS
24	3.3 kV MCC, 25 kA (5 kV MCC preset)	3.3 kV VCB, 25 kA	21.257 / 20.532	3.88 (reduced)	1,931	arc-rated clothing	PASS
25	6.6 kV switchgear, VCBB, 20 kA, IDMT clearing	6.6 kV VCBB, 20 kA	18.176 / 17.813	9.37 (reduced)	3,024	arc-rated clothing	PASS
26	11 kV switchgear, 25 kA (15 kV switchgear preset)	11 kV VCB, 25 kA	22.667 / 22.381	3.22 (reduced)	1,715	arc-rated clothing	PASS
27	415 V panel, MCCB: 25 ms at Iarc but 3 s at Iarc,min	415 V VCB, 10 kA	7.156 / 6.249	42.49 (reduced)	4,261	arc-flash suit; beyond category 4 — de-energise	FAIL
28	6.6 kV cable termination box narrower than 4 × the gap	6.6 kV VCB, 10 kA	8.829 / 8.720	1.33 (full)	975	arc-rated clothing	PASS
29	600 V, VCB, 20 kA: the low-voltage side of the reduced-case step	600 V VCB, 20 kA	16.272 / 14.368	2.40 (full)	940	arc-rated clothing	PASS
30	601 V, VCB, 20 kA: the interpolated side of the reduced-case step	601 V VCB, 20 kA	16.273 / 14.370	2.40 (full)	940	arc-rated clothing	PASS
31	240 V panel at exactly 2 kA: no sustained-arc note	240 V VCB, 2 kA	0.892 / 0.770	0.93 (full)	390	arc-rated PPE not required	PASS

Example 1 — IEEE 1584-2018 Annex D.1: 4.16 kV switchgear (VCB)

The standard's own medium-voltage worked example: Eq 1 at the three reference voltages, Eq 16-24 interpolation to 4.16 kV, Eq 11-14 enclosure correction; the reduced-current case governs.

Given: V_oc = 4,160 V, I_bf = 15 kA, VCB (vertical conductors in a box), T = 197 ms at I_arc and T_min = 223 ms at I_arc,min; gap G = 104 mm, working distance D = 914.4 mm, enclosure 1,143 H × 762 W × 508 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.042870) + 1.035·lg 15 − 0.083·lg 104} × P_I(15) = 10^1.0070 × 1.0940 = 11.117 kA; 2700 V: 10^{0.006500 + 1.001·lg 15 − 0.024·lg 104} × P_I(15) = 10^1.1354 × 0.9384 = 12.816 kA; 14 300 V: 10^{0.005795 + 1.015·lg 15 − 0.011·lg 104} × P_I(15) = 10^1.1773 × 0.9384 = 14.116 kA (VCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 4.16 kV: I_arc,1 = (12.816 − 11.117)/2.1 × (4.16 − 2.7) + 12.816 = 13.997; I_arc,2 = (14.116 − 12.816)/11.6 × (4.16 − 14.3) + 14.116 = 12.979 → V_oc > 2.7 kV so I_arc = I_arc,2 = 12.979 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 4.16⁵ = (-0.0018); k₃V_oc⁴ = 8.3137×10⁻⁵ × 4.16⁴ = 0.0249; k₄V_oc³ = −0.0019382 × 4.16³ = (-0.1395); k₅V_oc² = 0.022366 × 4.16² = 0.3871; k₆V_oc = −0.12645 × 4.16 = (-0.5260); k₇ = 0.3023; sum = 0.0469; applied to each reference current, I_arc,min = 11.117/12.816/14.116 × (1 − 0.5 × 0.0469) = 10.856/12.515/13.786 kA, interpolated as above to 12.675 kA
Enclosure correction (Eq 11–15)	1,143 H × 762 W × 508 D mm → typical box, Table 7 (typical, VCB). W₁ = [660.4 + (762 − 660.4) × (4.16 + 4)/20]/25.4 (Eq 11) = 27.632 in; H₁ = 1,143/25.4 (VCB height stays actual size) = 45.000 in; EES = (45.000 + 27.632)/2 = 36.316 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 36.316² + 0.03441 × 36.316 + 0.4325 = 1.2838 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 11.117 kA): exponent = k₁ 0.7534 + k₂·lg 104 1.1416 + k₃·11.117/P_E(15) 1.1873 + k₁₁·lg 15 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 11.117 1.0010 + lg(1/1.2838) (-0.1085) = -0.7571; E = 12.552/50 × 197 × 10^-0.7571 (k₁₂ = -1.598) = 8.652 J/cm²; 2700 V (Eq 4, I* = I_arc = 12.816 kA): exponent = k₁ 2.4002 + k₂·lg 104 0.3328 + k₃·12.816/P_E(15) 0.3225 + k₁₁·lg 15 0.0000 + k₁₂·lg 914.4 (-4.6460) + k₁₃·lg 12.816 1.0832 + lg(1/1.2838) (-0.1085) = -0.6159; E = 12.552/50 × 197 × 10^-0.6159 (k₁₂ = -1.569) = 11.977 J/cm²; 14 300 V (Eq 5, I* = I_arc = 14.116 kA): exponent = k₁ 3.8259 + k₂·lg 104 0.2219 + k₃·14.116/P_E(15) (-1.0026) + k₁₁·lg 15 0.0000 + k₁₂·lg 914.4 (-4.6431) + k₁₃·lg 14.116 1.1382 + lg(1/1.2838) (-0.1085) = -0.5682; E = 12.552/50 × 197 × 10^-0.5682 (k₁₂ = -1.568) = 13.367 J/cm²
Interpolated full-current energy (Eq 19–21)	At 4.16 kV: E₁ = (11.977 − 8.652)/2.1 × (4.16 − 2.7) + 11.977 = 14.288; E₂ = (13.367 − 11.977)/11.6 × (4.16 − 14.3) + 13.367 = 12.152 → V_oc > 2.7 kV so E = E₂ = 12.152 J/cm² = 2.904 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 10.856 kA, T_min = 223 ms): exponent = k₁ 0.7534 + k₂·lg 104 1.1416 + k₃·10.856/P_E(15) 1.1595 + k₁₁·lg 15 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 10.856 0.9911 + lg(1/1.2838) (-0.1085) = -0.7948; E = 12.552/50 × 223 × 10^-0.7948 (k₁₂ = -1.598) = 8.980 J/cm²; 2700 V (I_arc,min = 12.515 kA, T_min = 223 ms): exponent = k₁ 2.4002 + k₂·lg 104 0.3328 + k₃·12.515/P_E(15) 0.3149 + k₁₁·lg 15 0.0000 + k₁₂·lg 914.4 (-4.6460) + k₁₃·lg 12.515 1.0731 + lg(1/1.2838) (-0.1085) = -0.6335; E = 12.552/50 × 223 × 10^-0.6335 (k₁₂ = -1.569) = 13.018 J/cm²; 14 300 V (I_arc,min = 13.786 kA, T_min = 223 ms): exponent = k₁ 3.8259 + k₂·lg 104 0.2219 + k₃·13.786/P_E(15) (-0.9791) + k₁₁·lg 15 0.0000 + k₁₂·lg 914.4 (-4.6431) + k₁₃·lg 13.786 1.1280 + lg(1/1.2838) (-0.1085) = -0.5549; E = 12.552/50 × 223 × 10^-0.5549 (k₁₂ = -1.568) = 15.602 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 4.16 kV: E₁ = (13.018 − 8.980)/2.1 × (4.16 − 2.7) + 13.018 = 15.825; E₂ = (15.602 − 13.018)/11.6 × (4.16 − 14.3) + 15.602 = 13.343 → V_oc > 2.7 kV so E = E₂ = 13.343 J/cm² = 3.189 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 914.4 × (5.0208/8.652)^1/(-1.598) = 1,285 mm; 2700 V 914.4 × (5.0208/11.977)^1/(-1.569) = 1,591 mm; 14 300 V 914.4 × (5.0208/13.367)^1/(-1.568) = 1,707 mm; reduced: 600 V 914.4 × (5.0208/8.980)^1/(-1.598) = 1,316 mm; 2700 V 914.4 × (5.0208/13.018)^1/(-1.569) = 1,678 mm; 14 300 V 914.4 × (5.0208/15.602)^1/(-1.568) = 1,884 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,591 − 1,285)/2.1 × (4.16 − 2.7) + 1,591 = 1,804; AFB₂ = (1,707 − 1,591)/11.6 × (4.16 − 14.3) + 1,707 = 1,606 → V_oc > 2.7 kV so AFB = AFB₂ = 1,606 mm; reduced: AFB₁ = (1,678 − 1,316)/2.1 × (4.16 − 2.7) + 1,678 = 1,930; AFB₂ = (1,884 − 1,678)/11.6 × (4.16 − 14.3) + 1,884 = 1,704 → V_oc > 2.7 kV so AFB = AFB₂ = 1,704 mm
Governing case	max(full 2.904, reduced 3.189 cal/cm²) → the reduced arcing-current case: E = 3.189 cal/cm² (13.343 J/cm²), AFB = max(1,606, 1,704) = 1,704 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 3.189 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 3.2 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 3.189 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 3.189 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(197, 223) = 223 ms → 223 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 3.19 cal/cm² at 914.4 mm, AFB 1,704 mm, arc-rated clothing; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	IEEE 1584-2018 Annex D.1, sample arc-flash incident energy calculation for a medium-voltage system (results D.9-D.72) (validation case `c0007-ieee1584-2018-annex-d1-mv-vcb`)

Example 2 — IEEE 1584-2018 Annex D.2: 480 V switchgear (VCB)

The standard's low-voltage worked example: Eq 25 final current, Eq 6 energy, Eq 10 boundary; a five-times longer clearing time at the reduced current makes that case govern and pushes PPE into the suit tier.

Given: V_oc = 480 V, I_bf = 45 kA, VCB (vertical conductors in a box), T = 61.3 ms at I_arc and T_min = 319 ms at I_arc,min; gap G = 32 mm, working distance D = 609.6 mm, enclosure 610 H × 610 W × 254 D mm.

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VCB 600 V coefficients of Table 1 = 10^{(-0.042870) + 1.035·lg 45 − 0.083·lg 32} × P_I(45) = 10^1.5433 × 0.9288 = 32.449 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.48)² × (1/32.449² − (0.6² − 0.48²)/(0.6² × 45²))] = 1/√[1.5625 × (0.000950 − 0.000178)] = 28.793 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 0.48⁵ = 0.0000; k₃V_oc⁴ = 8.3137×10⁻⁵ × 0.48⁴ = 0.0000; k₄V_oc³ = −0.0019382 × 0.48³ = (-0.0002); k₅V_oc² = 0.022366 × 0.48² = 0.0052; k₆V_oc = −0.12645 × 0.48 = (-0.0607); k₇ = 0.3023; sum = 0.2465; I_arc,min = I_arc(1 − 0.5 VarC_f) = 28.793 × (1 − 0.5 × 0.2465) = 25.244 kA
Enclosure correction (Eq 11–15)	610 H × 610 W × 254 D mm → typical box, Table 7 (typical, VCB). W₁ = 610/25.4 (508–660.4 mm: actual size) = 24.016 in; H₁ = 610/25.4 (508–660.4 mm: actual size) = 24.016 in; EES = (24.016 + 24.016)/2 = 24.016 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 24.016² + 0.03441 × 24.016 + 0.4325 = 1.0847 (Eq 14)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 32.449 kA in the k₃ term, I_arc = 28.793 kA in the k₁₃ term, T = 61.3 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 0.7534 + k₂·lg 32 0.8519 + k₃·32.449/P_E(45) 1.3607 + k₁₁·lg 45 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 28.793 1.3965 + lg(1/1.0847) (-0.0353) = -0.1233; E = 12.552/50 × 61.3 × 10^-0.1233 (k₁₂ = -1.598) = 11.585 J/cm² = 2.769 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 25.244 kA in the k₁₃ term, T_min = 319 ms; the k₃ term keeps the full I_arc,600 = 32.449 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 0.7534 + k₂·lg 32 0.8519 + k₃·32.449/P_E(45) 1.3607 + k₁₁·lg 45 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 25.244 1.3419 + lg(1/1.0847) (-0.0353) = -0.1780; E = 12.552/50 × 319 × 10^-0.1780 (k₁₂ = -1.598) = 53.156 J/cm² = 12.705 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 609.6 × (5.0208/11.585)^1/(-1.598) = 1,029 mm; reduced 609.6 × (5.0208/53.156)^1/(-1.598) = 2,669 mm
Governing case	max(full 2.769, reduced 12.705 cal/cm²) → the reduced arcing-current case: E = 12.705 cal/cm² (53.156 J/cm²), AFB = max(1,029, 2,669) = 2,669 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 12.705 cal/cm² > 1.2 cal/cm² → arc-flash suit, minimum arc rating 12.8 cal/cm² (category-equivalent 3, informational) — informational, not a pass/fail check → 12.705 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 12.705 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(61.3, 319) = 319 ms → 319 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 12.71 cal/cm² at 609.6 mm, AFB 2,669 mm, arc-flash suit; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	IEEE 1584-2018 Annex D.2, sample arc-flash incident energy calculation for a low-voltage system (results D.82-D.106) (validation case `c0007-ieee1584-2018-annex-d2-lv-vcb`)

Example 3 — 208 V lighting panel, 0.5 kA: shallow box, minimum gap and distance

Smallest LV inputs of the model (6.35 mm gap, 305 mm, 0.5 kA) in a shallow box (Eq 15) with the 240 V / 2 kA sustained-arc note; no PPE required.

Given: V_oc = 208 V, I_bf = 0.5 kA, VCB (vertical conductors in a box), T = 10 ms at I_arc and T_min = 10 ms at I_arc,min (same clearing time); gap G = 6.35 mm, working distance D = 305 mm, enclosure 200 H × 200 W × 100 D mm.

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VCB 600 V coefficients of Table 1 = 10^{(-0.042870) + 1.035·lg 0.5 − 0.083·lg 6.35} × P_I(0.5) = 10^-0.4211 × 1.0935 = 0.415 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.208)² × (1/0.415² − (0.6² − 0.208²)/(0.6² × 0.5²))] = 1/√[8.3210 × (5.814123 − 3.519289)] = 0.229 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 0.208⁵ = 0.0000; k₃V_oc⁴ = 8.3137×10⁻⁵ × 0.208⁴ = 0.0000; k₄V_oc³ = −0.0019382 × 0.208³ = 0.0000; k₅V_oc² = 0.022366 × 0.208² = 0.0010; k₆V_oc = −0.12645 × 0.208 = (-0.0263); k₇ = 0.3023; sum = 0.2769; I_arc,min = I_arc(1 − 0.5 VarC_f) = 0.229 × (1 − 0.5 × 0.2769) = 0.197 kA
Enclosure correction (Eq 11–15)	200 H × 200 W × 100 D mm → shallow box (V_oc < 600 V, H and W < 508 mm, D ≤ 203.2 mm), Table 7 (shallow, VCB). W₁ = 200 mm (shallow box, below 508 mm → actual size) = 7.874 in; H₁ = 200 mm (shallow box, below 508 mm → actual size) = 7.874 in; EES = (7.874 + 7.874)/2 = 7.874 in (Eq 13); CF = 1/(b₁EES² + b₂EES + b₃) = 1/(0.0022220 × 7.874² + (-0.02556) × 7.874 + 0.6222) = 1/0.5587 = 1.7899 (Eq 15)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 0.415 kA in the k₃ term, I_arc = 0.229 kA in the k₁₃ term, T = 10 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 0.7534 + k₂·lg 6.35 0.4544 + k₃·0.415/P_E(0.5) 1.3294 + k₁₁·lg 0.5 0.0000 + k₁₂·lg 305 (-3.9699) + k₁₃·lg 0.229 (-0.6129) + lg(1/1.7899) (-0.2528) = -2.2985; E = 12.552/50 × 10 × 10^-2.2985 (k₁₂ = -1.598) = 0.013 J/cm² = 0.003 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 0.197 kA in the k₁₃ term, T_min = 10 ms; the k₃ term keeps the full I_arc,600 = 0.415 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 0.7534 + k₂·lg 6.35 0.4544 + k₃·0.415/P_E(0.5) 1.3294 + k₁₁·lg 0.5 0.0000 + k₁₂·lg 305 (-3.9699) + k₁₃·lg 0.197 (-0.6749) + lg(1/1.7899) (-0.2528) = -2.3605; E = 12.552/50 × 10 × 10^-2.3605 (k₁₂ = -1.598) = 0.011 J/cm² = 0.003 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 305 × (5.0208/0.013)^1/(-1.598) = 7 mm; reduced 305 × (5.0208/0.011)^1/(-1.598) = 7 mm
Governing case	max(full 0.003, reduced 0.003 cal/cm²) → the full arcing-current case: E = 0.003 cal/cm² (0.013 J/cm²), AFB = max(7, 7) = 7 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = <0.01 cal/cm² ≤ 1.2 cal/cm² → arc-rated PPE not required (non-melting or untreated natural-fibre clothing is still required) — informational, not a pass/fail check → 0.003 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 0.003 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(10, 10) = 10 ms → 10 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = <0.01 cal/cm² at 305 mm, AFB 7 mm, arc-rated PPE not required; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first). At 240 V or below with less than 2 kA available, IEEE 1584-2018 notes that a sustained arc is possible but less likely; the model still applies. The arc-flash boundary (7 mm) is closer than 305 mm, the shortest distance the model is fitted for: the 1.2 cal/cm² boundary effectively sits at the equipment face.
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VCB, 600 V coefficients) Iarc,600 = 0.415 kA; Eq 25 at 0.208 kV Iarc = 0.229 kA; Eq 2 VarCf = 0.2769, Iarc,min = 0.197 kA; Eq 11-13 shallow box W1 = 7.874 in, H1 = 7.874 in, EES = 7.874 in, Eq 15 CF = 1.7899; Eq 6 E = 0.013 J/cm² at 10 ms (full) and 0.011 J/cm² at 10 ms (reduced); Eq 10 AFB = 7 / 7 mm; full case governs: 0.013 J/cm² = 0.003 cal/cm², AFB 7 mm, PPE tier none. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 0 (Iarc 0.229 kA, E 0.013 J/cm², AFB 7 mm; reduced 0.197 kA, 0.011 J/cm², 7 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-208v-lighting-panel-shallow-box-min-gap`)

Example 4 — 400 V VCBB panel, 20 kA, 10 ms current-limiting clearing

A fast current-limiting fuse keeps a 400 V VCBB panel under 1.2 cal/cm² so no arc-rated PPE is required. A current-limiting fuse also limits the let-through current, which the IEEE 1584 model ignores (it uses the prospective bolted current), so this result is conservative.

Given: V_oc = 400 V, I_bf = 20 kA, VCBB (vertical conductors terminating in a barrier in a box), T = 10 ms at I_arc and T_min = 10 ms at I_arc,min (same clearing time); gap G = 25 mm, working distance D = 914.4 mm, enclosure 1,000 H × 200 W × 100 D mm.

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VCBB 600 V coefficients of Table 1 = 10^{(-0.017432) + 0.98·lg 20 − 0.05·lg 25} × P_I(20) = 10^1.1877 × 1.1337 = 17.465 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.4)² × (1/17.465² − (0.6² − 0.4²)/(0.6² × 20²))] = 1/√[2.2500 × (0.003278 − 0.001389)] = 15.337 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCBB): k₁V_oc⁶ = 1.138×10⁻⁶ × 0.4⁶ = 0.0000; k₂V_oc⁵ = −6.0287×10⁻⁵ × 0.4⁵ = 0.0000; k₃V_oc⁴ = 0.0012758 × 0.4⁴ = 0.0000; k₄V_oc³ = −0.013778 × 0.4³ = (-0.0009); k₅V_oc² = 0.080217 × 0.4² = 0.0128; k₆V_oc = −0.24066 × 0.4 = (-0.0963); k₇ = 0.3352; sum = 0.2510; I_arc,min = I_arc(1 − 0.5 VarC_f) = 15.337 × (1 − 0.5 × 0.2510) = 13.412 kA
Enclosure correction (Eq 11–15)	1,000 H × 200 W × 100 D mm → typical box, Table 7 (typical, VCBB). W₁ = 200 mm (below 508 mm → 20 in) = 20.000 in; H₁ = [660.4 + (1,000 − 660.4) × (0.4 + 10)/24]/25.4 (Eq 12) = 31.794 in; EES = (31.794 + 20.000)/2 = 25.897 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0002976) × 25.897² + 0.03200 × 25.897 + 0.4790 = 1.1081 (Eq 14)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 17.465 kA in the k₃ term, I_arc = 15.337 kA in the k₁₃ term, T = 10 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 3.0685 + k₂·lg 25 0.3635 + k₃·17.465/P_E(20) (-0.0756) + k₁₁·lg 20 (-0.0781) + k₁₂·lg 914.4 (-5.3567) + k₁₃·lg 15.337 1.4110 + lg(1/1.1081) (-0.0446) = -0.7120; E = 12.552/50 × 10 × 10^-0.7120 (k₁₂ = -1.809) = 0.487 J/cm² = 0.116 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 13.412 kA in the k₁₃ term, T_min = 10 ms; the k₃ term keeps the full I_arc,600 = 17.465 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 3.0685 + k₂·lg 25 0.3635 + k₃·17.465/P_E(20) (-0.0756) + k₁₁·lg 20 (-0.0781) + k₁₂·lg 914.4 (-5.3567) + k₁₃·lg 13.412 1.3417 + lg(1/1.1081) (-0.0446) = -0.7813; E = 12.552/50 × 10 × 10^-0.7813 (k₁₂ = -1.809) = 0.415 J/cm² = 0.099 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 914.4 × (5.0208/0.487)^1/(-1.809) = 252 mm; reduced 914.4 × (5.0208/0.415)^1/(-1.809) = 231 mm
Governing case	max(full 0.116, reduced 0.099 cal/cm²) → the full arcing-current case: E = 0.116 cal/cm² (0.487 J/cm²), AFB = max(252, 231) = 252 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 0.116 cal/cm² ≤ 1.2 cal/cm² → arc-rated PPE not required (non-melting or untreated natural-fibre clothing is still required) — informational, not a pass/fail check → 0.116 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 0.116 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(10, 10) = 10 ms → 10 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 0.12 cal/cm² at 914.4 mm, AFB 252 mm, arc-rated PPE not required; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first). The arc-flash boundary (252 mm) is closer than 305 mm, the shortest distance the model is fitted for: the 1.2 cal/cm² boundary effectively sits at the equipment face.
Reference	IEEE 1584-2018 calculator V2.6.6 sample case 74 (IEEE DataPort open-access spreadsheet V2.6.6, 2019-08-29, as exported by LiaungYip/arcflash). Hand calculation, IEEE 1584-2018 Eq 1 (VCBB, 600 V coefficients) Iarc,600 = 17.465 kA; Eq 25 at 0.4 kV Iarc = 15.337 kA; Eq 2 VarCf = 0.2510, Iarc,min = 13.412 kA; Eq 11-13 typical box W1 = 20.000 in, H1 = 31.794 in, EES = 25.897 in, Eq 14 CF = 1.1081; Eq 6 E = 0.487 J/cm² at 10 ms (full) and 0.415 J/cm² at 10 ms (reduced); Eq 10 AFB = 252 / 231 mm; full case governs: 0.487 J/cm² = 0.116 cal/cm², AFB 252 mm, PPE tier none. (validation case `c0007-ieee1584-calculator-vcbb-0.4kv-20ka`)

Example 5 — 400 V busway tap-off box, 106 kA (HCB, shallow box)

Horizontal conductors in a shallow LV box at the maximum LV bolted fault current; Eq 15 shallow-box correction.

Given: V_oc = 400 V, I_bf = 106 kA, HCB (horizontal conductors in a box), T = 100 ms at I_arc and T_min = 100 ms at I_arc,min (same clearing time); gap G = 6.35 mm, working distance D = 914.4 mm, enclosure 200 H × 200 W × 100 D mm.

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the HCB 600 V coefficients of Table 1 = 10^{0.054922 + 0.988·lg 106 − 0.11·lg 6.35} × P_I(106) = 10^1.9676 × 0.6228 = 57.801 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.4)² × (1/57.801² − (0.6² − 0.4²)/(0.6² × 106²))] = 1/√[2.2500 × (0.000299 − 0.000049)] = 42.175 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, HCB): k₂V_oc⁵ = −3.097×10⁻⁶ × 0.4⁵ = 0.0000; k₃V_oc⁴ = 1.6405×10⁻⁴ × 0.4⁴ = 0.0000; k₄V_oc³ = −0.0033609 × 0.4³ = (-0.0002); k₅V_oc² = 0.033308 × 0.4² = 0.0053; k₆V_oc = −0.16182 × 0.4 = (-0.0647); k₇ = 0.3463; sum = 0.2867; I_arc,min = I_arc(1 − 0.5 VarC_f) = 42.175 × (1 − 0.5 × 0.2867) = 36.130 kA
Enclosure correction (Eq 11–15)	200 H × 200 W × 100 D mm → shallow box (V_oc < 600 V, H and W < 508 mm, D ≤ 203.2 mm), Table 7 (shallow, HCB). W₁ = 200 mm (shallow box, below 508 mm → actual size) = 7.874 in; H₁ = 200 mm (shallow box, below 508 mm → actual size) = 7.874 in; EES = (7.874 + 7.874)/2 = 7.874 in (Eq 13); CF = 1/(b₁EES² + b₂EES + b₃) = 1/((-0.0005556) × 7.874² + 0.03722 × 7.874 + 0.4778) = 1/0.7364 = 1.3579 (Eq 15)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 57.801 kA in the k₃ term, I_arc = 42.175 kA in the k₁₃ term, T = 100 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 4.0737 + k₂·lg 6.35 0.2762 + k₃·57.801/P_E(106) (-0.3242) + k₁₁·lg 106 0.0000 + k₁₂·lg 914.4 (-6.0111) + k₁₃·lg 42.175 1.6836 + lg(1/1.3579) (-0.1329) = -0.4347; E = 12.552/50 × 100 × 10^-0.4347 (k₁₂ = -2.03) = 9.226 J/cm² = 2.205 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 36.130 kA in the k₁₃ term, T_min = 100 ms; the k₃ term keeps the full I_arc,600 = 57.801 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 4.0737 + k₂·lg 6.35 0.2762 + k₃·57.801/P_E(106) (-0.3242) + k₁₁·lg 106 0.0000 + k₁₂·lg 914.4 (-6.0111) + k₁₃·lg 36.130 1.6139 + lg(1/1.3579) (-0.1329) = -0.5043; E = 12.552/50 × 100 × 10^-0.5043 (k₁₂ = -2.03) = 7.860 J/cm² = 1.879 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 914.4 × (5.0208/9.226)^1/(-2.03) = 1,234 mm; reduced 914.4 × (5.0208/7.860)^1/(-2.03) = 1,140 mm
Governing case	max(full 2.205, reduced 1.879 cal/cm²) → the full arcing-current case: E = 2.205 cal/cm² (9.226 J/cm²), AFB = max(1,234, 1,140) = 1,234 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 2.205 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 2.3 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 2.205 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 2.205 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 100) = 100 ms → 100 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 2.21 cal/cm² at 914.4 mm, AFB 1,234 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (HCB, 600 V coefficients) Iarc,600 = 57.801 kA; Eq 25 at 0.4 kV Iarc = 42.175 kA; Eq 2 VarCf = 0.2867, Iarc,min = 36.130 kA; Eq 11-13 shallow box W1 = 7.874 in, H1 = 7.874 in, EES = 7.874 in, Eq 15 CF = 1.3579; Eq 6 E = 9.226 J/cm² at 100 ms (full) and 7.860 J/cm² at 100 ms (reduced); Eq 10 AFB = 1234 / 1140 mm; full case governs: 9.226 J/cm² = 2.205 cal/cm², AFB 1234 mm, PPE tier arc_rated_clothing. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 136 (Iarc 42.175 kA, E 9.226 J/cm², AFB 1234 mm; reduced 36.130 kA, 7.860 J/cm², 1140 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-400v-106ka-hcb-busway-tap-shallow-box`)

Example 6 — 400 V main switchboard, 106 kA, 1 s clearing: above 40 cal/cm²

A slow-clearing LV switchboard fault exceeds the 40 cal/cm² category-4 rating; the full-current case governs and the oversized enclosure is capped at 1244.6 mm.

Given: V_oc = 400 V, I_bf = 106 kA, VCB (vertical conductors in a box), T = 1,000 ms at I_arc and T_min = 1,000 ms at I_arc,min (same clearing time); gap G = 25 mm, working distance D = 609.6 mm, enclosure 1,500 H × 1,500 W × 100 D mm.

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VCB 600 V coefficients of Table 1 = 10^{(-0.042870) + 1.035·lg 106 − 0.083·lg 25} × P_I(106) = 10^1.9373 × 0.5848 = 50.620 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.4)² × (1/50.620² − (0.6² − 0.4²)/(0.6² × 106²))] = 1/√[2.2500 × (0.000390 − 0.000049)] = 36.112 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 0.4⁵ = 0.0000; k₃V_oc⁴ = 8.3137×10⁻⁵ × 0.4⁴ = 0.0000; k₄V_oc³ = −0.0019382 × 0.4³ = (-0.0001); k₅V_oc² = 0.022366 × 0.4² = 0.0036; k₆V_oc = −0.12645 × 0.4 = (-0.0506); k₇ = 0.3023; sum = 0.2551; I_arc,min = I_arc(1 − 0.5 VarC_f) = 36.112 × (1 − 0.5 × 0.2551) = 31.505 kA
Enclosure correction (Eq 11–15)	1,500 H × 1,500 W × 100 D mm → typical box, Table 7 (typical, VCB). W₁ = [660.4 + (1244.6 − 660.4) × (0.4 + 4)/20]/25.4 (Eq 11 (capped at 1244.6 mm from 1,500)) = 31.060 in; H₁ = 1244.6/25.4 (VCB height stays actual size (capped at 1244.6 mm from 1,500)) = 49.000 in; EES = (49.000 + 31.060)/2 = 40.030 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 40.030² + 0.03441 × 40.030 + 0.4325 = 1.3260 (Eq 14)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 50.620 kA in the k₃ term, I_arc = 36.112 kA in the k₁₃ term, T = 1,000 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 0.7534 + k₂·lg 25 0.7912 + k₃·50.620/P_E(106) 1.4311 + k₁₁·lg 106 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 36.112 1.4907 + lg(1/1.3260) (-0.1225) = -0.1067; E = 12.552/50 × 1,000 × 10^-0.1067 (k₁₂ = -1.598) = 196.378 J/cm² = 46.935 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 31.505 kA in the k₁₃ term, T_min = 1,000 ms; the k₃ term keeps the full I_arc,600 = 50.620 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 0.7534 + k₂·lg 25 0.7912 + k₃·50.620/P_E(106) 1.4311 + k₁₁·lg 106 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 31.505 1.4340 + lg(1/1.3260) (-0.1225) = -0.1634; E = 12.552/50 × 1,000 × 10^-0.1634 (k₁₂ = -1.598) = 172.335 J/cm² = 41.189 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 609.6 × (5.0208/196.378)^1/(-1.598) = 6,046 mm; reduced 609.6 × (5.0208/172.335)^1/(-1.598) = 5,572 mm
Governing case	max(full 46.935, reduced 41.189 cal/cm²) → the full arcing-current case: E = 46.935 cal/cm² (196.378 J/cm²), AFB = max(6,046, 5,572) = 6,046 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 46.935 cal/cm² > 1.2 cal/cm² → arc-flash suit, minimum arc rating 47.0 cal/cm² (beyond category 4 — de-energise) — informational, not a pass/fail check → 46.935 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E exceeds 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 46.935 vs limit 40.000 cal/cm² FAIL
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(1,000, 1,000) = 1,000 ms → 1,000 vs limit 2,000 ms PASS
Result	1/2 checks pass → FAIL; E = 46.94 cal/cm² at 609.6 mm, AFB 6,046 mm, arc-flash suit; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first). Enclosure dimensions above 1244.6 mm (49 in) are treated as 1244.6 mm in the equivalent size (Eq 11-12).
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VCB, 600 V coefficients) Iarc,600 = 50.620 kA; Eq 25 at 0.4 kV Iarc = 36.112 kA; Eq 2 VarCf = 0.2551, Iarc,min = 31.505 kA; Eq 11-13 typical box W1 = 31.060 in, H1 = 49.000 in, EES = 40.030 in, Eq 14 CF = 1.3260; Eq 6 E = 196.378 J/cm² at 1000 ms (full) and 172.335 J/cm² at 1000 ms (reduced); Eq 10 AFB = 6046 / 5572 mm; full case governs: 196.378 J/cm² = 46.935 cal/cm², AFB 6046 mm, PPE tier arc_flash_suit. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 17 (Iarc 36.112 kA, E 196.378 J/cm², AFB 6046 mm; reduced 31.505 kA, 172.335 J/cm², 5572 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-400v-106ka-main-switchboard-1s-over-40cal`)

Example 7 — 400 V open-air vertical bus, 106 kA, 1 s (VOA)

Open-air vertical electrodes at LV: CF = 1, no enclosure; a 1 s clearing time drives the energy far above 12 cal/cm².

Given: V_oc = 400 V, I_bf = 106 kA, VOA (vertical conductors in open air), T = 1,000 ms at I_arc and T_min = 1,000 ms at I_arc,min (same clearing time); gap G = 25 mm, working distance D = 609.6 mm, open air (no enclosure).

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VOA 600 V coefficients of Table 1 = 10^{0.043785 + 1.04·lg 106 − 0.18·lg 25} × P_I(106) = 10^1.8985 × 0.5848 = 46.292 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.4)² × (1/46.292² − (0.6² − 0.4²)/(0.6² × 106²))] = 1/√[2.2500 × (0.000467 − 0.000049)] = 32.639 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VOA): k₁V_oc⁶ = 9.5606×10⁻⁷ × 0.4⁶ = 0.0000; k₂V_oc⁵ = −5.1543×10⁻⁵ × 0.4⁵ = 0.0000; k₃V_oc⁴ = 0.0011161 × 0.4⁴ = 0.0000; k₄V_oc³ = −0.01242 × 0.4³ = (-0.0008); k₅V_oc² = 0.075125 × 0.4² = 0.0120; k₆V_oc = −0.23584 × 0.4 = (-0.0943); k₇ = 0.3370; sum = 0.2539; I_arc,min = I_arc(1 − 0.5 VarC_f) = 32.639 × (1 − 0.5 × 0.2539) = 28.496 kA
Enclosure correction (Eq 11–15)	VOA is an open-air configuration: no enclosure, CF = 1.
Incident energy, full current (Eq 6)	I* = I_arc,600 = 46.292 kA in the k₃ term, I_arc = 32.639 kA in the k₁₃ term, T = 1,000 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 0.6793 + k₂·lg 25 1.0429 + k₃·46.292/P_E(106) 0.9130 + k₁₁·lg 106 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 32.639 1.5092 + lg(1/1.0000) 0.0000 = -0.3062; E = 12.552/50 × 1,000 × 10^-0.3062 (k₁₂ = -1.598) = 124.045 J/cm² = 29.648 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 28.496 kA in the k₁₃ term, T_min = 1,000 ms; the k₃ term keeps the full I_arc,600 = 46.292 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 0.6793 + k₂·lg 25 1.0429 + k₃·46.292/P_E(106) 0.9130 + k₁₁·lg 106 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 28.496 1.4504 + lg(1/1.0000) 0.0000 = -0.3649; E = 12.552/50 × 1,000 × 10^-0.3649 (k₁₂ = -1.598) = 108.343 J/cm² = 25.895 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 609.6 × (5.0208/124.045)^1/(-1.598) = 4,536 mm; reduced 609.6 × (5.0208/108.343)^1/(-1.598) = 4,167 mm
Governing case	max(full 29.648, reduced 25.895 cal/cm²) → the full arcing-current case: E = 29.648 cal/cm² (124.045 J/cm²), AFB = max(4,536, 4,167) = 4,536 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 29.648 cal/cm² > 1.2 cal/cm² → arc-flash suit, minimum arc rating 29.7 cal/cm² (category-equivalent 4, informational) — informational, not a pass/fail check → 29.648 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 29.648 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(1,000, 1,000) = 1,000 ms → 1,000 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 29.65 cal/cm² at 609.6 mm, AFB 4,536 mm, arc-flash suit; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VOA, 600 V coefficients) Iarc,600 = 46.292 kA; Eq 25 at 0.4 kV Iarc = 32.639 kA; Eq 2 VarCf = 0.2539, Iarc,min = 28.496 kA; open air CF = 1; Eq 6 E = 124.045 J/cm² at 1000 ms (full) and 108.343 J/cm² at 1000 ms (reduced); Eq 10 AFB = 4536 / 4167 mm; full case governs: 124.045 J/cm² = 29.648 cal/cm², AFB 4536 mm, PPE tier arc_flash_suit. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 197 (Iarc 32.639 kA, E 124.045 J/cm², AFB 4536 mm; reduced 28.496 kA, 108.343 J/cm², 4167 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-400v-106ka-open-air-vertical-bus`)

Example 8 — 400 V open-air horizontal bus, 76.2 mm gap (maximum LV gap)

Horizontal open-air electrodes at the largest gap the LV model allows; arc-rated clothing tier.

Given: V_oc = 400 V, I_bf = 106 kA, HOA (horizontal conductors in open air), T = 100 ms at I_arc and T_min = 100 ms at I_arc,min (same clearing time); gap G = 76.2 mm, working distance D = 914.4 mm, open air (no enclosure).

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the HOA 600 V coefficients of Table 1 = 10^{0.111147 + 1.008·lg 106 − 0.24·lg 76.2} × P_I(106) = 10^1.7010 × 0.6264 = 31.467 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.4)² × (1/31.467² − (0.6² − 0.4²)/(0.6² × 106²))] = 1/√[2.2500 × (0.001010 − 0.000049)] = 21.511 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, HOA): k₂V_oc⁵ = −3.1555×10⁻⁶ × 0.4⁵ = 0.0000; k₃V_oc⁴ = 1.682×10⁻⁴ × 0.4⁴ = 0.0000; k₄V_oc³ = −0.0034607 × 0.4³ = (-0.0002); k₅V_oc² = 0.034124 × 0.4² = 0.0055; k₆V_oc = −0.1599 × 0.4 = (-0.0640); k₇ = 0.3463; sum = 0.2876; I_arc,min = I_arc(1 − 0.5 VarC_f) = 21.511 × (1 − 0.5 × 0.2876) = 18.418 kA
Enclosure correction (Eq 11–15)	HOA is an open-air configuration: no enclosure, CF = 1.
Incident energy, full current (Eq 6)	I* = I_arc,600 = 31.467 kA in the k₃ term, I_arc = 21.511 kA in the k₁₃ term, T = 100 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 3.4704 + k₂·lg 76.2 0.8751 + k₃·31.467/P_E(106) (-0.1241) + k₁₁·lg 106 0.0000 + k₁₂·lg 914.4 (-5.8927) + k₁₃·lg 21.511 1.3860 + lg(1/1.0000) 0.0000 = -0.2853; E = 12.552/50 × 100 × 10^-0.2853 (k₁₂ = -1.99) = 13.016 J/cm² = 3.111 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 18.418 kA in the k₁₃ term, T_min = 100 ms; the k₃ term keeps the full I_arc,600 = 31.467 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 3.4704 + k₂·lg 76.2 0.8751 + k₃·31.467/P_E(106) (-0.1241) + k₁₁·lg 106 0.0000 + k₁₂·lg 914.4 (-5.8927) + k₁₃·lg 18.418 1.3159 + lg(1/1.0000) 0.0000 = -0.3554; E = 12.552/50 × 100 × 10^-0.3554 (k₁₂ = -1.99) = 11.076 J/cm² = 2.647 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 914.4 × (5.0208/13.016)^1/(-1.99) = 1,476 mm; reduced 914.4 × (5.0208/11.076)^1/(-1.99) = 1,361 mm
Governing case	max(full 3.111, reduced 2.647 cal/cm²) → the full arcing-current case: E = 3.111 cal/cm² (13.016 J/cm²), AFB = max(1,476, 1,361) = 1,476 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 3.111 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 3.2 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 3.111 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 3.111 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 100) = 100 ms → 100 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 3.11 cal/cm² at 914.4 mm, AFB 1,476 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (HOA, 600 V coefficients) Iarc,600 = 31.467 kA; Eq 25 at 0.4 kV Iarc = 21.511 kA; Eq 2 VarCf = 0.2876, Iarc,min = 18.418 kA; open air CF = 1; Eq 6 E = 13.016 J/cm² at 100 ms (full) and 11.076 J/cm² at 100 ms (reduced); Eq 10 AFB = 1476 / 1361 mm; full case governs: 13.016 J/cm² = 3.111 cal/cm², AFB 1476 mm, PPE tier arc_rated_clothing. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 258 (Iarc 21.511 kA, E 13.016 J/cm², AFB 1476 mm; reduced 18.418 kA, 11.076 J/cm², 1361 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-400v-open-air-horizontal-bus-max-lv-gap`)

Example 9 — 415 V MCC bucket, 25 kA (shallow LV MCC preset, VCBB)

The lv_mcc_panel_shallow preset supplies gap 25 mm, 457.2 mm and a 355.6 × 304.8 × 203.2 mm shallow box (Eq 15); a slower reduced-current clearing time makes the reduced case govern.

Given: V_oc = 415 V, I_bf = 25 kA, VCBB (vertical conductors terminating in a barrier in a box), T = 50 ms at I_arc and T_min = 200 ms at I_arc,min; gap G = 25 mm, working distance D = 457.2 mm, enclosure 355.6 H × 304.8 W × 203.2 D mm (from the LV_MCC_Panel_Shallow preset where not given; MCP lv_mcc_panel_shallow).

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VCBB 600 V coefficients of Table 1 = 10^{(-0.017432) + 0.98·lg 25 − 0.05·lg 25} × P_I(25) = 10^1.2827 × 1.1344 = 21.749 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.415)² × (1/21.749² − (0.6² − 0.415²)/(0.6² × 25²))] = 1/√[2.0903 × (0.002114 − 0.000835)] = 19.336 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCBB): k₁V_oc⁶ = 1.138×10⁻⁶ × 0.415⁶ = 0.0000; k₂V_oc⁵ = −6.0287×10⁻⁵ × 0.415⁵ = 0.0000; k₃V_oc⁴ = 0.0012758 × 0.415⁴ = 0.0000; k₄V_oc³ = −0.013778 × 0.415³ = (-0.0010); k₅V_oc² = 0.080217 × 0.415² = 0.0138; k₆V_oc = −0.24066 × 0.415 = (-0.0999); k₇ = 0.3352; sum = 0.2482; I_arc,min = I_arc(1 − 0.5 VarC_f) = 19.336 × (1 − 0.5 × 0.2482) = 16.936 kA
Enclosure correction (Eq 11–15)	355.6 H × 304.8 W × 203.2 D mm → shallow box (V_oc < 600 V, H and W < 508 mm, D ≤ 203.2 mm), Table 7 (shallow, VCBB). W₁ = 304.8 mm (shallow box, below 508 mm → actual size) = 12.000 in; H₁ = 355.6 mm (shallow box, below 508 mm → actual size) = 14.000 in; EES = (14.000 + 12.000)/2 = 13.000 in (Eq 13); CF = 1/(b₁EES² + b₂EES + b₃) = 1/((-0.0027780) × 13.000² + 0.11940 × 13.000 + (-0.2778)) = 1/0.8049 = 1.2424 (Eq 15)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 21.749 kA in the k₃ term, I_arc = 19.336 kA in the k₁₃ term, T = 50 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 3.0685 + k₂·lg 25 0.3635 + k₃·21.749/P_E(25) (-0.0752) + k₁₁·lg 25 (-0.0839) + k₁₂·lg 457.2 (-4.8121) + k₁₃·lg 19.336 1.5308 + lg(1/1.2424) (-0.0942) = -0.1028; E = 12.552/50 × 50 × 10^-0.1028 (k₁₂ = -1.809) = 9.906 J/cm² = 2.368 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 16.936 kA in the k₁₃ term, T_min = 200 ms; the k₃ term keeps the full I_arc,600 = 21.749 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 3.0685 + k₂·lg 25 0.3635 + k₃·21.749/P_E(25) (-0.0752) + k₁₁·lg 25 (-0.0839) + k₁₂·lg 457.2 (-4.8121) + k₁₃·lg 16.936 1.4623 + lg(1/1.2424) (-0.0942) = -0.1713; E = 12.552/50 × 200 × 10^-0.1713 (k₁₂ = -1.809) = 33.844 J/cm² = 8.089 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 457.2 × (5.0208/9.906)^1/(-1.809) = 666 mm; reduced 457.2 × (5.0208/33.844)^1/(-1.809) = 1,313 mm
Governing case	max(full 2.368, reduced 8.089 cal/cm²) → the reduced arcing-current case: E = 8.089 cal/cm² (33.844 J/cm²), AFB = max(666, 1,313) = 1,313 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 8.089 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 8.1 cal/cm² (category-equivalent 3, informational) — informational, not a pass/fail check → 8.089 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 8.089 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(50, 200) = 200 ms → 200 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 8.09 cal/cm² at 457.2 mm, AFB 1,313 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VCBB, 600 V coefficients) Iarc,600 = 21.749 kA; Eq 25 at 0.415 kV Iarc = 19.336 kA; Eq 2 VarCf = 0.2482, Iarc,min = 16.936 kA; Eq 11-13 shallow box W1 = 12.000 in, H1 = 14.000 in, EES = 13.000 in, Eq 15 CF = 1.2424; Eq 6 E = 9.906 J/cm² at 50 ms (full) and 33.844 J/cm² at 200 ms (reduced); Eq 10 AFB = 666 / 1313 mm; reduced case governs: 33.844 J/cm² = 8.089 cal/cm², AFB 1313 mm, PPE tier arc_rated_clothing. Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-415v-mcc-bucket-shallow-panel-preset`)

Example 10 — 415 V LV switchgear, 40 kA, ACB short-time delay (LV switchgear preset)

The lv_switchgear preset (32 mm gap, 609.6 mm, 508 mm cube) with a 250 ms short-time delay; full and reduced cases at different times, arc-flash suit required. Built-in sanity check: at a 508 mm cube W₁ = H₁ = 20 in, so the enclosure correction factor is ≈ 1.0000 — the box the model's coefficients were fitted to.

Given: V_oc = 415 V, I_bf = 40 kA, VCB (vertical conductors in a box), T = 250 ms at I_arc and T_min = 400 ms at I_arc,min; gap G = 32 mm, working distance D = 609.6 mm, enclosure 508 H × 508 W × 508 D mm (from the LV_Switchgear preset where not given; MCP lv_switchgear).

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VCB 600 V coefficients of Table 1 = 10^{(-0.042870) + 1.035·lg 40 − 0.083·lg 32} × P_I(40) = 10^1.4903 × 0.9646 = 29.831 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.415)² × (1/29.831² − (0.6² − 0.415²)/(0.6² × 40²))] = 1/√[2.0903 × (0.001124 − 0.000326)] = 24.489 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 0.415⁵ = 0.0000; k₃V_oc⁴ = 8.3137×10⁻⁵ × 0.415⁴ = 0.0000; k₄V_oc³ = −0.0019382 × 0.415³ = (-0.0001); k₅V_oc² = 0.022366 × 0.415² = 0.0039; k₆V_oc = −0.12645 × 0.415 = (-0.0525); k₇ = 0.3023; sum = 0.2535; I_arc,min = I_arc(1 − 0.5 VarC_f) = 24.489 × (1 − 0.5 × 0.2535) = 21.385 kA
Enclosure correction (Eq 11–15)	508 H × 508 W × 508 D mm → typical box, Table 7 (typical, VCB). W₁ = 508/25.4 (508–660.4 mm: actual size) = 20.000 in; H₁ = 508/25.4 (508–660.4 mm: actual size) = 20.000 in; EES = (20.000 + 20.000)/2 = 20.000 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 20.000² + 0.03441 × 20.000 + 0.4325 = 0.9999 (Eq 14)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 29.831 kA in the k₃ term, I_arc = 24.489 kA in the k₁₃ term, T = 250 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 0.7534 + k₂·lg 32 0.8519 + k₃·29.831/P_E(40) 1.3551 + k₁₁·lg 40 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 24.489 1.3292 + lg(1/0.9999) 0.0000 = -0.1609; E = 12.552/50 × 250 × 10^-0.1609 (k₁₂ = -1.598) = 43.334 J/cm² = 10.357 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 21.385 kA in the k₁₃ term, T_min = 400 ms; the k₃ term keeps the full I_arc,600 = 29.831 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 0.7534 + k₂·lg 32 0.8519 + k₃·29.831/P_E(40) 1.3551 + k₁₁·lg 40 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 21.385 1.2729 + lg(1/0.9999) 0.0000 = -0.2172; E = 12.552/50 × 400 × 10^-0.2172 (k₁₂ = -1.598) = 60.900 J/cm² = 14.555 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 609.6 × (5.0208/43.334)^1/(-1.598) = 2,349 mm; reduced 609.6 × (5.0208/60.900)^1/(-1.598) = 2,906 mm
Governing case	max(full 10.357, reduced 14.555 cal/cm²) → the reduced arcing-current case: E = 14.555 cal/cm² (60.900 J/cm²), AFB = max(2,349, 2,906) = 2,906 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 14.555 cal/cm² > 1.2 cal/cm² → arc-flash suit, minimum arc rating 14.6 cal/cm² (category-equivalent 3, informational) — informational, not a pass/fail check → 14.555 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 14.555 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(250, 400) = 400 ms → 400 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 14.55 cal/cm² at 609.6 mm, AFB 2,906 mm, arc-flash suit; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VCB, 600 V coefficients) Iarc,600 = 29.831 kA; Eq 25 at 0.415 kV Iarc = 24.489 kA; Eq 2 VarCf = 0.2535, Iarc,min = 21.385 kA; Eq 11-13 typical box W1 = 20.000 in, H1 = 20.000 in, EES = 20.000 in, Eq 14 CF = 0.9999; Eq 6 E = 43.334 J/cm² at 250 ms (full) and 60.900 J/cm² at 400 ms (reduced); Eq 10 AFB = 2349 / 2906 mm; reduced case governs: 60.900 J/cm² = 14.555 cal/cm², AFB 2906 mm, PPE tier arc_flash_suit. Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-415v-lv-switchgear-preset-acb-short-time-delay`)

Example 11 — 600 V VCBB switchboard: top of the LV range (Eq 25 = Iarc,600)

At exactly 600 V the Eq 25 correction vanishes and the final current equals Iarc,600; 1 s clearing puts the energy in the arc-flash-suit tier.

Given: V_oc = 600 V, I_bf = 20 kA, VCBB (vertical conductors terminating in a barrier in a box), T = 1,000 ms at I_arc and T_min = 1,000 ms at I_arc,min (same clearing time); gap G = 25 mm, working distance D = 609.6 mm, enclosure 600 H × 1,000 W × 100 D mm.

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VCBB 600 V coefficients of Table 1 = 10^{(-0.017432) + 0.98·lg 20 − 0.05·lg 25} × P_I(20) = 10^1.1877 × 1.1337 = 17.465 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.6)² × (1/17.465² − (0.6² − 0.6²)/(0.6² × 20²))] = 1/√[1.0000 × (0.003278 − 0.000000)] = 17.465 kA (at 600 V exactly, Eq 25 returns I_arc,600)
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCBB): k₁V_oc⁶ = 1.138×10⁻⁶ × 0.6⁶ = 0.0000; k₂V_oc⁵ = −6.0287×10⁻⁵ × 0.6⁵ = 0.0000; k₃V_oc⁴ = 0.0012758 × 0.6⁴ = 0.0002; k₄V_oc³ = −0.013778 × 0.6³ = (-0.0030); k₅V_oc² = 0.080217 × 0.6² = 0.0289; k₆V_oc = −0.24066 × 0.6 = (-0.1444); k₇ = 0.3352; sum = 0.2169; I_arc,min = I_arc(1 − 0.5 VarC_f) = 17.465 × (1 − 0.5 × 0.2169) = 15.571 kA
Enclosure correction (Eq 11–15)	600 H × 1,000 W × 100 D mm → typical box, Table 7 (typical, VCBB). W₁ = [660.4 + (1,000 − 660.4) × (0.6 + 10)/24]/25.4 (Eq 11) = 31.905 in; H₁ = 600/25.4 (508–660.4 mm: actual size) = 23.622 in; EES = (23.622 + 31.905)/2 = 27.764 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0002976) × 27.764² + 0.03200 × 27.764 + 0.4790 = 1.1380 (Eq 14)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 17.465 kA in the k₃ term, I_arc = 17.465 kA in the k₁₃ term, T = 1,000 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 3.0685 + k₂·lg 25 0.3635 + k₃·17.465/P_E(20) (-0.0756) + k₁₁·lg 20 (-0.0781) + k₁₂·lg 609.6 (-5.0381) + k₁₃·lg 17.465 1.4782 + lg(1/1.1380) (-0.0562) = -0.3378; E = 12.552/50 × 1,000 × 10^-0.3378 (k₁₂ = -1.809) = 115.321 J/cm² = 27.562 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 15.571 kA in the k₁₃ term, T_min = 1,000 ms; the k₃ term keeps the full I_arc,600 = 17.465 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 3.0685 + k₂·lg 25 0.3635 + k₃·17.465/P_E(20) (-0.0756) + k₁₁·lg 20 (-0.0781) + k₁₂·lg 609.6 (-5.0381) + k₁₃·lg 15.571 1.4188 + lg(1/1.1380) (-0.0562) = -0.3972; E = 12.552/50 × 1,000 × 10^-0.3972 (k₁₂ = -1.809) = 100.596 J/cm² = 24.043 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 609.6 × (5.0208/115.321)^1/(-1.809) = 3,447 mm; reduced 609.6 × (5.0208/100.596)^1/(-1.809) = 3,196 mm
Governing case	max(full 27.562, reduced 24.043 cal/cm²) → the full arcing-current case: E = 27.562 cal/cm² (115.321 J/cm²), AFB = max(3,447, 3,196) = 3,447 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 27.562 cal/cm² > 1.2 cal/cm² → arc-flash suit, minimum arc rating 27.6 cal/cm² (category-equivalent 4, informational) — informational, not a pass/fail check → 27.562 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 27.562 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(1,000, 1,000) = 1,000 ms → 1,000 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 27.56 cal/cm² at 609.6 mm, AFB 3,447 mm, arc-flash suit; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VCBB, 600 V coefficients) Iarc,600 = 17.465 kA; Eq 25 at 0.6 kV Iarc = 17.465 kA; Eq 2 VarCf = 0.2169, Iarc,min = 15.571 kA; Eq 11-13 typical box W1 = 31.905 in, H1 = 23.622 in, EES = 27.764 in, Eq 14 CF = 1.1380; Eq 6 E = 115.321 J/cm² at 1000 ms (full) and 100.596 J/cm² at 1000 ms (reduced); Eq 10 AFB = 3447 / 3196 mm; full case governs: 115.321 J/cm² = 27.562 cal/cm², AFB 3447 mm, PPE tier arc_flash_suit. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 83 (Iarc 17.465 kA, E 115.321 J/cm², AFB 3447 mm; reduced 15.571 kA, 100.596 J/cm², 3196 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-600v-vcbb-top-of-lv-range`)

Example 12 — 1 kV VOA open-air bus, 20 kA, 10 ms

Open-air vertical electrodes in the 600 V-2.7 kV band where Eq 18 blends both interpolation branches; energy well under 1.2 cal/cm².

Given: V_oc = 1,000 V, I_bf = 20 kA, VOA (vertical conductors in open air), T = 10 ms at I_arc and T_min = 10 ms at I_arc,min (same clearing time); gap G = 19.05 mm, working distance D = 914.4 mm, open air (no enclosure).

Arcing current at the reference voltages (Eq 1)	600 V: 10^{0.043785 + 1.04·lg 20 − 0.18·lg 19.05} × P_I(20) = 10^1.1665 × 1.0782 = 15.818 kA; 2700 V: 10^{(-0.023950) + 1.006·lg 20 − 0.0188·lg 19.05} × P_I(20) = 10^1.2608 × 0.9323 = 16.998 kA; 14 300 V: 10^{0.005371 + 1.0102·lg 20 − 0.029·lg 19.05} × P_I(20) = 10^1.2826 × 0.9323 = 17.870 kA (VOA coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 1 kV: I_arc,1 = (16.998 − 15.818)/2.1 × (1 − 2.7) + 16.998 = 16.043; I_arc,2 = (17.870 − 16.998)/11.6 × (1 − 14.3) + 17.870 = 16.870; I_arc,3 = 16.043 × (2.7 − 1)/2.1 + 16.870 × (1 − 0.6)/2.1 = 16.200 kA (0.6 < V_oc ≤ 2.7 kV)
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VOA): k₁V_oc⁶ = 9.5606×10⁻⁷ × 1⁶ = 0.0000; k₂V_oc⁵ = −5.1543×10⁻⁵ × 1⁵ = (-0.0001); k₃V_oc⁴ = 0.0011161 × 1⁴ = 0.0011; k₄V_oc³ = −0.01242 × 1³ = (-0.0124); k₅V_oc² = 0.075125 × 1² = 0.0751; k₆V_oc = −0.23584 × 1 = (-0.2358); k₇ = 0.3370; sum = 0.1649; applied to each reference current, I_arc,min = 15.818/16.998/17.870 × (1 − 0.5 × 0.1649) = 14.514/15.597/16.397 kA, interpolated as above to 14.865 kA
Enclosure correction (Eq 11–15)	VOA is an open-air configuration: no enclosure, CF = 1.
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 15.818 kA): exponent = k₁ 0.6793 + k₂·lg 19.05 0.9548 + k₃·15.818/P_E(20) 0.8969 + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 15.818 1.1956 + lg(1/1.0000) 0.0000 = -1.0053; E = 12.552/50 × 10 × 10^-1.0053 (k₁₂ = -1.598) = 0.248 J/cm²; 2700 V (Eq 4, I* = I_arc = 16.998 kA): exponent = k₁ 3.8807 + k₂·lg 19.05 0.1344 + k₃·16.998/P_E(20) (-1.7375) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.4861) + k₁₃·lg 16.998 1.3719 + lg(1/1.0000) 0.0000 = -0.8366; E = 12.552/50 × 10 × 10^-0.8366 (k₁₂ = -1.515) = 0.366 J/cm²; 14 300 V (Eq 5, I* = I_arc = 17.870 kA): exponent = k₁ 3.4055 + k₂·lg 19.05 0.1536 + k₃·17.870/P_E(20) (-0.8936) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.5424) + k₁₃·lg 17.870 1.2258 + lg(1/1.0000) 0.0000 = -0.6511; E = 12.552/50 × 10 × 10^-0.6511 (k₁₂ = -1.534) = 0.561 J/cm²
Interpolated full-current energy (Eq 19–21)	At 1 kV: E₁ = (0.366 − 0.248)/2.1 × (1 − 2.7) + 0.366 = 0.270; E₂ = (0.561 − 0.366)/11.6 × (1 − 14.3) + 0.561 = 0.337; E₃ = 0.270 × (2.7 − 1)/2.1 + 0.337 × (1 − 0.6)/2.1 = 0.283 J/cm² (0.6 < V_oc ≤ 2.7 kV) = 0.068 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 14.514 kA, T_min = 10 ms): exponent = k₁ 0.6793 + k₂·lg 19.05 0.9548 + k₃·14.514/P_E(20) 0.8230 + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 14.514 1.1583 + lg(1/1.0000) 0.0000 = -1.1165; E = 12.552/50 × 10 × 10^-1.1165 (k₁₂ = -1.598) = 0.192 J/cm²; 2700 V (I_arc,min = 15.597 kA, T_min = 10 ms): exponent = k₁ 3.8807 + k₂·lg 19.05 0.1344 + k₃·15.597/P_E(20) (-1.5943) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.4861) + k₁₃·lg 15.597 1.3302 + lg(1/1.0000) 0.0000 = -0.7350; E = 12.552/50 × 10 × 10^-0.7350 (k₁₂ = -1.515) = 0.462 J/cm²; 14 300 V (I_arc,min = 16.397 kA, T_min = 10 ms): exponent = k₁ 3.4055 + k₂·lg 19.05 0.1536 + k₃·16.397/P_E(20) (-0.8199) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.5424) + k₁₃·lg 16.397 1.1893 + lg(1/1.0000) 0.0000 = -0.6140; E = 12.552/50 × 10 × 10^-0.6140 (k₁₂ = -1.534) = 0.611 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 1 kV: E₁ = (0.462 − 0.192)/2.1 × (1 − 2.7) + 0.462 = 0.243; E₂ = (0.611 − 0.462)/11.6 × (1 − 14.3) + 0.611 = 0.440; E₃ = 0.243 × (2.7 − 1)/2.1 + 0.440 × (1 − 0.6)/2.1 = 0.281 J/cm² (0.6 < V_oc ≤ 2.7 kV) = 0.067 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 914.4 × (5.0208/0.248)^1/(-1.598) = 139 mm; 2700 V 914.4 × (5.0208/0.366)^1/(-1.515) = 162 mm; 14 300 V 914.4 × (5.0208/0.561)^1/(-1.534) = 219 mm; reduced: 600 V 914.4 × (5.0208/0.192)^1/(-1.598) = 119 mm; 2700 V 914.4 × (5.0208/0.462)^1/(-1.515) = 189 mm; 14 300 V 914.4 × (5.0208/0.611)^1/(-1.534) = 232 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (162 − 139)/2.1 × (1 − 2.7) + 162 = 144; AFB₂ = (219 − 162)/11.6 × (1 − 14.3) + 219 = 154; AFB₃ = 144 × (2.7 − 1)/2.1 + 154 × (1 − 0.6)/2.1 = 146 mm (0.6 < V_oc ≤ 2.7 kV); reduced: AFB₁ = (189 − 119)/2.1 × (1 − 2.7) + 189 = 132; AFB₂ = (232 − 189)/11.6 × (1 − 14.3) + 232 = 183; AFB₃ = 132 × (2.7 − 1)/2.1 + 183 × (1 − 0.6)/2.1 = 142 mm (0.6 < V_oc ≤ 2.7 kV)
Governing case	max(full 0.068, reduced 0.067 cal/cm²) → the full arcing-current case: E = 0.068 cal/cm² (0.283 J/cm²), AFB = max(146, 142) = 146 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 0.068 cal/cm² ≤ 1.2 cal/cm² → arc-rated PPE not required (non-melting or untreated natural-fibre clothing is still required) — informational, not a pass/fail check → 0.068 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 0.068 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(10, 10) = 10 ms → 10 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 0.07 cal/cm² at 914.4 mm, AFB 146 mm, arc-rated PPE not required; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first). The arc-flash boundary (146 mm) is closer than 305 mm, the shortest distance the model is fitted for: the 1.2 cal/cm² boundary effectively sits at the equipment face.
Reference	IEEE 1584-2018 calculator V2.6.6 sample case 219 (IEEE DataPort open-access spreadsheet V2.6.6, 2019-08-29, as exported by LiaungYip/arcflash). Hand calculation, IEEE 1584-2018 Eq 1 (VOA) Iarc,600/2700/14300 = 15.818/16.998/17.870 kA; Eq 16-18 at 1 kV Iarc = 16.200 kA; Eq 2 VarCf = 0.1649, Iarc,min = 14.865 kA; open air CF = 1; Eq 3-5 E600/2700/14300 = 0.248/0.366/0.561 J/cm² (full, 10 ms), 0.192/0.462/0.611 J/cm² (reduced, 10 ms); Eq 19-21 E = 0.283 / 0.281 J/cm²; Eq 7-9 + 22-24 AFB = 146 / 142 mm; full case governs: 0.283 J/cm² = 0.068 cal/cm², AFB 146 mm, PPE tier none. (validation case `c0007-ieee1584-calculator-voa-1kv-20ka`)

Example 13 — 10 kV HCB, 20 kA, narrow 600 × 200 mm box

Horizontal conductors in a box above 600 V: Eq 3-5 at each reference voltage interpolated with Eq 19-24; full-current case governs.

Given: V_oc = 10,000 V, I_bf = 20 kA, HCB (horizontal conductors in a box), T = 100 ms at I_arc and T_min = 100 ms at I_arc,min (same clearing time); gap G = 19.05 mm, working distance D = 609.6 mm, enclosure 600 H × 200 W × 100 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{0.054922 + 0.988·lg 20 − 0.11·lg 19.05} × P_I(20) = 10^1.1996 × 1.0514 = 16.646 kA; 2700 V: 10^{0.001011 + 1.003·lg 20 − 0.0249·lg 19.05} × P_I(20) = 10^1.2741 × 0.9691 = 18.215 kA; 14 300 V: 10^{0.008693 + 0.999·lg 20 − 0.02·lg 19.05} × P_I(20) = 10^1.2828 × 0.9864 = 18.919 kA (HCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 10 kV: I_arc,1 = (18.215 − 16.646)/2.1 × (10 − 2.7) + 18.215 = 23.670; I_arc,2 = (18.919 − 18.215)/11.6 × (10 − 14.3) + 18.919 = 18.658 → V_oc > 2.7 kV so I_arc = I_arc,2 = 18.658 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, HCB): k₂V_oc⁵ = −3.097×10⁻⁶ × 10⁵ = (-0.3097); k₃V_oc⁴ = 1.6405×10⁻⁴ × 10⁴ = 1.6405; k₄V_oc³ = −0.0033609 × 10³ = (-3.3609); k₅V_oc² = 0.033308 × 10² = 3.3308; k₆V_oc = −0.16182 × 10 = (-1.6182); k₇ = 0.3463; sum = 0.0288; applied to each reference current, I_arc,min = 16.646/18.215/18.919 × (1 − 0.5 × 0.0288) = 16.406/17.953/18.647 kA, interpolated as above to 18.390 kA
Enclosure correction (Eq 11–15)	600 H × 200 W × 100 D mm → typical box, Table 7 (typical, HCB). W₁ = 200 mm (below 508 mm → 20 in) = 20.000 in; H₁ = 600/25.4 (508–660.4 mm: actual size) = 23.622 in; EES = (23.622 + 20.000)/2 = 21.811 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0001923) × 21.811² + 0.01935 × 21.811 + 0.6899 = 1.0205 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 16.646 kA): exponent = k₁ 4.0737 + k₂·lg 19.05 0.4403 + k₃·16.646/P_E(20) (-0.2931) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-5.6536) + k₁₃·lg 16.646 1.2653 + lg(1/1.0205) (-0.0088) = -0.1762; E = 12.552/50 × 100 × 10^-0.1762 (k₁₂ = -2.03) = 16.730 J/cm²; 2700 V (Eq 4, I* = I_arc = 18.215 kA): exponent = k₁ 3.4864 + k₂·lg 19.05 0.2265 + k₃·18.215/P_E(20) (-0.1815) + k₁₁·lg 20 0.0351 + k₁₂·lg 609.6 (-4.7986) + k₁₃·lg 18.215 1.3298 + lg(1/1.0205) (-0.0088) = 0.0889; E = 12.552/50 × 100 × 10^0.0889 (k₁₂ = -1.723) = 30.807 J/cm²; 14 300 V (Eq 5, I* = I_arc = 18.919 kA): exponent = k₁ 3.0445 + k₂·lg 19.05 0.1600 + k₃·18.919/P_E(20) 0.2350 + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.6092) + k₁₃·lg 18.919 1.3842 + lg(1/1.0205) (-0.0088) = 0.2057; E = 12.552/50 × 100 × 10^0.2057 (k₁₂ = -1.655) = 40.309 J/cm²
Interpolated full-current energy (Eq 19–21)	At 10 kV: E₁ = (30.807 − 16.730)/2.1 × (10 − 2.7) + 30.807 = 79.741; E₂ = (40.309 − 30.807)/11.6 × (10 − 14.3) + 40.309 = 36.786 → V_oc > 2.7 kV so E = E₂ = 36.786 J/cm² = 8.792 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 16.406 kA, T_min = 100 ms): exponent = k₁ 4.0737 + k₂·lg 19.05 0.4403 + k₃·16.406/P_E(20) (-0.2889) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-5.6536) + k₁₃·lg 16.406 1.2588 + lg(1/1.0205) (-0.0088) = -0.1785; E = 12.552/50 × 100 × 10^-0.1785 (k₁₂ = -2.03) = 16.642 J/cm²; 2700 V (I_arc,min = 17.953 kA, T_min = 100 ms): exponent = k₁ 3.4864 + k₂·lg 19.05 0.2265 + k₃·17.953/P_E(20) (-0.1789) + k₁₁·lg 20 0.0351 + k₁₂·lg 609.6 (-4.7986) + k₁₃·lg 17.953 1.3231 + lg(1/1.0205) (-0.0088) = 0.0849; E = 12.552/50 × 100 × 10^0.0849 (k₁₂ = -1.723) = 30.523 J/cm²; 14 300 V (I_arc,min = 18.647 kA, T_min = 100 ms): exponent = k₁ 3.0445 + k₂·lg 19.05 0.1600 + k₃·18.647/P_E(20) 0.2317 + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.6092) + k₁₃·lg 18.647 1.3773 + lg(1/1.0205) (-0.0088) = 0.1955; E = 12.552/50 × 100 × 10^0.1955 (k₁₂ = -1.655) = 39.373 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 10 kV: E₁ = (30.523 − 16.642)/2.1 × (10 − 2.7) + 30.523 = 78.775; E₂ = (39.373 − 30.523)/11.6 × (10 − 14.3) + 39.373 = 36.092 → V_oc > 2.7 kV so E = E₂ = 36.092 J/cm² = 8.626 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 609.6 × (5.0208/16.730)^1/(-2.03) = 1,103 mm; 2700 V 609.6 × (5.0208/30.807)^1/(-1.723) = 1,747 mm; 14 300 V 609.6 × (5.0208/40.309)^1/(-1.655) = 2,146 mm; reduced: 600 V 609.6 × (5.0208/16.642)^1/(-2.03) = 1,100 mm; 2700 V 609.6 × (5.0208/30.523)^1/(-1.723) = 1,738 mm; 14 300 V 609.6 × (5.0208/39.373)^1/(-1.655) = 2,116 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,747 − 1,103)/2.1 × (10 − 2.7) + 1,747 = 3,986; AFB₂ = (2,146 − 1,747)/11.6 × (10 − 14.3) + 2,146 = 1,998 → V_oc > 2.7 kV so AFB = AFB₂ = 1,998 mm; reduced: AFB₁ = (1,738 − 1,100)/2.1 × (10 − 2.7) + 1,738 = 3,954; AFB₂ = (2,116 − 1,738)/11.6 × (10 − 14.3) + 2,116 = 1,976 → V_oc > 2.7 kV so AFB = AFB₂ = 1,976 mm
Governing case	max(full 8.792, reduced 8.626 cal/cm²) → the full arcing-current case: E = 8.792 cal/cm² (36.786 J/cm²), AFB = max(1,998, 1,976) = 1,998 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 8.792 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 8.8 cal/cm² (category-equivalent 3, informational) — informational, not a pass/fail check → 8.792 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 8.792 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 100) = 100 ms → 100 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 8.79 cal/cm² at 609.6 mm, AFB 1,998 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	IEEE 1584-2018 calculator V2.6.6 sample case 167 (IEEE DataPort open-access spreadsheet V2.6.6, 2019-08-29, as exported by LiaungYip/arcflash). Hand calculation, IEEE 1584-2018 Eq 1 (HCB) Iarc,600/2700/14300 = 16.646/18.215/18.919 kA; Eq 16-18 at 10 kV Iarc = 18.658 kA; Eq 2 VarCf = 0.0288, Iarc,min = 18.390 kA; Eq 11-13 typical box W1 = 20.000 in, H1 = 23.622 in, EES = 21.811 in, Eq 14 CF = 1.0205; Eq 3-5 E600/2700/14300 = 16.730/30.807/40.309 J/cm² (full, 100 ms), 16.642/30.523/39.373 J/cm² (reduced, 100 ms); Eq 19-21 E = 36.786 / 36.092 J/cm²; Eq 7-9 + 22-24 AFB = 1998 / 1976 mm; full case governs: 36.786 J/cm² = 8.792 cal/cm², AFB 1998 mm, PPE tier arc_rated_clothing. (validation case `c0007-ieee1584-calculator-hcb-10kv-20ka`)

Example 14 — 10 kV HOA open-air bus, 20 kA

Horizontal open-air electrodes above 600 V with CF = 1; shows the Table 2 variation factor falling with voltage.

Given: V_oc = 10,000 V, I_bf = 20 kA, HOA (horizontal conductors in open air), T = 100 ms at I_arc and T_min = 100 ms at I_arc,min (same clearing time); gap G = 19.05 mm, working distance D = 609.6 mm, open air (no enclosure).

Arcing current at the reference voltages (Eq 1)	600 V: 10^{0.111147 + 1.008·lg 20 − 0.24·lg 19.05} × P_I(20) = 10^1.1154 × 1.0860 = 14.166 kA; 2700 V: 10^{0.000435 + 1.006·lg 20 − 0.038·lg 19.05} × P_I(20) = 10^1.2606 × 0.9790 = 17.842 kA; 14 300 V: 10^{0.000904 + 0.999·lg 20 − 0.02·lg 19.05} × P_I(20) = 10^1.2750 × 0.9790 = 18.443 kA (HOA coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 10 kV: I_arc,1 = (17.842 − 14.166)/2.1 × (10 − 2.7) + 17.842 = 30.620; I_arc,2 = (18.443 − 17.842)/11.6 × (10 − 14.3) + 18.443 = 18.220 → V_oc > 2.7 kV so I_arc = I_arc,2 = 18.220 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, HOA): k₂V_oc⁵ = −3.1555×10⁻⁶ × 10⁵ = (-0.3155); k₃V_oc⁴ = 1.682×10⁻⁴ × 10⁴ = 1.6820; k₄V_oc³ = −0.0034607 × 10³ = (-3.4607); k₅V_oc² = 0.034124 × 10² = 3.4124; k₆V_oc = −0.1599 × 10 = (-1.5990); k₇ = 0.3463; sum = 0.0654; applied to each reference current, I_arc,min = 14.166/17.842/18.443 × (1 − 0.5 × 0.0654) = 13.702/17.258/17.840 kA, interpolated as above to 17.624 kA
Enclosure correction (Eq 11–15)	HOA is an open-air configuration: no enclosure, CF = 1.
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 14.166 kA): exponent = k₁ 3.4704 + k₂·lg 19.05 0.5952 + k₃·14.166/P_E(20) (-0.1708) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-5.5422) + k₁₃·lg 14.166 1.1973 + lg(1/1.0000) 0.0000 = -0.4502; E = 12.552/50 × 100 × 10^-0.4502 (k₁₂ = -1.99) = 8.904 J/cm²; 2700 V (Eq 4, I* = I_arc = 17.842 kA): exponent = k₁ 3.6163 + k₂·lg 19.05 0.1907 + k₃·17.842/P_E(20) (-0.6939) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.5647) + k₁₃·lg 17.842 1.3490 + lg(1/1.0000) 0.0000 = -0.1026; E = 12.552/50 × 100 × 10^-0.1026 (k₁₂ = -1.639) = 19.822 J/cm²; 14 300 V (Eq 5, I* = I_arc = 18.443 kA): exponent = k₁ 2.0405 + k₂·lg 19.05 0.2265 + k₃·18.443/P_E(20) 0.9467 + k₁₁·lg 20 (-0.0651) + k₁₂·lg 609.6 (-4.5480) + k₁₃·lg 18.443 1.4570 + lg(1/1.0000) 0.0000 = 0.0577; E = 12.552/50 × 100 × 10^0.0577 (k₁₂ = -1.633) = 28.669 J/cm²
Interpolated full-current energy (Eq 19–21)	At 10 kV: E₁ = (19.822 − 8.904)/2.1 × (10 − 2.7) + 19.822 = 57.777; E₂ = (28.669 − 19.822)/11.6 × (10 − 14.3) + 28.669 = 25.390 → V_oc > 2.7 kV so E = E₂ = 25.390 J/cm² = 6.068 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 13.702 kA, T_min = 100 ms): exponent = k₁ 3.4704 + k₂·lg 19.05 0.5952 + k₃·13.702/P_E(20) (-0.1652) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-5.5422) + k₁₃·lg 13.702 1.1823 + lg(1/1.0000) 0.0000 = -0.4596; E = 12.552/50 × 100 × 10^-0.4596 (k₁₂ = -1.99) = 8.712 J/cm²; 2700 V (I_arc,min = 17.258 kA, T_min = 100 ms): exponent = k₁ 3.6163 + k₂·lg 19.05 0.1907 + k₃·17.258/P_E(20) (-0.6712) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.5647) + k₁₃·lg 17.258 1.3335 + lg(1/1.0000) 0.0000 = -0.0955; E = 12.552/50 × 100 × 10^-0.0955 (k₁₂ = -1.639) = 20.150 J/cm²; 14 300 V (I_arc,min = 17.840 kA, T_min = 100 ms): exponent = k₁ 2.0405 + k₂·lg 19.05 0.2265 + k₃·17.840/P_E(20) 0.9157 + k₁₁·lg 20 (-0.0651) + k₁₂·lg 609.6 (-4.5480) + k₁₃·lg 17.840 1.4403 + lg(1/1.0000) 0.0000 = 0.0101; E = 12.552/50 × 100 × 10^0.0101 (k₁₂ = -1.633) = 25.693 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 10 kV: E₁ = (20.150 − 8.712)/2.1 × (10 − 2.7) + 20.150 = 59.911; E₂ = (25.693 − 20.150)/11.6 × (10 − 14.3) + 25.693 = 23.638 → V_oc > 2.7 kV so E = E₂ = 23.638 J/cm² = 5.650 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 609.6 × (5.0208/8.904)^1/(-1.99) = 813 mm; 2700 V 609.6 × (5.0208/19.822)^1/(-1.639) = 1,409 mm; 14 300 V 609.6 × (5.0208/28.669)^1/(-1.633) = 1,772 mm; reduced: 600 V 609.6 × (5.0208/8.712)^1/(-1.99) = 804 mm; 2700 V 609.6 × (5.0208/20.150)^1/(-1.639) = 1,423 mm; 14 300 V 609.6 × (5.0208/25.693)^1/(-1.633) = 1,657 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,409 − 813)/2.1 × (10 − 2.7) + 1,409 = 3,481; AFB₂ = (1,772 − 1,409)/11.6 × (10 − 14.3) + 1,772 = 1,637 → V_oc > 2.7 kV so AFB = AFB₂ = 1,637 mm; reduced: AFB₁ = (1,423 − 804)/2.1 × (10 − 2.7) + 1,423 = 3,575; AFB₂ = (1,657 − 1,423)/11.6 × (10 − 14.3) + 1,657 = 1,570 → V_oc > 2.7 kV so AFB = AFB₂ = 1,570 mm
Governing case	max(full 6.068, reduced 5.650 cal/cm²) → the full arcing-current case: E = 6.068 cal/cm² (25.390 J/cm²), AFB = max(1,637, 1,570) = 1,637 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 6.068 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 6.1 cal/cm² (category-equivalent 2, informational) — informational, not a pass/fail check → 6.068 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 6.068 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 100) = 100 ms → 100 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 6.07 cal/cm² at 609.6 mm, AFB 1,637 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	IEEE 1584-2018 calculator V2.6.6 sample case 287 (IEEE DataPort open-access spreadsheet V2.6.6, 2019-08-29, as exported by LiaungYip/arcflash). Hand calculation, IEEE 1584-2018 Eq 1 (HOA) Iarc,600/2700/14300 = 14.166/17.842/18.443 kA; Eq 16-18 at 10 kV Iarc = 18.220 kA; Eq 2 VarCf = 0.0654, Iarc,min = 17.624 kA; open air CF = 1; Eq 3-5 E600/2700/14300 = 8.904/19.822/28.669 J/cm² (full, 100 ms), 8.712/20.150/25.693 J/cm² (reduced, 100 ms); Eq 19-21 E = 25.390 / 23.638 J/cm²; Eq 7-9 + 22-24 AFB = 1637 / 1570 mm; full case governs: 25.390 J/cm² = 6.068 cal/cm², AFB 1637 mm, PPE tier arc_rated_clothing. (validation case `c0007-ieee1584-calculator-hoa-10kv-20ka`)

Example 15 — 10 kV VCBB, 254 mm gap (maximum HV gap): reduced current governs

Largest HV gap with a 1500 mm enclosure capped at 1244.6 mm; the reduced-current case gives slightly more energy even at the same clearing time.

Given: V_oc = 10,000 V, I_bf = 20 kA, VCBB (vertical conductors terminating in a barrier in a box), T = 100 ms at I_arc and T_min = 100 ms at I_arc,min (same clearing time); gap G = 254 mm, working distance D = 609.6 mm, enclosure 1,500 H × 1,500 W × 100 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.017432) + 0.98·lg 20 − 0.05·lg 254} × P_I(20) = 10^1.1373 × 1.1337 = 15.553 kA; 2700 V: 10^{0.002823 + 0.995·lg 20 − 0.0125·lg 254} × P_I(20) = 10^1.2673 × 0.9435 = 17.458 kA; 14 300 V: 10^{0.014827 + 1.01·lg 20 − 0.01·lg 254} × P_I(20) = 10^1.3048 × 0.9435 = 19.034 kA (VCBB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 10 kV: I_arc,1 = (17.458 − 15.553)/2.1 × (10 − 2.7) + 17.458 = 24.081; I_arc,2 = (19.034 − 17.458)/11.6 × (10 − 14.3) + 19.034 = 18.450 → V_oc > 2.7 kV so I_arc = I_arc,2 = 18.450 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCBB): k₁V_oc⁶ = 1.138×10⁻⁶ × 10⁶ = 1.1380; k₂V_oc⁵ = −6.0287×10⁻⁵ × 10⁵ = (-6.0287); k₃V_oc⁴ = 0.0012758 × 10⁴ = 12.7580; k₄V_oc³ = −0.013778 × 10³ = (-13.7780); k₅V_oc² = 0.080217 × 10² = 8.0217; k₆V_oc = −0.24066 × 10 = (-2.4066); k₇ = 0.3352; sum = 0.0396; applied to each reference current, I_arc,min = 15.553/17.458/19.034 × (1 − 0.5 × 0.0396) = 15.245/17.112/18.657 kA, interpolated as above to 18.085 kA
Enclosure correction (Eq 11–15)	1,500 H × 1,500 W × 100 D mm → typical box, Table 7 (typical, VCBB). W₁ = [660.4 + (1244.6 − 660.4) × (10 + 10)/24]/25.4 (Eq 11 (capped at 1244.6 mm from 1,500)) = 45.167 in; H₁ = [660.4 + (1244.6 − 660.4) × (10 + 10)/24]/25.4 (Eq 12 (capped at 1244.6 mm from 1,500)) = 45.167 in; EES = (45.167 + 45.167)/2 = 45.167 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0002976) × 45.167² + 0.03200 × 45.167 + 0.4790 = 1.3172 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 15.553 kA): exponent = k₁ 3.0685 + k₂·lg 254 0.6253 + k₃·15.553/P_E(20) (-0.0673) + k₁₁·lg 20 (-0.0781) + k₁₂·lg 609.6 (-5.0381) + k₁₃·lg 15.553 1.4183 + lg(1/1.3172) (-0.1197) = -0.1912; E = 12.552/50 × 100 × 10^-0.1912 (k₁₂ = -1.809) = 16.164 J/cm²; 2700 V (Eq 4, I* = I_arc = 17.458 kA): exponent = k₁ 3.8706 + k₂·lg 254 0.4449 + k₃·17.458/P_E(20) (-0.6816) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.8515) + k₁₃·lg 17.458 1.3538 + lg(1/1.3172) (-0.1197) = 0.0165; E = 12.552/50 × 100 × 10^0.0165 (k₁₂ = -1.742) = 26.077 J/cm²; 14 300 V (Eq 5, I* = I_arc = 19.034 kA): exponent = k₁ 3.6443 + k₂·lg 254 0.5170 + k₃·19.034/P_E(20) (-0.5907) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.6705) + k₁₃·lg 19.034 1.3563 + lg(1/1.3172) (-0.1197) = 0.1368; E = 12.552/50 × 100 × 10^0.1368 (k₁₂ = -1.677) = 34.401 J/cm²
Interpolated full-current energy (Eq 19–21)	At 10 kV: E₁ = (26.077 − 16.164)/2.1 × (10 − 2.7) + 26.077 = 60.534; E₂ = (34.401 − 26.077)/11.6 × (10 − 14.3) + 34.401 = 31.315 → V_oc > 2.7 kV so E = E₂ = 31.315 J/cm² = 7.485 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 15.245 kA, T_min = 100 ms): exponent = k₁ 3.0685 + k₂·lg 254 0.6253 + k₃·15.245/P_E(20) (-0.0660) + k₁₁·lg 20 (-0.0781) + k₁₂·lg 609.6 (-5.0381) + k₁₃·lg 15.245 1.4079 + lg(1/1.3172) (-0.1197) = -0.2002; E = 12.552/50 × 100 × 10^-0.2002 (k₁₂ = -1.809) = 15.832 J/cm²; 2700 V (I_arc,min = 17.112 kA, T_min = 100 ms): exponent = k₁ 3.8706 + k₂·lg 254 0.4449 + k₃·17.112/P_E(20) (-0.6680) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.8515) + k₁₃·lg 17.112 1.3443 + lg(1/1.3172) (-0.1197) = 0.0205; E = 12.552/50 × 100 × 10^0.0205 (k₁₂ = -1.742) = 26.320 J/cm²; 14 300 V (I_arc,min = 18.657 kA, T_min = 100 ms): exponent = k₁ 3.6443 + k₂·lg 254 0.5170 + k₃·18.657/P_E(20) (-0.5789) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.6705) + k₁₃·lg 18.657 1.3471 + lg(1/1.3172) (-0.1197) = 0.1393; E = 12.552/50 × 100 × 10^0.1393 (k₁₂ = -1.677) = 34.599 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 10 kV: E₁ = (26.320 − 15.832)/2.1 × (10 − 2.7) + 26.320 = 62.777; E₂ = (34.599 − 26.320)/11.6 × (10 − 14.3) + 34.599 = 31.530 → V_oc > 2.7 kV so E = E₂ = 31.530 J/cm² = 7.536 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 609.6 × (5.0208/16.164)^1/(-1.809) = 1,163 mm; 2700 V 609.6 × (5.0208/26.077)^1/(-1.742) = 1,570 mm; 14 300 V 609.6 × (5.0208/34.401)^1/(-1.677) = 1,921 mm; reduced: 600 V 609.6 × (5.0208/15.832)^1/(-1.809) = 1,150 mm; 2700 V 609.6 × (5.0208/26.320)^1/(-1.742) = 1,578 mm; 14 300 V 609.6 × (5.0208/34.599)^1/(-1.677) = 1,927 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,570 − 1,163)/2.1 × (10 − 2.7) + 1,570 = 2,981; AFB₂ = (1,921 − 1,570)/11.6 × (10 − 14.3) + 1,921 = 1,790 → V_oc > 2.7 kV so AFB = AFB₂ = 1,790 mm; reduced: AFB₁ = (1,578 − 1,150)/2.1 × (10 − 2.7) + 1,578 = 3,065; AFB₂ = (1,927 − 1,578)/11.6 × (10 − 14.3) + 1,927 = 1,798 → V_oc > 2.7 kV so AFB = AFB₂ = 1,798 mm
Governing case	max(full 7.485, reduced 7.536 cal/cm²) → the reduced arcing-current case: E = 7.536 cal/cm² (31.530 J/cm²), AFB = max(1,790, 1,798) = 1,798 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 7.536 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 7.6 cal/cm² (category-equivalent 2, informational) — informational, not a pass/fail check → 7.536 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 7.536 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 100) = 100 ms → 100 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 7.54 cal/cm² at 609.6 mm, AFB 1,798 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first). Enclosure dimensions above 1244.6 mm (49 in) are treated as 1244.6 mm in the equivalent size (Eq 11-12).
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VCBB) Iarc,600/2700/14300 = 15.553/17.458/19.034 kA; Eq 16-18 at 10 kV Iarc = 18.450 kA; Eq 2 VarCf = 0.0396, Iarc,min = 18.085 kA; Eq 11-13 typical box W1 = 45.167 in, H1 = 45.167 in, EES = 45.167 in, Eq 14 CF = 1.3172; Eq 3-5 E600/2700/14300 = 16.164/26.077/34.401 J/cm² (full, 100 ms), 15.832/26.320/34.599 J/cm² (reduced, 100 ms); Eq 19-21 E = 31.315 / 31.530 J/cm²; Eq 7-9 + 22-24 AFB = 1790 / 1798 mm; reduced case governs: 31.530 J/cm² = 7.536 cal/cm², AFB 1798 mm, PPE tier arc_rated_clothing. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 109 (Iarc 18.450 kA, E 31.315 J/cm², AFB 1790 mm; reduced 18.085 kA, 31.530 J/cm², 1798 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-10kv-vcbb-max-hv-gap-reduced-current-governs`)

Example 16 — 11 kV switchgear, 1 kA weak source, 2.5 s backup clearing: beyond the 2 s cap

The 15kv_switchgear preset with the working distance overridden to 1800 mm (remote operation); a 2.5 s backup clearing time fails the 2 s reasonable-maximum check even though the energy stays below 1.2 cal/cm².

Given: V_oc = 11,000 V, I_bf = 1 kA, VCB (vertical conductors in a box), T = 2,500 ms at I_arc and T_min = 2,500 ms at I_arc,min (same clearing time); gap G = 152 mm, working distance D = 1,800 mm, enclosure 1,143 H × 762 W × 762 D mm (from the 15kV_Switchgear preset where not given; MCP 15kv_switchgear).

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.042870) + 1.035·lg 1 − 0.083·lg 152} × P_I(1) = 10^-0.2240 × 1.0949 = 0.654 kA; 2700 V: 10^{0.006500 + 1.001·lg 1 − 0.024·lg 152} × P_I(1) = 10^-0.0459 × 0.9698 = 0.873 kA; 14 300 V: 10^{0.005795 + 1.015·lg 1 − 0.011·lg 152} × P_I(1) = 10^-0.0182 × 0.9698 = 0.930 kA (VCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 11 kV: I_arc,1 = (0.873 − 0.654)/2.1 × (11 − 2.7) + 0.873 = 1.737; I_arc,2 = (0.930 − 0.873)/11.6 × (11 − 14.3) + 0.930 = 0.914 → V_oc > 2.7 kV so I_arc = I_arc,2 = 0.914 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 11⁵ = (-0.2298); k₃V_oc⁴ = 8.3137×10⁻⁵ × 11⁴ = 1.2172; k₄V_oc³ = −0.0019382 × 11³ = (-2.5797); k₅V_oc² = 0.022366 × 11² = 2.7063; k₆V_oc = −0.12645 × 11 = (-1.3910); k₇ = 0.3023; sum = 0.0253; applied to each reference current, I_arc,min = 0.654/0.873/0.930 × (1 − 0.5 × 0.0253) = 0.646/0.862/0.918 kA, interpolated as above to 0.902 kA
Enclosure correction (Eq 11–15)	1,143 H × 762 W × 762 D mm → typical box, Table 7 (typical, VCB). W₁ = [660.4 + (762 − 660.4) × (11 + 4)/20]/25.4 (Eq 11) = 29.000 in; H₁ = 1,143/25.4 (VCB height stays actual size) = 45.000 in; EES = (45.000 + 29.000)/2 = 37.000 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 37.000² + 0.03441 × 37.000 + 0.4325 = 1.2922 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 0.654 kA): exponent = k₁ 0.7534 + k₂·lg 152 1.2349 + k₃·0.654/P_E(1) 1.0465 + k₁₁·lg 1 0.0000 + k₁₂·lg 1,800 (-5.2019) + k₁₃·lg 0.654 (-0.1766) + lg(1/1.2922) (-0.1113) = -2.4551; E = 12.552/50 × 2,500 × 10^-2.4551 (k₁₂ = -1.598) = 2.201 J/cm²; 2700 V (Eq 4, I* = I_arc = 0.873 kA): exponent = k₁ 2.4002 + k₂·lg 152 0.3600 + k₃·0.873/P_E(1) 0.3187 + k₁₁·lg 1 0.0000 + k₁₂·lg 1,800 (-5.1075) + k₁₃·lg 0.873 (-0.0579) + lg(1/1.2922) (-0.1113) = -2.1978; E = 12.552/50 × 2,500 × 10^-2.1978 (k₁₂ = -1.569) = 3.980 J/cm²; 14 300 V (Eq 5, I* = I_arc = 0.930 kA): exponent = k₁ 3.8259 + k₂·lg 152 0.2400 + k₃·0.930/P_E(1) (-0.9587) + k₁₁·lg 1 0.0000 + k₁₂·lg 1,800 (-5.1043) + k₁₃·lg 0.930 (-0.0312) + lg(1/1.2922) (-0.1113) = -2.1396; E = 12.552/50 × 2,500 × 10^-2.1396 (k₁₂ = -1.568) = 4.551 J/cm²
Interpolated full-current energy (Eq 19–21)	At 11 kV: E₁ = (3.980 − 2.201)/2.1 × (11 − 2.7) + 3.980 = 11.012; E₂ = (4.551 − 3.980)/11.6 × (11 − 14.3) + 4.551 = 4.388 → V_oc > 2.7 kV so E = E₂ = 4.388 J/cm² = 1.049 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 0.646 kA, T_min = 2,500 ms): exponent = k₁ 0.7534 + k₂·lg 152 1.2349 + k₃·0.646/P_E(1) 1.0333 + k₁₁·lg 1 0.0000 + k₁₂·lg 1,800 (-5.2019) + k₁₃·lg 0.646 (-0.1819) + lg(1/1.2922) (-0.1113) = -2.4736; E = 12.552/50 × 2,500 × 10^-2.4736 (k₁₂ = -1.598) = 2.109 J/cm²; 2700 V (I_arc,min = 0.862 kA, T_min = 2,500 ms): exponent = k₁ 2.4002 + k₂·lg 152 0.3600 + k₃·0.862/P_E(1) 0.3147 + k₁₁·lg 1 0.0000 + k₁₂·lg 1,800 (-5.1075) + k₁₃·lg 0.862 (-0.0633) + lg(1/1.2922) (-0.1113) = -2.2073; E = 12.552/50 × 2,500 × 10^-2.2073 (k₁₂ = -1.569) = 3.894 J/cm²; 14 300 V (I_arc,min = 0.918 kA, T_min = 2,500 ms): exponent = k₁ 3.8259 + k₂·lg 152 0.2400 + k₃·0.918/P_E(1) (-0.9466) + k₁₁·lg 1 0.0000 + k₁₂·lg 1,800 (-5.1043) + k₁₃·lg 0.918 (-0.0367) + lg(1/1.2922) (-0.1113) = -2.1330; E = 12.552/50 × 2,500 × 10^-2.1330 (k₁₂ = -1.568) = 4.621 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 11 kV: E₁ = (3.894 − 2.109)/2.1 × (11 − 2.7) + 3.894 = 10.951; E₂ = (4.621 − 3.894)/11.6 × (11 − 14.3) + 4.621 = 4.414 → V_oc > 2.7 kV so E = E₂ = 4.414 J/cm² = 1.055 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 1,800 × (5.0208/2.201)^1/(-1.598) = 1,074 mm; 2700 V 1,800 × (5.0208/3.980)^1/(-1.569) = 1,552 mm; 14 300 V 1,800 × (5.0208/4.551)^1/(-1.568) = 1,691 mm; reduced: 600 V 1,800 × (5.0208/2.109)^1/(-1.598) = 1,046 mm; 2700 V 1,800 × (5.0208/3.894)^1/(-1.569) = 1,531 mm; 14 300 V 1,800 × (5.0208/4.621)^1/(-1.568) = 1,707 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,552 − 1,074)/2.1 × (11 − 2.7) + 1,552 = 3,441; AFB₂ = (1,691 − 1,552)/11.6 × (11 − 14.3) + 1,691 = 1,651 → V_oc > 2.7 kV so AFB = AFB₂ = 1,651 mm; reduced: AFB₁ = (1,531 − 1,046)/2.1 × (11 − 2.7) + 1,531 = 3,448; AFB₂ = (1,707 − 1,531)/11.6 × (11 − 14.3) + 1,707 = 1,657 → V_oc > 2.7 kV so AFB = AFB₂ = 1,657 mm
Governing case	max(full 1.049, reduced 1.055 cal/cm²) → the reduced arcing-current case: E = 1.055 cal/cm² (4.414 J/cm²), AFB = max(1,651, 1,657) = 1,657 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 1.055 cal/cm² ≤ 1.2 cal/cm² → arc-rated PPE not required (non-melting or untreated natural-fibre clothing is still required). Caveat: the clearing time exceeds 2 s, so the exposure assumption behind this energy is invalid — fix the clearing time before relying on the PPE result — informational, not a pass/fail check → 1.055 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 1.055 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(2,500, 2,500) = 2,500 ms; sensitivity with both times capped at 2 s: incident energy 1.05 → 0.84 cal/cm² (the uncapped figure is reported) — most other tools report the capped figure → 2,500 vs limit 2,000 ms FAIL
Result	1/2 checks pass → FAIL; E = 1.05 cal/cm² at 1,800 mm, AFB 1,657 mm, arc-rated PPE not required; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first). Arc duration exceeds 2 s. IEEE 1584-2018 suggests 2 s as a reasonable maximum exposure where a worker can move away; the energy here uses the full time entered.
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VCB) Iarc,600/2700/14300 = 0.654/0.873/0.930 kA; Eq 16-18 at 11 kV Iarc = 0.914 kA; Eq 2 VarCf = 0.0253, Iarc,min = 0.902 kA; Eq 11-13 typical box W1 = 29.000 in, H1 = 45.000 in, EES = 37.000 in, Eq 14 CF = 1.2922; Eq 3-5 E600/2700/14300 = 2.201/3.980/4.551 J/cm² (full, 2500 ms), 2.109/3.894/4.621 J/cm² (reduced, 2500 ms); Eq 19-21 E = 4.388 / 4.414 J/cm²; Eq 7-9 + 22-24 AFB = 1651 / 1657 mm; reduced case governs: 4.414 J/cm² = 1.055 cal/cm², AFB 1657 mm, PPE tier none. Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-11kv-switchgear-preset-2.5s-backup-clearing`)

Example 17 — 15 kV, 0.2 kA: minimum HV fault current, 1 s clearing

Smallest fault current and highest voltage of the model; 1 s clearing still leaves the energy below 1.2 cal/cm², reduced case governs. The 457.2 mm working distance is deliberately below the 914.4 mm typical at 15 kV, to pin the model at its bounds; it is not a realistic study point.

Given: V_oc = 15,000 V, I_bf = 0.2 kA, VCB (vertical conductors in a box), T = 1,000 ms at I_arc and T_min = 1,000 ms at I_arc,min (same clearing time); gap G = 152 mm, working distance D = 457.2 mm, enclosure 1,000 H × 1,000 W × 100 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.042870) + 1.035·lg 0.2 − 0.083·lg 152} × P_I(0.2) = 10^-0.9474 × 1.0926 = 0.123 kA; 2700 V: 10^{0.006500 + 1.001·lg 0.2 − 0.024·lg 152} × P_I(0.2) = 10^-0.7455 × 0.9723 = 0.175 kA; 14 300 V: 10^{0.005795 + 1.015·lg 0.2 − 0.011·lg 152} × P_I(0.2) = 10^-0.7277 × 0.9723 = 0.182 kA (VCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 15 kV: I_arc,1 = (0.175 − 0.123)/2.1 × (15 − 2.7) + 0.175 = 0.475; I_arc,2 = (0.182 − 0.175)/11.6 × (15 − 14.3) + 0.182 = 0.182 → V_oc > 2.7 kV so I_arc = I_arc,2 = 0.182 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 15⁵ = (-1.0836); k₃V_oc⁴ = 8.3137×10⁻⁵ × 15⁴ = 4.2088; k₄V_oc³ = −0.0019382 × 15³ = (-6.5414); k₅V_oc² = 0.022366 × 15² = 5.0324; k₆V_oc = −0.12645 × 15 = (-1.8968); k₇ = 0.3023; sum = 0.0217; applied to each reference current, I_arc,min = 0.123/0.175/0.182 × (1 − 0.5 × 0.0217) = 0.122/0.173/0.180 kA, interpolated as above to 0.180 kA
Enclosure correction (Eq 11–15)	1,000 H × 1,000 W × 100 D mm → typical box, Table 7 (typical, VCB). W₁ = [660.4 + (1,000 − 660.4) × (15 + 4)/20]/25.4 (Eq 11) = 38.702 in; H₁ = 1,000/25.4 (VCB height stays actual size) = 39.370 in; EES = (39.370 + 38.702)/2 = 39.036 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 39.036² + 0.03441 × 39.036 + 0.4325 = 1.3155 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 0.123 kA): exponent = k₁ 0.7534 + k₂·lg 152 1.2349 + k₃·0.123/P_E(0.2) 0.9892 + k₁₁·lg 0.2 0.0000 + k₁₂·lg 457.2 (-4.2508) + k₁₃·lg 0.123 (-0.8698) + lg(1/1.3155) (-0.1191) = -2.2624; E = 12.552/50 × 1,000 × 10^-2.2624 (k₁₂ = -1.598) = 1.372 J/cm²; 2700 V (Eq 4, I* = I_arc = 0.175 kA): exponent = k₁ 2.4002 + k₂·lg 152 0.3600 + k₃·0.175/P_E(0.2) 0.3182 + k₁₁·lg 0.2 0.0000 + k₁₂·lg 457.2 (-4.1737) + k₁₃·lg 0.175 (-0.7409) + lg(1/1.3155) (-0.1191) = -1.9553; E = 12.552/50 × 1,000 × 10^-1.9553 (k₁₂ = -1.569) = 2.782 J/cm²; 14 300 V (Eq 5, I* = I_arc = 0.182 kA): exponent = k₁ 3.8259 + k₂·lg 152 0.2400 + k₃·0.182/P_E(0.2) (-0.9358) + k₁₁·lg 0.2 0.0000 + k₁₂·lg 457.2 (-4.1710) + k₁₃·lg 0.182 (-0.7325) + lg(1/1.3155) (-0.1191) = -1.8925; E = 12.552/50 × 1,000 × 10^-1.8925 (k₁₂ = -1.568) = 3.215 J/cm²
Interpolated full-current energy (Eq 19–21)	At 15 kV: E₁ = (2.782 − 1.372)/2.1 × (15 − 2.7) + 2.782 = 11.042; E₂ = (3.215 − 2.782)/11.6 × (15 − 14.3) + 3.215 = 3.241 → V_oc > 2.7 kV so E = E₂ = 3.241 J/cm² = 0.775 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 0.122 kA, T_min = 1,000 ms): exponent = k₁ 0.7534 + k₂·lg 152 1.2349 + k₃·0.122/P_E(0.2) 0.9784 + k₁₁·lg 0.2 0.0000 + k₁₂·lg 457.2 (-4.2508) + k₁₃·lg 0.122 (-0.8744) + lg(1/1.3155) (-0.1191) = -2.2776; E = 12.552/50 × 1,000 × 10^-2.2776 (k₁₂ = -1.598) = 1.325 J/cm²; 2700 V (I_arc,min = 0.173 kA, T_min = 1,000 ms): exponent = k₁ 2.4002 + k₂·lg 152 0.3600 + k₃·0.173/P_E(0.2) 0.3147 + k₁₁·lg 0.2 0.0000 + k₁₂·lg 457.2 (-4.1737) + k₁₃·lg 0.173 (-0.7456) + lg(1/1.3155) (-0.1191) = -1.9634; E = 12.552/50 × 1,000 × 10^-1.9634 (k₁₂ = -1.569) = 2.731 J/cm²; 14 300 V (I_arc,min = 0.180 kA, T_min = 1,000 ms): exponent = k₁ 3.8259 + k₂·lg 152 0.2400 + k₃·0.180/P_E(0.2) (-0.9257) + k₁₁·lg 0.2 0.0000 + k₁₂·lg 457.2 (-4.1710) + k₁₃·lg 0.180 (-0.7372) + lg(1/1.3155) (-0.1191) = -1.8871; E = 12.552/50 × 1,000 × 10^-1.8871 (k₁₂ = -1.568) = 3.256 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 15 kV: E₁ = (2.731 − 1.325)/2.1 × (15 − 2.7) + 2.731 = 10.968; E₂ = (3.256 − 2.731)/11.6 × (15 − 14.3) + 3.256 = 3.287 → V_oc > 2.7 kV so E = E₂ = 3.287 J/cm² = 0.786 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 457.2 × (5.0208/1.372)^1/(-1.598) = 203 mm; 2700 V 457.2 × (5.0208/2.782)^1/(-1.569) = 314 mm; 14 300 V 457.2 × (5.0208/3.215)^1/(-1.568) = 344 mm; reduced: 600 V 457.2 × (5.0208/1.325)^1/(-1.598) = 199 mm; 2700 V 457.2 × (5.0208/2.731)^1/(-1.569) = 310 mm; 14 300 V 457.2 × (5.0208/3.256)^1/(-1.568) = 347 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (314 − 203)/2.1 × (15 − 2.7) + 314 = 963; AFB₂ = (344 − 314)/11.6 × (15 − 14.3) + 344 = 346 → V_oc > 2.7 kV so AFB = AFB₂ = 346 mm; reduced: AFB₁ = (310 − 199)/2.1 × (15 − 2.7) + 310 = 963; AFB₂ = (347 − 310)/11.6 × (15 − 14.3) + 347 = 349 → V_oc > 2.7 kV so AFB = AFB₂ = 349 mm
Governing case	max(full 0.775, reduced 0.786 cal/cm²) → the reduced arcing-current case: E = 0.786 cal/cm² (3.287 J/cm²), AFB = max(346, 349) = 349 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 0.786 cal/cm² ≤ 1.2 cal/cm² → arc-rated PPE not required (non-melting or untreated natural-fibre clothing is still required) — informational, not a pass/fail check → 0.786 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 0.786 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(1,000, 1,000) = 1,000 ms → 1,000 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 0.79 cal/cm² at 457.2 mm, AFB 349 mm, arc-rated PPE not required; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VCB) Iarc,600/2700/14300 = 0.123/0.175/0.182 kA; Eq 16-18 at 15 kV Iarc = 0.182 kA; Eq 2 VarCf = 0.0217, Iarc,min = 0.180 kA; Eq 11-13 typical box W1 = 38.702 in, H1 = 39.370 in, EES = 39.036 in, Eq 14 CF = 1.3155; Eq 3-5 E600/2700/14300 = 1.372/2.782/3.215 J/cm² (full, 1000 ms), 1.325/2.731/3.256 J/cm² (reduced, 1000 ms); Eq 19-21 E = 3.241 / 3.287 J/cm²; Eq 7-9 + 22-24 AFB = 346 / 349 mm; reduced case governs: 3.287 J/cm² = 0.786 cal/cm², AFB 349 mm, PPE tier none. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 54 (Iarc 0.182 kA, E 3.241 J/cm², AFB 346 mm; reduced 0.180 kA, 3.287 J/cm², 349 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-15kv-0.2ka-minimum-hv-fault-current`)

Example 18 — 15 kV outdoor open-air vertical bus (15 kV switchgear preset gap and distance)

The 15kv_switchgear preset supplies the 152 mm gap and 914.4 mm working distance for an open-air VOA bus; enclosure dimensions are not used.

Given: V_oc = 15,000 V, I_bf = 20 kA, VOA (vertical conductors in open air), T = 100 ms at I_arc and T_min = 100 ms at I_arc,min (same clearing time); gap G = 152 mm, working distance D = 914.4 mm, open air (no enclosure) (from the 15kV_Switchgear preset where not given; MCP 15kv_switchgear).

Arcing current at the reference voltages (Eq 1)	600 V: 10^{0.043785 + 1.04·lg 20 − 0.18·lg 152} × P_I(20) = 10^1.0041 × 1.0782 = 10.884 kA; 2700 V: 10^{(-0.023950) + 1.006·lg 20 − 0.0188·lg 152} × P_I(20) = 10^1.2439 × 0.9323 = 16.347 kA; 14 300 V: 10^{0.005371 + 1.0102·lg 20 − 0.029·lg 152} × P_I(20) = 10^1.2564 × 0.9323 = 16.826 kA (VOA coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 15 kV: I_arc,1 = (16.347 − 10.884)/2.1 × (15 − 2.7) + 16.347 = 48.344; I_arc,2 = (16.826 − 16.347)/11.6 × (15 − 14.3) + 16.826 = 16.855 → V_oc > 2.7 kV so I_arc = I_arc,2 = 16.855 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VOA): k₁V_oc⁶ = 9.5606×10⁻⁷ × 15⁶ = 10.8901; k₂V_oc⁵ = −5.1543×10⁻⁵ × 15⁵ = (-39.1405); k₃V_oc⁴ = 0.0011161 × 15⁴ = 56.5026; k₄V_oc³ = −0.01242 × 15³ = (-41.9175); k₅V_oc² = 0.075125 × 15² = 16.9031; k₆V_oc = −0.23584 × 15 = (-3.5376); k₇ = 0.3370; sum = 0.0372; applied to each reference current, I_arc,min = 10.884/16.347/16.826 × (1 − 0.5 × 0.0372) = 10.682/16.043/16.513 kA, interpolated as above to 16.541 kA
Enclosure correction (Eq 11–15)	VOA is an open-air configuration: no enclosure, CF = 1.
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 10.884 kA): exponent = k₁ 0.6793 + k₂·lg 152 1.6277 + k₃·10.884/P_E(20) 0.6172 + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 10.884 1.0337 + lg(1/1.0000) 0.0000 = -0.7741; E = 12.552/50 × 100 × 10^-0.7741 (k₁₂ = -1.598) = 4.223 J/cm²; 2700 V (Eq 4, I* = I_arc = 16.347 kA): exponent = k₁ 3.8807 + k₂·lg 152 0.2291 + k₃·16.347/P_E(20) (-1.6710) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.4861) + k₁₃·lg 16.347 1.3530 + lg(1/1.0000) 0.0000 = -0.6943; E = 12.552/50 × 100 × 10^-0.6943 (k₁₂ = -1.515) = 5.075 J/cm²; 14 300 V (Eq 5, I* = I_arc = 16.826 kA): exponent = k₁ 3.4055 + k₂·lg 152 0.2618 + k₃·16.826/P_E(20) (-0.8414) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.5424) + k₁₃·lg 16.826 1.2002 + lg(1/1.0000) 0.0000 = -0.5163; E = 12.552/50 × 100 × 10^-0.5163 (k₁₂ = -1.534) = 7.647 J/cm²
Interpolated full-current energy (Eq 19–21)	At 15 kV: E₁ = (5.075 − 4.223)/2.1 × (15 − 2.7) + 5.075 = 10.066; E₂ = (7.647 − 5.075)/11.6 × (15 − 14.3) + 7.647 = 7.802 → V_oc > 2.7 kV so E = E₂ = 7.802 J/cm² = 1.865 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 10.682 kA, T_min = 100 ms): exponent = k₁ 0.6793 + k₂·lg 152 1.6277 + k₃·10.682/P_E(20) 0.6057 + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 10.682 1.0256 + lg(1/1.0000) 0.0000 = -0.7937; E = 12.552/50 × 100 × 10^-0.7937 (k₁₂ = -1.598) = 4.037 J/cm²; 2700 V (I_arc,min = 16.043 kA, T_min = 100 ms): exponent = k₁ 3.8807 + k₂·lg 152 0.2291 + k₃·16.043/P_E(20) (-1.6399) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.4861) + k₁₃·lg 16.043 1.3439 + lg(1/1.0000) 0.0000 = -0.6723; E = 12.552/50 × 100 × 10^-0.6723 (k₁₂ = -1.515) = 5.339 J/cm²; 14 300 V (I_arc,min = 16.513 kA, T_min = 100 ms): exponent = k₁ 3.4055 + k₂·lg 152 0.2618 + k₃·16.513/P_E(20) (-0.8257) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.5424) + k₁₃·lg 16.513 1.1922 + lg(1/1.0000) 0.0000 = -0.5086; E = 12.552/50 × 100 × 10^-0.5086 (k₁₂ = -1.534) = 7.783 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 15 kV: E₁ = (5.339 − 4.037)/2.1 × (15 − 2.7) + 5.339 = 12.966; E₂ = (7.783 − 5.339)/11.6 × (15 − 14.3) + 7.783 = 7.931 → V_oc > 2.7 kV so E = E₂ = 7.931 J/cm² = 1.895 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 914.4 × (5.0208/4.223)^1/(-1.598) = 821 mm; 2700 V 914.4 × (5.0208/5.075)^1/(-1.515) = 921 mm; 14 300 V 914.4 × (5.0208/7.647)^1/(-1.534) = 1,203 mm; reduced: 600 V 914.4 × (5.0208/4.037)^1/(-1.598) = 798 mm; 2700 V 914.4 × (5.0208/5.339)^1/(-1.515) = 952 mm; 14 300 V 914.4 × (5.0208/7.783)^1/(-1.534) = 1,217 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (921 − 821)/2.1 × (15 − 2.7) + 921 = 1,509; AFB₂ = (1,203 − 921)/11.6 × (15 − 14.3) + 1,203 = 1,220 → V_oc > 2.7 kV so AFB = AFB₂ = 1,220 mm; reduced: AFB₁ = (952 − 798)/2.1 × (15 − 2.7) + 952 = 1,857; AFB₂ = (1,217 − 952)/11.6 × (15 − 14.3) + 1,217 = 1,233 → V_oc > 2.7 kV so AFB = AFB₂ = 1,233 mm
Governing case	max(full 1.865, reduced 1.895 cal/cm²) → the reduced arcing-current case: E = 1.895 cal/cm² (7.931 J/cm²), AFB = max(1,220, 1,233) = 1,233 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 1.895 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 1.9 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 1.895 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 1.895 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 100) = 100 ms → 100 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 1.90 cal/cm² at 914.4 mm, AFB 1,233 mm, arc-rated clothing; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VOA) Iarc,600/2700/14300 = 10.884/16.347/16.826 kA; Eq 16-18 at 15 kV Iarc = 16.855 kA; Eq 2 VarCf = 0.0372, Iarc,min = 16.541 kA; open air CF = 1; Eq 3-5 E600/2700/14300 = 4.223/5.075/7.647 J/cm² (full, 100 ms), 4.037/5.339/7.783 J/cm² (reduced, 100 ms); Eq 19-21 E = 7.802 / 7.931 J/cm²; Eq 7-9 + 22-24 AFB = 1220 / 1233 mm; reduced case governs: 7.931 J/cm² = 1.895 cal/cm², AFB 1233 mm, PPE tier arc_rated_clothing. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 237 (Iarc 16.855 kA, E 7.802 J/cm², AFB 1220 mm; reduced 16.541 kA, 7.931 J/cm², 1233 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-15kv-outdoor-open-air-vertical-bus-preset`)

Example 19 — 15 kV open-air horizontal bus (15 kV MCC preset gap and distance)

HOA electrodes with the 15kv_mcc preset (152 mm, 914.4 mm); the full-current case governs for horizontal open-air electrodes.

Given: V_oc = 15,000 V, I_bf = 20 kA, HOA (horizontal conductors in open air), T = 100 ms at I_arc and T_min = 100 ms at I_arc,min (same clearing time); gap G = 152 mm, working distance D = 914.4 mm, open air (no enclosure) (from the 15kV_MCC preset where not given; MCP 15kv_mcc).

Arcing current at the reference voltages (Eq 1)	600 V: 10^{0.111147 + 1.008·lg 20 − 0.24·lg 152} × P_I(20) = 10^0.8989 × 1.0860 = 8.605 kA; 2700 V: 10^{0.000435 + 1.006·lg 20 − 0.038·lg 152} × P_I(20) = 10^1.2264 × 0.9790 = 16.488 kA; 14 300 V: 10^{0.000904 + 0.999·lg 20 − 0.02·lg 152} × P_I(20) = 10^1.2570 × 0.9790 = 17.693 kA (HOA coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 15 kV: I_arc,1 = (16.488 − 8.605)/2.1 × (15 − 2.7) + 16.488 = 62.656; I_arc,2 = (17.693 − 16.488)/11.6 × (15 − 14.3) + 17.693 = 17.766 → V_oc > 2.7 kV so I_arc = I_arc,2 = 17.766 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, HOA): k₂V_oc⁵ = −3.1555×10⁻⁶ × 15⁵ = (-2.3962); k₃V_oc⁴ = 1.682×10⁻⁴ × 15⁴ = 8.5151; k₄V_oc³ = −0.0034607 × 15³ = (-11.6799); k₅V_oc² = 0.034124 × 15² = 7.6779; k₆V_oc = −0.1599 × 15 = (-2.3985); k₇ = 0.3463; sum = 0.0647; applied to each reference current, I_arc,min = 8.605/16.488/17.693 × (1 − 0.5 × 0.0647) = 8.327/15.954/17.120 kA, interpolated as above to 17.190 kA
Enclosure correction (Eq 11–15)	HOA is an open-air configuration: no enclosure, CF = 1.
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 8.605 kA): exponent = k₁ 3.4704 + k₂·lg 152 1.0146 + k₃·8.605/P_E(20) (-0.1037) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-5.8927) + k₁₃·lg 8.605 0.9722 + lg(1/1.0000) 0.0000 = -0.5393; E = 12.552/50 × 100 × 10^-0.5393 (k₁₂ = -1.99) = 7.252 J/cm²; 2700 V (Eq 4, I* = I_arc = 16.488 kA): exponent = k₁ 3.6163 + k₂·lg 152 0.3251 + k₃·16.488/P_E(20) (-0.6413) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.8533) + k₁₃·lg 16.488 1.3121 + lg(1/1.0000) 0.0000 = -0.2411; E = 12.552/50 × 100 × 10^-0.2411 (k₁₂ = -1.639) = 14.409 J/cm²; 14 300 V (Eq 5, I* = I_arc = 17.693 kA): exponent = k₁ 2.0405 + k₂·lg 152 0.3862 + k₃·17.693/P_E(20) 0.9082 + k₁₁·lg 20 (-0.0651) + k₁₂·lg 914.4 (-4.8355) + k₁₃·lg 17.693 1.4362 + lg(1/1.0000) 0.0000 = -0.1295; E = 12.552/50 × 100 × 10^-0.1295 (k₁₂ = -1.633) = 18.631 J/cm²
Interpolated full-current energy (Eq 19–21)	At 15 kV: E₁ = (14.409 − 7.252)/2.1 × (15 − 2.7) + 14.409 = 56.329; E₂ = (18.631 − 14.409)/11.6 × (15 − 14.3) + 18.631 = 18.885 → V_oc > 2.7 kV so E = E₂ = 18.885 J/cm² = 4.514 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 8.327 kA, T_min = 100 ms): exponent = k₁ 3.4704 + k₂·lg 152 1.0146 + k₃·8.327/P_E(20) (-0.1004) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-5.8927) + k₁₃·lg 8.327 0.9573 + lg(1/1.0000) 0.0000 = -0.5508; E = 12.552/50 × 100 × 10^-0.5508 (k₁₂ = -1.99) = 7.063 J/cm²; 2700 V (I_arc,min = 15.954 kA, T_min = 100 ms): exponent = k₁ 3.6163 + k₂·lg 152 0.3251 + k₃·15.954/P_E(20) (-0.6205) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.8533) + k₁₃·lg 15.954 1.2967 + lg(1/1.0000) 0.0000 = -0.2357; E = 12.552/50 × 100 × 10^-0.2357 (k₁₂ = -1.639) = 14.588 J/cm²; 14 300 V (I_arc,min = 17.120 kA, T_min = 100 ms): exponent = k₁ 2.0405 + k₂·lg 152 0.3862 + k₃·17.120/P_E(20) 0.8788 + k₁₁·lg 20 (-0.0651) + k₁₂·lg 914.4 (-4.8355) + k₁₃·lg 17.120 1.4198 + lg(1/1.0000) 0.0000 = -0.1754; E = 12.552/50 × 100 × 10^-0.1754 (k₁₂ = -1.633) = 16.764 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 15 kV: E₁ = (14.588 − 7.063)/2.1 × (15 − 2.7) + 14.588 = 58.665; E₂ = (16.764 − 14.588)/11.6 × (15 − 14.3) + 16.764 = 16.895 → V_oc > 2.7 kV so E = E₂ = 16.895 J/cm² = 4.038 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 914.4 × (5.0208/7.252)^1/(-1.99) = 1,100 mm; 2700 V 914.4 × (5.0208/14.409)^1/(-1.639) = 1,740 mm; 14 300 V 914.4 × (5.0208/18.631)^1/(-1.633) = 2,041 mm; reduced: 600 V 914.4 × (5.0208/7.063)^1/(-1.99) = 1,085 mm; 2700 V 914.4 × (5.0208/14.588)^1/(-1.639) = 1,753 mm; 14 300 V 914.4 × (5.0208/16.764)^1/(-1.633) = 1,913 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,740 − 1,100)/2.1 × (15 − 2.7) + 1,740 = 5,487; AFB₂ = (2,041 − 1,740)/11.6 × (15 − 14.3) + 2,041 = 2,059 → V_oc > 2.7 kV so AFB = AFB₂ = 2,059 mm; reduced: AFB₁ = (1,753 − 1,085)/2.1 × (15 − 2.7) + 1,753 = 5,662; AFB₂ = (1,913 − 1,753)/11.6 × (15 − 14.3) + 1,913 = 1,923 → V_oc > 2.7 kV so AFB = AFB₂ = 1,923 mm
Governing case	max(full 4.514, reduced 4.038 cal/cm²) → the full arcing-current case: E = 4.514 cal/cm² (18.885 J/cm²), AFB = max(2,059, 1,923) = 2,059 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 4.514 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 4.6 cal/cm² (category-equivalent 2, informational) — informational, not a pass/fail check → 4.514 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 4.514 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 100) = 100 ms → 100 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 4.51 cal/cm² at 914.4 mm, AFB 2,059 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (HOA) Iarc,600/2700/14300 = 8.605/16.488/17.693 kA; Eq 16-18 at 15 kV Iarc = 17.766 kA; Eq 2 VarCf = 0.0647, Iarc,min = 17.190 kA; open air CF = 1; Eq 3-5 E600/2700/14300 = 7.252/14.409/18.631 J/cm² (full, 100 ms), 7.063/14.588/16.764 J/cm² (reduced, 100 ms); Eq 19-21 E = 18.885 / 16.895 J/cm²; Eq 7-9 + 22-24 AFB = 2059 / 1923 mm; full case governs: 18.885 J/cm² = 4.514 cal/cm², AFB 2059 mm, PPE tier arc_rated_clothing. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 297 (Iarc 17.766 kA, E 18.885 J/cm², AFB 2059 mm; reduced 17.190 kA, 16.895 J/cm², 1923 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-15kv-open-air-horizontal-bus-mcc-preset`)

Example 20 — 15 kV switchgear, 65 kA, 1 s clearing: extreme hazard (>120 cal/cm²)

Maximum HV fault current at 15 kV with 1 s clearing; the reduced-current case governs and the energy is three times the 40 cal/cm² category-4 rating — beyond category 4, de-energise. The 12.1 m arc-flash boundary would cover most of a switchroom: in practice the answer is to remove the hazard (faster clearing, arc-flash relaying, remote racking), not to set a boundary.

Given: V_oc = 15,000 V, I_bf = 65 kA, VCB (vertical conductors in a box), T = 1,000 ms at I_arc and T_min = 1,000 ms at I_arc,min (same clearing time); gap G = 104 mm, working distance D = 609.6 mm, enclosure 600 H × 1,000 W × 100 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.042870) + 1.035·lg 65 − 0.083·lg 104} × P_I(65) = 10^1.6661 × 0.7821 = 36.252 kA; 2700 V: 10^{0.006500 + 1.001·lg 65 − 0.024·lg 104} × P_I(65) = 10^1.7728 × 0.8903 = 52.765 kA; 14 300 V: 10^{0.005795 + 1.015·lg 65 − 0.011·lg 104} × P_I(65) = 10^1.8237 × 0.8903 = 59.325 kA (VCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 15 kV: I_arc,1 = (52.765 − 36.252)/2.1 × (15 − 2.7) + 52.765 = 149.482; I_arc,2 = (59.325 − 52.765)/11.6 × (15 − 14.3) + 59.325 = 59.721 → V_oc > 2.7 kV so I_arc = I_arc,2 = 59.721 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 15⁵ = (-1.0836); k₃V_oc⁴ = 8.3137×10⁻⁵ × 15⁴ = 4.2088; k₄V_oc³ = −0.0019382 × 15³ = (-6.5414); k₅V_oc² = 0.022366 × 15² = 5.0324; k₆V_oc = −0.12645 × 15 = (-1.8968); k₇ = 0.3023; sum = 0.0217; applied to each reference current, I_arc,min = 36.252/52.765/59.325 × (1 − 0.5 × 0.0217) = 35.859/52.192/58.682 kA, interpolated as above to 59.073 kA
Enclosure correction (Eq 11–15)	600 H × 1,000 W × 100 D mm → typical box, Table 7 (typical, VCB). W₁ = [660.4 + (1,000 − 660.4) × (15 + 4)/20]/25.4 (Eq 11) = 38.702 in; H₁ = 600/25.4 (508–660.4 mm: actual size) = 23.622 in; EES = (23.622 + 38.702)/2 = 31.162 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 31.162² + 0.03441 × 31.162 + 0.4325 = 1.2115 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 36.252 kA): exponent = k₁ 0.7534 + k₂·lg 104 1.1416 + k₃·36.252/P_E(65) 1.2499 + k₁₁·lg 65 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 36.252 1.4923 + lg(1/1.2115) (-0.0833) = 0.1033; E = 12.552/50 × 1,000 × 10^0.1033 (k₁₂ = -1.598) = 318.457 J/cm²; 2700 V (Eq 4, I* = I_arc = 52.765 kA): exponent = k₁ 2.4002 + k₂·lg 104 0.3328 + k₃·52.765/P_E(65) 0.3230 + k₁₁·lg 65 0.0000 + k₁₂·lg 609.6 (-4.3697) + k₁₃·lg 52.765 1.6841 + lg(1/1.2115) (-0.0833) = 0.2870; E = 12.552/50 × 1,000 × 10^0.2870 (k₁₂ = -1.569) = 486.148 J/cm²; 14 300 V (Eq 5, I* = I_arc = 59.325 kA): exponent = k₁ 3.8259 + k₂·lg 104 0.2219 + k₃·59.325/P_E(65) (-1.0249) + k₁₁·lg 65 0.0000 + k₁₂·lg 609.6 (-4.3670) + k₁₃·lg 59.325 1.7555 + lg(1/1.2115) (-0.0833) = 0.3281; E = 12.552/50 × 1,000 × 10^0.3281 (k₁₂ = -1.568) = 534.361 J/cm²
Interpolated full-current energy (Eq 19–21)	At 15 kV: E₁ = (486.148 − 318.457)/2.1 × (15 − 2.7) + 486.148 = 1,468.340; E₂ = (534.361 − 486.148)/11.6 × (15 − 14.3) + 534.361 = 537.270 → V_oc > 2.7 kV so E = E₂ = 537.270 J/cm² = 128.411 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 35.859 kA, T_min = 1,000 ms): exponent = k₁ 0.7534 + k₂·lg 104 1.1416 + k₃·35.859/P_E(65) 1.2363 + k₁₁·lg 65 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 35.859 1.4877 + lg(1/1.2115) (-0.0833) = 0.0852; E = 12.552/50 × 1,000 × 10^0.0852 (k₁₂ = -1.598) = 305.465 J/cm²; 2700 V (I_arc,min = 52.192 kA, T_min = 1,000 ms): exponent = k₁ 2.4002 + k₂·lg 104 0.3328 + k₃·52.192/P_E(65) 0.3195 + k₁₁·lg 65 0.0000 + k₁₂·lg 609.6 (-4.3697) + k₁₃·lg 52.192 1.6795 + lg(1/1.2115) (-0.0833) = 0.2789; E = 12.552/50 × 1,000 × 10^0.2789 (k₁₂ = -1.569) = 477.127 J/cm²; 14 300 V (I_arc,min = 58.682 kA, T_min = 1,000 ms): exponent = k₁ 3.8259 + k₂·lg 104 0.2219 + k₃·58.682/P_E(65) (-1.0138) + k₁₁·lg 65 0.0000 + k₁₂·lg 609.6 (-4.3670) + k₁₃·lg 58.682 1.7508 + lg(1/1.2115) (-0.0833) = 0.3345; E = 12.552/50 × 1,000 × 10^0.3345 (k₁₂ = -1.568) = 542.328 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 15 kV: E₁ = (477.127 − 305.465)/2.1 × (15 − 2.7) + 477.127 = 1,482.580; E₂ = (542.328 − 477.127)/11.6 × (15 − 14.3) + 542.328 = 546.263 → V_oc > 2.7 kV so E = E₂ = 546.263 J/cm² = 130.560 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 609.6 × (5.0208/318.457)^1/(-1.598) = 8,182 mm; 2700 V 609.6 × (5.0208/486.148)^1/(-1.569) = 11,241 mm; 14 300 V 609.6 × (5.0208/534.361)^1/(-1.568) = 11,962 mm; reduced: 600 V 609.6 × (5.0208/305.465)^1/(-1.598) = 7,972 mm; 2700 V 609.6 × (5.0208/477.127)^1/(-1.569) = 11,108 mm; 14 300 V 609.6 × (5.0208/542.328)^1/(-1.568) = 12,076 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (11,241 − 8,182)/2.1 × (15 − 2.7) + 11,241 = 29,158; AFB₂ = (11,962 − 11,241)/11.6 × (15 − 14.3) + 11,962 = 12,006 → V_oc > 2.7 kV so AFB = AFB₂ = 12,006 mm; reduced: AFB₁ = (11,108 − 7,972)/2.1 × (15 − 2.7) + 11,108 = 29,476; AFB₂ = (12,076 − 11,108)/11.6 × (15 − 14.3) + 12,076 = 12,134 → V_oc > 2.7 kV so AFB = AFB₂ = 12,134 mm
Governing case	max(full 128.411, reduced 130.560 cal/cm²) → the reduced arcing-current case: E = 130.560 cal/cm² (546.263 J/cm²), AFB = max(12,006, 12,134) = 12,134 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 130.560 cal/cm² > 1.2 cal/cm² → arc-flash suit, minimum arc rating 130.6 cal/cm² (beyond category 4 — de-energise) — informational, not a pass/fail check → 130.560 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E exceeds 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 130.560 vs limit 40.000 cal/cm² FAIL
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(1,000, 1,000) = 1,000 ms → 1,000 vs limit 2,000 ms PASS
Result	1/2 checks pass → FAIL; E = 130.56 cal/cm² at 609.6 mm, AFB 12,134 mm, arc-flash suit; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Hand calculation, IEEE 1584-2018 Eq 1 (VCB) Iarc,600/2700/14300 = 36.252/52.765/59.325 kA; Eq 16-18 at 15 kV Iarc = 59.721 kA; Eq 2 VarCf = 0.0217, Iarc,min = 59.073 kA; Eq 11-13 typical box W1 = 38.702 in, H1 = 23.622 in, EES = 31.162 in, Eq 14 CF = 1.2115; Eq 3-5 E600/2700/14300 = 318.457/486.148/534.361 J/cm² (full, 1000 ms), 305.465/477.127/542.328 J/cm² (reduced, 1000 ms); Eq 19-21 E = 537.270 / 546.263 J/cm²; Eq 7-9 + 22-24 AFB = 12006 / 12134 mm; reduced case governs: 546.263 J/cm² = 130.560 cal/cm², AFB 12134 mm, PPE tier arc_flash_suit. Cross-checked against IEEE 1584-2018 calculator V2.6.6 sample case 59 (Iarc 59.721 kA, E 537.270 J/cm², AFB 12006 mm; reduced 59.073 kA, 546.263 J/cm², 12134 mm). Independently cross-checked: the same inputs through github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases) agree with every expected value within its tolerance. (validation case `c0007-15kv-65ka-1s-vcb-extreme-hazard`)

Example 21 — 690 V switchboard, VCB, 30 kA: the 0.6–2.7 kV blend inside a box

690 V is common on Australian mine sites. Just above 600 V the model switches from Eq 25 to the Eq 16–24 blend between the 600 V and 2700 V results, and here the blend interacts with a typical-box correction factor (Eq 14 with the Table 6 voltage term in Eq 11).

Given: V_oc = 690 V, I_bf = 30 kA, VCB (vertical conductors in a box), T = 100 ms at I_arc and T_min = 150 ms at I_arc,min; gap G = 32 mm, working distance D = 609.6 mm, enclosure 762 H × 610 W × 508 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.042870) + 1.035·lg 30 − 0.083·lg 32} × P_I(30) = 10^1.3610 × 1.0292 = 23.634 kA; 2700 V: 10^{0.006500 + 1.001·lg 30 − 0.024·lg 32} × P_I(30) = 10^1.4490 × 0.9251 = 26.011 kA; 14 300 V: 10^{0.005795 + 1.015·lg 30 − 0.011·lg 32} × P_I(30) = 10^1.4885 × 0.9251 = 28.490 kA (VCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 0.69 kV: I_arc,1 = (26.011 − 23.634)/2.1 × (0.69 − 2.7) + 26.011 = 23.736; I_arc,2 = (28.490 − 26.011)/11.6 × (0.69 − 14.3) + 28.490 = 25.581; I_arc,3 = 23.736 × (2.7 − 0.69)/2.1 + 25.581 × (0.69 − 0.6)/2.1 = 23.815 kA (0.6 < V_oc ≤ 2.7 kV)
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 0.69⁵ = 0.0000; k₃V_oc⁴ = 8.3137×10⁻⁵ × 0.69⁴ = 0.0000; k₄V_oc³ = −0.0019382 × 0.69³ = (-0.0006); k₅V_oc² = 0.022366 × 0.69² = 0.0106; k₆V_oc = −0.12645 × 0.69 = (-0.0873); k₇ = 0.3023; sum = 0.2250; applied to each reference current, I_arc,min = 23.634/26.011/28.490 × (1 − 0.5 × 0.2250) = 20.975/23.084/25.284 kA, interpolated as above to 21.135 kA
Enclosure correction (Eq 11–15)	762 H × 610 W × 508 D mm → typical box, Table 7 (typical, VCB). W₁ = 610/25.4 (508–660.4 mm: actual size) = 24.016 in; H₁ = 762/25.4 (VCB height stays actual size) = 30.000 in; EES = (30.000 + 24.016)/2 = 27.008 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 27.008² + 0.03441 × 27.008 + 0.4325 = 1.1416 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 23.634 kA): exponent = k₁ 0.7534 + k₂·lg 32 0.8519 + k₃·23.634/P_E(30) 1.3415 + k₁₁·lg 30 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 23.634 1.3145 + lg(1/1.1416) (-0.0575) = -0.2467; E = 12.552/50 × 100 × 10^-0.2467 (k₁₂ = -1.598) = 14.223 J/cm²; 2700 V (Eq 4, I* = I_arc = 26.011 kA): exponent = k₁ 2.4002 + k₂·lg 32 0.2483 + k₃·26.011/P_E(30) 0.3320 + k₁₁·lg 30 0.0000 + k₁₂·lg 609.6 (-4.3697) + k₁₃·lg 26.011 1.3837 + lg(1/1.1416) (-0.0575) = -0.0630; E = 12.552/50 × 100 × 10^-0.0630 (k₁₂ = -1.569) = 21.716 J/cm²; 14 300 V (Eq 5, I* = I_arc = 28.490 kA): exponent = k₁ 3.8259 + k₂·lg 32 0.1656 + k₃·28.490/P_E(30) (-1.0263) + k₁₁·lg 30 0.0000 + k₁₂·lg 609.6 (-4.3670) + k₁₃·lg 28.490 1.4401 + lg(1/1.1416) (-0.0575) = -0.0191; E = 12.552/50 × 100 × 10^-0.0191 (k₁₂ = -1.568) = 24.021 J/cm²
Interpolated full-current energy (Eq 19–21)	At 0.69 kV: E₁ = (21.716 − 14.223)/2.1 × (0.69 − 2.7) + 21.716 = 14.545; E₂ = (24.021 − 21.716)/11.6 × (0.69 − 14.3) + 24.021 = 21.316; E₃ = 14.545 × (2.7 − 0.69)/2.1 + 21.316 × (0.69 − 0.6)/2.1 = 14.835 J/cm² (0.6 < V_oc ≤ 2.7 kV) = 3.546 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 20.975 kA, T_min = 150 ms): exponent = k₁ 0.7534 + k₂·lg 32 0.8519 + k₃·20.975/P_E(30) 1.1906 + k₁₁·lg 30 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 20.975 1.2649 + lg(1/1.1416) (-0.0575) = -0.4473; E = 12.552/50 × 150 × 10^-0.4473 (k₁₂ = -1.598) = 13.444 J/cm²; 2700 V (I_arc,min = 23.084 kA, T_min = 150 ms): exponent = k₁ 2.4002 + k₂·lg 32 0.2483 + k₃·23.084/P_E(30) 0.2946 + k₁₁·lg 30 0.0000 + k₁₂·lg 609.6 (-4.3697) + k₁₃·lg 23.084 1.3330 + lg(1/1.1416) (-0.0575) = -0.1510; E = 12.552/50 × 150 × 10^-0.1510 (k₁₂ = -1.569) = 26.597 J/cm²; 14 300 V (I_arc,min = 25.284 kA, T_min = 150 ms): exponent = k₁ 3.8259 + k₂·lg 32 0.1656 + k₃·25.284/P_E(30) (-0.9108) + k₁₁·lg 30 0.0000 + k₁₂·lg 609.6 (-4.3670) + k₁₃·lg 25.284 1.3888 + lg(1/1.1416) (-0.0575) = 0.0450; E = 12.552/50 × 150 × 10^0.0450 (k₁₂ = -1.568) = 41.768 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 0.69 kV: E₁ = (26.597 − 13.444)/2.1 × (0.69 − 2.7) + 26.597 = 14.008; E₂ = (41.768 − 26.597)/11.6 × (0.69 − 14.3) + 41.768 = 23.968; E₃ = 14.008 × (2.7 − 0.69)/2.1 + 23.968 × (0.69 − 0.6)/2.1 = 14.435 J/cm² (0.6 < V_oc ≤ 2.7 kV) = 3.450 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 609.6 × (5.0208/14.223)^1/(-1.598) = 1,170 mm; 2700 V 609.6 × (5.0208/21.716)^1/(-1.569) = 1,550 mm; 14 300 V 609.6 × (5.0208/24.021)^1/(-1.568) = 1,654 mm; reduced: 600 V 609.6 × (5.0208/13.444)^1/(-1.598) = 1,129 mm; 2700 V 609.6 × (5.0208/26.597)^1/(-1.569) = 1,764 mm; 14 300 V 609.6 × (5.0208/41.768)^1/(-1.568) = 2,354 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,550 − 1,170)/2.1 × (0.69 − 2.7) + 1,550 = 1,186; AFB₂ = (1,654 − 1,550)/11.6 × (0.69 − 14.3) + 1,654 = 1,532; AFB₃ = 1,186 × (2.7 − 0.69)/2.1 + 1,532 × (0.69 − 0.6)/2.1 = 1,201 mm (0.6 < V_oc ≤ 2.7 kV); reduced: AFB₁ = (1,764 − 1,129)/2.1 × (0.69 − 2.7) + 1,764 = 1,156; AFB₂ = (2,354 − 1,764)/11.6 × (0.69 − 14.3) + 2,354 = 1,662; AFB₃ = 1,156 × (2.7 − 0.69)/2.1 + 1,662 × (0.69 − 0.6)/2.1 = 1,178 mm (0.6 < V_oc ≤ 2.7 kV)
Governing case	max(full 3.546, reduced 3.450 cal/cm²) → the full arcing-current case: E = 3.546 cal/cm² (14.835 J/cm²), AFB = max(1,201, 1,178) = 1,201 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 3.546 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 3.6 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 3.546 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 3.546 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 150) = 150 ms → 150 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 3.55 cal/cm² at 609.6 mm, AFB 1,201 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases): Iarc,600/2700/14300 = 23.634/26.011/28.490 kA (full), 20.975/23.084/25.284 kA (reduced); E600/2700/14300 = 14.223/21.716/24.021 J/cm² (full, 100 ms), 13.444/26.597/41.768 J/cm² (reduced, 150 ms); Iarc = 23.815 kA, Iarc,min = 21.135 kA, VarCf = 0.2250, typical box CF = 1.1416 (EES 27.008 in); E = 14.835 / 14.435 J/cm², AFB = 1201 / 1178 mm (full / reduced); full case governs: 3.546 cal/cm², AFB 1201 mm. (validation case `c0007-690v-vcb-blend-band-enclosed`)

Example 22 — 1 kV mine distribution board, VCBB, 25 kA: blend band with a barrier

A 1 kV board (typical of mine trailing-cable distribution) with VCBB terminations: the blend band again, with the VCBB coefficients and its distinct Table 6 constants and a reduced-current clearing time longer than the full one.

Given: V_oc = 1,000 V, I_bf = 25 kA, VCBB (vertical conductors terminating in a barrier in a box), T = 200 ms at I_arc and T_min = 300 ms at I_arc,min; gap G = 32 mm, working distance D = 609.6 mm, enclosure 914.4 H × 762 W × 508 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.017432) + 0.98·lg 25 − 0.05·lg 32} × P_I(25) = 10^1.2773 × 1.1344 = 21.482 kA; 2700 V: 10^{0.002823 + 0.995·lg 25 − 0.0125·lg 32} × P_I(25) = 10^1.3750 × 0.9400 = 22.288 kA; 14 300 V: 10^{0.014827 + 1.01·lg 25 − 0.01·lg 32} × P_I(25) = 10^1.4117 × 0.9400 = 24.255 kA (VCBB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 1 kV: I_arc,1 = (22.288 − 21.482)/2.1 × (1 − 2.7) + 22.288 = 21.635; I_arc,2 = (24.255 − 22.288)/11.6 × (1 − 14.3) + 24.255 = 21.999; I_arc,3 = 21.635 × (2.7 − 1)/2.1 + 21.999 × (1 − 0.6)/2.1 = 21.705 kA (0.6 < V_oc ≤ 2.7 kV)
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCBB): k₁V_oc⁶ = 1.138×10⁻⁶ × 1⁶ = 0.0000; k₂V_oc⁵ = −6.0287×10⁻⁵ × 1⁵ = (-0.0001); k₃V_oc⁴ = 0.0012758 × 1⁴ = 0.0013; k₄V_oc³ = −0.013778 × 1³ = (-0.0138); k₅V_oc² = 0.080217 × 1² = 0.0802; k₆V_oc = −0.24066 × 1 = (-0.2407); k₇ = 0.3352; sum = 0.1622; applied to each reference current, I_arc,min = 21.482/22.288/24.255 × (1 − 0.5 × 0.1622) = 19.739/20.480/22.287 kA, interpolated as above to 19.944 kA
Enclosure correction (Eq 11–15)	914.4 H × 762 W × 508 D mm → typical box, Table 7 (typical, VCBB). W₁ = [660.4 + (762 − 660.4) × (1 + 10)/24]/25.4 (Eq 11) = 27.833 in; H₁ = [660.4 + (914.4 − 660.4) × (1 + 10)/24]/25.4 (Eq 12) = 30.583 in; EES = (30.583 + 27.833)/2 = 29.208 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0002976) × 29.208² + 0.03200 × 29.208 + 0.4790 = 1.1598 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 21.482 kA): exponent = k₁ 3.0685 + k₂·lg 32 0.3913 + k₃·21.482/P_E(25) (-0.0743) + k₁₁·lg 25 (-0.0839) + k₁₂·lg 609.6 (-5.0381) + k₁₃·lg 21.482 1.5852 + lg(1/1.1598) (-0.0644) = -0.2157; E = 12.552/50 × 200 × 10^-0.2157 (k₁₂ = -1.809) = 30.551 J/cm²; 2700 V (Eq 4, I* = I_arc = 22.288 kA): exponent = k₁ 3.8706 + k₂·lg 32 0.2785 + k₃·22.288/P_E(25) (-0.6987) + k₁₁·lg 25 0.0000 + k₁₂·lg 609.6 (-4.8515) + k₁₃·lg 22.288 1.4694 + lg(1/1.1598) (-0.0644) = 0.0039; E = 12.552/50 × 200 × 10^0.0039 (k₁₂ = -1.742) = 50.656 J/cm²; 14 300 V (Eq 5, I* = I_arc = 24.255 kA): exponent = k₁ 3.6443 + k₂·lg 32 0.3236 + k₃·24.255/P_E(25) (-0.6044) + k₁₁·lg 25 0.0000 + k₁₂·lg 609.6 (-4.6705) + k₁₃·lg 24.255 1.4679 + lg(1/1.1598) (-0.0644) = 0.0965; E = 12.552/50 × 200 × 10^0.0965 (k₁₂ = -1.677) = 62.708 J/cm²
Interpolated full-current energy (Eq 19–21)	At 1 kV: E₁ = (50.656 − 30.551)/2.1 × (1 − 2.7) + 50.656 = 34.381; E₂ = (62.708 − 50.656)/11.6 × (1 − 14.3) + 62.708 = 48.890; E₃ = 34.381 × (2.7 − 1)/2.1 + 48.890 × (1 − 0.6)/2.1 = 37.144 J/cm² (0.6 < V_oc ≤ 2.7 kV) = 8.878 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 19.739 kA, T_min = 300 ms): exponent = k₁ 3.0685 + k₂·lg 32 0.3913 + k₃·19.739/P_E(25) (-0.0683) + k₁₁·lg 25 (-0.0839) + k₁₂·lg 609.6 (-5.0381) + k₁₃·lg 19.739 1.5414 + lg(1/1.1598) (-0.0644) = -0.2534; E = 12.552/50 × 300 × 10^-0.2534 (k₁₂ = -1.809) = 42.017 J/cm²; 2700 V (I_arc,min = 20.480 kA, T_min = 300 ms): exponent = k₁ 3.8706 + k₂·lg 32 0.2785 + k₃·20.480/P_E(25) (-0.6420) + k₁₁·lg 25 0.0000 + k₁₂·lg 609.6 (-4.8515) + k₁₃·lg 20.480 1.4293 + lg(1/1.1598) (-0.0644) = 0.0205; E = 12.552/50 × 300 × 10^0.0205 (k₁₂ = -1.742) = 78.950 J/cm²; 14 300 V (I_arc,min = 22.287 kA, T_min = 300 ms): exponent = k₁ 3.6443 + k₂·lg 32 0.3236 + k₃·22.287/P_E(25) (-0.5553) + k₁₁·lg 25 0.0000 + k₁₂·lg 609.6 (-4.6705) + k₁₃·lg 22.287 1.4289 + lg(1/1.1598) (-0.0644) = 0.1066; E = 12.552/50 × 300 × 10^0.1066 (k₁₂ = -1.677) = 96.270 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 1 kV: E₁ = (78.950 − 42.017)/2.1 × (1 − 2.7) + 78.950 = 49.052; E₂ = (96.270 − 78.950)/11.6 × (1 − 14.3) + 96.270 = 76.411; E₃ = 49.052 × (2.7 − 1)/2.1 + 76.411 × (1 − 0.6)/2.1 = 54.263 J/cm² (0.6 < V_oc ≤ 2.7 kV) = 12.969 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 609.6 × (5.0208/30.551)^1/(-1.809) = 1,654 mm; 2700 V 609.6 × (5.0208/50.656)^1/(-1.742) = 2,298 mm; 14 300 V 609.6 × (5.0208/62.708)^1/(-1.677) = 2,747 mm; reduced: 600 V 609.6 × (5.0208/42.017)^1/(-1.809) = 1,973 mm; 2700 V 609.6 × (5.0208/78.950)^1/(-1.742) = 2,964 mm; 14 300 V 609.6 × (5.0208/96.270)^1/(-1.677) = 3,548 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (2,298 − 1,654)/2.1 × (1 − 2.7) + 2,298 = 1,777; AFB₂ = (2,747 − 2,298)/11.6 × (1 − 14.3) + 2,747 = 2,232; AFB₃ = 1,777 × (2.7 − 1)/2.1 + 2,232 × (1 − 0.6)/2.1 = 1,863 mm (0.6 < V_oc ≤ 2.7 kV); reduced: AFB₁ = (2,964 − 1,973)/2.1 × (1 − 2.7) + 2,964 = 2,162; AFB₂ = (3,548 − 2,964)/11.6 × (1 − 14.3) + 3,548 = 2,879; AFB₃ = 2,162 × (2.7 − 1)/2.1 + 2,879 × (1 − 0.6)/2.1 = 2,298 mm (0.6 < V_oc ≤ 2.7 kV)
Governing case	max(full 8.878, reduced 12.969 cal/cm²) → the reduced arcing-current case: E = 12.969 cal/cm² (54.263 J/cm²), AFB = max(1,863, 2,298) = 2,298 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 12.969 cal/cm² > 1.2 cal/cm² → arc-flash suit, minimum arc rating 13.0 cal/cm² (category-equivalent 3, informational) — informational, not a pass/fail check → 12.969 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 12.969 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(200, 300) = 300 ms → 300 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 12.97 cal/cm² at 609.6 mm, AFB 2,298 mm, arc-flash suit; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases): Iarc,600/2700/14300 = 21.482/22.288/24.255 kA (full), 19.739/20.480/22.287 kA (reduced); E600/2700/14300 = 30.551/50.656/62.708 J/cm² (full, 200 ms), 42.017/78.950/96.270 J/cm² (reduced, 300 ms); Iarc = 21.705 kA, Iarc,min = 19.944 kA, VarCf = 0.1622, typical box CF = 1.1598 (EES 29.208 in); E = 37.144 / 54.263 J/cm², AFB = 1863 / 2298 mm (full / reduced); reduced case governs: 12.969 cal/cm², AFB 2298 mm. (validation case `c0007-1kv-vcbb-mine-distribution-enclosed`)

Example 23 — 2700 V exactly, VCB, 20 kA: the top of the blend band

At exactly 2.7 kV Eq 18 weights E₁ by zero and E₂ by one, and both E₁ and E₂ equal the 2700 V intermediate, so the result must be the 2700 V reference value: a continuity check where the blend hands over to Eq 17.

Given: V_oc = 2,700 V, I_bf = 20 kA, VCB (vertical conductors in a box), T = 150 ms at I_arc and T_min = 150 ms at I_arc,min (same clearing time); gap G = 104 mm, working distance D = 914.4 mm, enclosure 914.4 H × 914.4 W × 914.4 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.042870) + 1.035·lg 20 − 0.083·lg 104} × P_I(20) = 10^1.1363 × 1.0782 = 14.756 kA; 2700 V: 10^{0.006500 + 1.001·lg 20 − 0.024·lg 104} × P_I(20) = 10^1.2604 × 0.9323 = 16.982 kA; 14 300 V: 10^{0.005795 + 1.015·lg 20 − 0.011·lg 104} × P_I(20) = 10^1.3042 × 0.9323 = 18.781 kA (VCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 2.7 kV: I_arc,1 = (16.982 − 14.756)/2.1 × (2.7 − 2.7) + 16.982 = 16.982; I_arc,2 = (18.781 − 16.982)/11.6 × (2.7 − 14.3) + 18.781 = 16.982; I_arc,3 = 16.982 × (2.7 − 2.7)/2.1 + 16.982 × (2.7 − 0.6)/2.1 = 16.982 kA (0.6 < V_oc ≤ 2.7 kV)
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 2.7⁵ = (-0.0002); k₃V_oc⁴ = 8.3137×10⁻⁵ × 2.7⁴ = 0.0044; k₄V_oc³ = −0.0019382 × 2.7³ = (-0.0381); k₅V_oc² = 0.022366 × 2.7² = 0.1630; k₆V_oc = −0.12645 × 2.7 = (-0.3414); k₇ = 0.3023; sum = 0.0900; applied to each reference current, I_arc,min = 14.756/16.982/18.781 × (1 − 0.5 × 0.0900) = 14.092/16.219/17.937 kA, interpolated as above to 16.219 kA
Enclosure correction (Eq 11–15)	914.4 H × 914.4 W × 914.4 D mm → typical box, Table 7 (typical, VCB). W₁ = [660.4 + (914.4 − 660.4) × (2.7 + 4)/20]/25.4 (Eq 11) = 29.350 in; H₁ = 914.4/25.4 (VCB height stays actual size) = 36.000 in; EES = (36.000 + 29.350)/2 = 32.675 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 32.675² + 0.03441 × 32.675 + 0.4325 = 1.2344 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 14.756 kA): exponent = k₁ 0.7534 + k₂·lg 104 1.1416 + k₃·14.756/P_E(20) 1.1993 + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 14.756 1.1187 + lg(1/1.2344) (-0.0915) = -0.6103; E = 12.552/50 × 150 × 10^-0.6103 (k₁₂ = -1.598) = 9.237 J/cm²; 2700 V (Eq 4, I* = I_arc = 16.982 kA): exponent = k₁ 2.4002 + k₂·lg 104 0.3328 + k₃·16.982/P_E(20) 0.3226 + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.6460) + k₁₃·lg 16.982 1.2027 + lg(1/1.2344) (-0.0915) = -0.4792; E = 12.552/50 × 150 × 10^-0.4792 (k₁₂ = -1.569) = 12.492 J/cm²; 14 300 V (Eq 5, I* = I_arc = 18.781 kA): exponent = k₁ 3.8259 + k₂·lg 104 0.2219 + k₃·18.781/P_E(20) (-1.0070) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.6431) + k₁₃·lg 18.781 1.2610 + lg(1/1.2344) (-0.0915) = -0.4327; E = 12.552/50 × 150 × 10^-0.4327 (k₁₂ = -1.568) = 13.904 J/cm²
Interpolated full-current energy (Eq 19–21)	At 2.7 kV: E₁ = (12.492 − 9.237)/2.1 × (2.7 − 2.7) + 12.492 = 12.492; E₂ = (13.904 − 12.492)/11.6 × (2.7 − 14.3) + 13.904 = 12.492; E₃ = 12.492 × (2.7 − 2.7)/2.1 + 12.492 × (2.7 − 0.6)/2.1 = 12.492 J/cm² (0.6 < V_oc ≤ 2.7 kV) = 2.986 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 14.092 kA, T_min = 150 ms): exponent = k₁ 0.7534 + k₂·lg 104 1.1416 + k₃·14.092/P_E(20) 1.1454 + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 14.092 1.0996 + lg(1/1.2344) (-0.0915) = -0.6834; E = 12.552/50 × 150 × 10^-0.6834 (k₁₂ = -1.598) = 7.806 J/cm²; 2700 V (I_arc,min = 16.219 kA, T_min = 150 ms): exponent = k₁ 2.4002 + k₂·lg 104 0.3328 + k₃·16.219/P_E(20) 0.3081 + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.6460) + k₁₃·lg 16.219 1.1831 + lg(1/1.2344) (-0.0915) = -0.5132; E = 12.552/50 × 150 × 10^-0.5132 (k₁₂ = -1.569) = 11.550 J/cm²; 14 300 V (I_arc,min = 17.937 kA, T_min = 150 ms): exponent = k₁ 3.8259 + k₂·lg 104 0.2219 + k₃·17.937/P_E(20) (-0.9617) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.6431) + k₁₃·lg 17.937 1.2412 + lg(1/1.2344) (-0.0915) = -0.4072; E = 12.552/50 × 150 × 10^-0.4072 (k₁₂ = -1.568) = 14.745 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 2.7 kV: E₁ = (11.550 − 7.806)/2.1 × (2.7 − 2.7) + 11.550 = 11.550; E₂ = (14.745 − 11.550)/11.6 × (2.7 − 14.3) + 14.745 = 11.550; E₃ = 11.550 × (2.7 − 2.7)/2.1 + 11.550 × (2.7 − 0.6)/2.1 = 11.550 J/cm² (0.6 < V_oc ≤ 2.7 kV) = 2.761 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 914.4 × (5.0208/9.237)^1/(-1.598) = 1,339 mm; 2700 V 914.4 × (5.0208/12.492)^1/(-1.569) = 1,635 mm; 14 300 V 914.4 × (5.0208/13.904)^1/(-1.568) = 1,751 mm; reduced: 600 V 914.4 × (5.0208/7.806)^1/(-1.598) = 1,205 mm; 2700 V 914.4 × (5.0208/11.550)^1/(-1.569) = 1,555 mm; 14 300 V 914.4 × (5.0208/14.745)^1/(-1.568) = 1,818 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,635 − 1,339)/2.1 × (2.7 − 2.7) + 1,635 = 1,635; AFB₂ = (1,751 − 1,635)/11.6 × (2.7 − 14.3) + 1,751 = 1,635; AFB₃ = 1,635 × (2.7 − 2.7)/2.1 + 1,635 × (2.7 − 0.6)/2.1 = 1,635 mm (0.6 < V_oc ≤ 2.7 kV); reduced: AFB₁ = (1,555 − 1,205)/2.1 × (2.7 − 2.7) + 1,555 = 1,555; AFB₂ = (1,818 − 1,555)/11.6 × (2.7 − 14.3) + 1,818 = 1,555; AFB₃ = 1,555 × (2.7 − 2.7)/2.1 + 1,555 × (2.7 − 0.6)/2.1 = 1,555 mm (0.6 < V_oc ≤ 2.7 kV)
Governing case	max(full 2.986, reduced 2.761 cal/cm²) → the full arcing-current case: E = 2.986 cal/cm² (12.492 J/cm²), AFB = max(1,635, 1,555) = 1,635 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 2.986 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 3.0 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 2.986 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 2.986 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(150, 150) = 150 ms → 150 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 2.99 cal/cm² at 914.4 mm, AFB 1,635 mm, arc-rated clothing; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases): Iarc,600/2700/14300 = 14.756/16.982/18.781 kA (full), 14.092/16.219/17.937 kA (reduced); E600/2700/14300 = 9.237/12.492/13.904 J/cm² (full, 150 ms), 7.806/11.550/14.745 J/cm² (reduced, 150 ms); Iarc = 16.982 kA, Iarc,min = 16.219 kA, VarCf = 0.0900, typical box CF = 1.2344 (EES 32.675 in); E = 12.492 / 11.550 J/cm², AFB = 1635 / 1555 mm (full / reduced); full case governs: 2.986 cal/cm², AFB 1635 mm. (validation case `c0007-2700v-vcb-exactly-at-reference-voltage`)

Example 24 — 3.3 kV MCC, 25 kA (5 kV MCC preset)

A 3.3 kV motor control centre — a standard Australian HV motor voltage — using the 5kv_mcc preset (104 mm gap, 914.4 mm working distance, 660.4 mm cube).

Given: V_oc = 3,300 V, I_bf = 25 kA, VCB (vertical conductors in a box), T = 120 ms at I_arc and T_min = 150 ms at I_arc,min; gap G = 104 mm, working distance D = 914.4 mm, enclosure 660.4 H × 660.4 W × 660.4 D mm (from the 5kV_MCC preset where not given; MCP 5kv_mcc).

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.042870) + 1.035·lg 25 − 0.083·lg 104} × P_I(25) = 10^1.2366 × 1.0562 = 18.211 kA; 2700 V: 10^{0.006500 + 1.001·lg 25 − 0.024·lg 104} × P_I(25) = 10^1.3574 × 0.9281 = 21.137 kA; 14 300 V: 10^{0.005795 + 1.015·lg 25 − 0.011·lg 104} × P_I(25) = 10^1.4025 × 0.9281 = 23.449 kA (VCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 3.3 kV: I_arc,1 = (21.137 − 18.211)/2.1 × (3.3 − 2.7) + 21.137 = 21.973; I_arc,2 = (23.449 − 21.137)/11.6 × (3.3 − 14.3) + 23.449 = 21.257 → V_oc > 2.7 kV so I_arc = I_arc,2 = 21.257 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 3.3⁵ = (-0.0006); k₃V_oc⁴ = 8.3137×10⁻⁵ × 3.3⁴ = 0.0099; k₄V_oc³ = −0.0019382 × 3.3³ = (-0.0697); k₅V_oc² = 0.022366 × 3.3² = 0.2436; k₆V_oc = −0.12645 × 3.3 = (-0.4173); k₇ = 0.3023; sum = 0.0682; applied to each reference current, I_arc,min = 18.211/21.137/23.449 × (1 − 0.5 × 0.0682) = 17.590/20.416/22.650 kA, interpolated as above to 20.532 kA
Enclosure correction (Eq 11–15)	660.4 H × 660.4 W × 660.4 D mm → typical box, Table 7 (typical, VCB). W₁ = 660.4/25.4 (508–660.4 mm: actual size) = 26.000 in; H₁ = 660.4/25.4 (508–660.4 mm: actual size) = 26.000 in; EES = (26.000 + 26.000)/2 = 26.000 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 26.000² + 0.03441 × 26.000 + 0.4325 = 1.1230 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 18.211 kA): exponent = k₁ 0.7534 + k₂·lg 104 1.1416 + k₃·18.211/P_E(25) 1.2087 + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 18.211 1.2061 + lg(1/1.1230) (-0.0504) = -0.4724; E = 12.552/50 × 120 × 10^-0.4724 (k₁₂ = -1.598) = 10.151 J/cm²; 2700 V (Eq 4, I* = I_arc = 21.137 kA): exponent = k₁ 2.4002 + k₂·lg 104 0.3328 + k₃·21.137/P_E(25) 0.3227 + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.6460) + k₁₃·lg 21.137 1.2956 + lg(1/1.1230) (-0.0504) = -0.3451; E = 12.552/50 × 120 × 10^-0.3451 (k₁₂ = -1.569) = 13.609 J/cm²; 14 300 V (Eq 5, I* = I_arc = 23.449 kA): exponent = k₁ 3.8259 + k₂·lg 104 0.2219 + k₃·23.449/P_E(25) (-1.0103) + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.6431) + k₁₃·lg 23.449 1.3564 + lg(1/1.1230) (-0.0504) = -0.2996; E = 12.552/50 × 120 × 10^-0.2996 (k₁₂ = -1.568) = 15.113 J/cm²
Interpolated full-current energy (Eq 19–21)	At 3.3 kV: E₁ = (13.609 − 10.151)/2.1 × (3.3 − 2.7) + 13.609 = 14.597; E₂ = (15.113 − 13.609)/11.6 × (3.3 − 14.3) + 15.113 = 13.687 → V_oc > 2.7 kV so E = E₂ = 13.687 J/cm² = 3.271 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 17.590 kA, T_min = 150 ms): exponent = k₁ 0.7534 + k₂·lg 104 1.1416 + k₃·17.590/P_E(25) 1.1675 + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 17.590 1.1917 + lg(1/1.1230) (-0.0504) = -0.5280; E = 12.552/50 × 150 × 10^-0.5280 (k₁₂ = -1.598) = 11.164 J/cm²; 2700 V (I_arc,min = 20.416 kA, T_min = 150 ms): exponent = k₁ 2.4002 + k₂·lg 104 0.3328 + k₃·20.416/P_E(25) 0.3117 + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.6460) + k₁₃·lg 20.416 1.2809 + lg(1/1.1230) (-0.0504) = -0.3708; E = 12.552/50 × 150 × 10^-0.3708 (k₁₂ = -1.569) = 16.033 J/cm²; 14 300 V (I_arc,min = 22.650 kA, T_min = 150 ms): exponent = k₁ 3.8259 + k₂·lg 104 0.2219 + k₃·22.650/P_E(25) (-0.9759) + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.6431) + k₁₃·lg 22.650 1.3415 + lg(1/1.1230) (-0.0504) = -0.2800; E = 12.552/50 × 150 × 10^-0.2800 (k₁₂ = -1.568) = 19.761 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 3.3 kV: E₁ = (16.033 − 11.164)/2.1 × (3.3 − 2.7) + 16.033 = 17.424; E₂ = (19.761 − 16.033)/11.6 × (3.3 − 14.3) + 19.761 = 16.225 → V_oc > 2.7 kV so E = E₂ = 16.225 J/cm² = 3.878 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 914.4 × (5.0208/10.151)^1/(-1.598) = 1,421 mm; 2700 V 914.4 × (5.0208/13.609)^1/(-1.569) = 1,726 mm; 14 300 V 914.4 × (5.0208/15.113)^1/(-1.568) = 1,847 mm; reduced: 600 V 914.4 × (5.0208/11.164)^1/(-1.598) = 1,508 mm; 2700 V 914.4 × (5.0208/16.033)^1/(-1.569) = 1,916 mm; 14 300 V 914.4 × (5.0208/19.761)^1/(-1.568) = 2,191 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,726 − 1,421)/2.1 × (3.3 − 2.7) + 1,726 = 1,814; AFB₂ = (1,847 − 1,726)/11.6 × (3.3 − 14.3) + 1,847 = 1,733 → V_oc > 2.7 kV so AFB = AFB₂ = 1,733 mm; reduced: AFB₁ = (1,916 − 1,508)/2.1 × (3.3 − 2.7) + 1,916 = 2,033; AFB₂ = (2,191 − 1,916)/11.6 × (3.3 − 14.3) + 2,191 = 1,931 → V_oc > 2.7 kV so AFB = AFB₂ = 1,931 mm
Governing case	max(full 3.271, reduced 3.878 cal/cm²) → the reduced arcing-current case: E = 3.878 cal/cm² (16.225 J/cm²), AFB = max(1,733, 1,931) = 1,931 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 3.878 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 3.9 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 3.878 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 3.878 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(120, 150) = 150 ms → 150 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 3.88 cal/cm² at 914.4 mm, AFB 1,931 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases): Iarc,600/2700/14300 = 18.211/21.137/23.449 kA (full), 17.590/20.416/22.650 kA (reduced); E600/2700/14300 = 10.152/13.609/15.113 J/cm² (full, 120 ms), 11.164/16.033/19.761 J/cm² (reduced, 150 ms); Iarc = 21.257 kA, Iarc,min = 20.532 kA, VarCf = 0.0682, typical box CF = 1.1230 (EES 26.000 in); E = 13.687 / 16.225 J/cm², AFB = 1733 / 1931 mm (full / reduced); reduced case governs: 3.878 cal/cm², AFB 1931 mm. (validation case `c0007-3.3kv-mcc-preset-25ka`)

Example 25 — 6.6 kV switchgear, VCBB, 20 kA, IDMT clearing

6.6 kV cable-terminated switchgear cleared by an IDMT relay: an everyday Australian industrial study point between the 2700 V and 14 300 V references.

Given: V_oc = 6,600 V, I_bf = 20 kA, VCBB (vertical conductors terminating in a barrier in a box), T = 250 ms at I_arc and T_min = 300 ms at I_arc,min; gap G = 104 mm, working distance D = 914.4 mm, enclosure 1,143 H × 762 W × 762 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.017432) + 0.98·lg 20 − 0.05·lg 104} × P_I(20) = 10^1.1567 × 1.1337 = 16.263 kA; 2700 V: 10^{0.002823 + 0.995·lg 20 − 0.0125·lg 104} × P_I(20) = 10^1.2721 × 0.9435 = 17.654 kA; 14 300 V: 10^{0.014827 + 1.01·lg 20 − 0.01·lg 104} × P_I(20) = 10^1.3087 × 0.9435 = 19.205 kA (VCBB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 6.6 kV: I_arc,1 = (17.654 − 16.263)/2.1 × (6.6 − 2.7) + 17.654 = 20.238; I_arc,2 = (19.205 − 17.654)/11.6 × (6.6 − 14.3) + 19.205 = 18.176 → V_oc > 2.7 kV so I_arc = I_arc,2 = 18.176 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCBB): k₁V_oc⁶ = 1.138×10⁻⁶ × 6.6⁶ = 0.0941; k₂V_oc⁵ = −6.0287×10⁻⁵ × 6.6⁵ = (-0.7550); k₃V_oc⁴ = 0.0012758 × 6.6⁴ = 2.4208; k₄V_oc³ = −0.013778 × 6.6³ = (-3.9611); k₅V_oc² = 0.080217 × 6.6² = 3.4943; k₆V_oc = −0.24066 × 6.6 = (-1.5884); k₇ = 0.3352; sum = 0.0399; applied to each reference current, I_arc,min = 16.263/17.654/19.205 × (1 − 0.5 × 0.0399) = 15.939/17.302/18.822 kA, interpolated as above to 17.813 kA
Enclosure correction (Eq 11–15)	1,143 H × 762 W × 762 D mm → typical box, Table 7 (typical, VCBB). W₁ = [660.4 + (762 − 660.4) × (6.6 + 10)/24]/25.4 (Eq 11) = 28.767 in; H₁ = [660.4 + (1,143 − 660.4) × (6.6 + 10)/24]/25.4 (Eq 12) = 39.142 in; EES = (39.142 + 28.767)/2 = 33.954 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0002976) × 33.954² + 0.03200 × 33.954 + 0.4790 = 1.2224 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 16.263 kA): exponent = k₁ 3.0685 + k₂·lg 104 0.5244 + k₃·16.263/P_E(20) (-0.0704) + k₁₁·lg 20 (-0.0781) + k₁₂·lg 914.4 (-5.3567) + k₁₃·lg 16.263 1.4413 + lg(1/1.2224) (-0.0872) = -0.5581; E = 12.552/50 × 250 × 10^-0.5581 (k₁₂ = -1.809) = 17.360 J/cm²; 2700 V (Eq 4, I* = I_arc = 17.654 kA): exponent = k₁ 3.8706 + k₂·lg 104 0.3732 + k₃·17.654/P_E(20) (-0.6892) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-5.1583) + k₁₃·lg 17.654 1.3591 + lg(1/1.2224) (-0.0872) = -0.3319; E = 12.552/50 × 250 × 10^-0.3319 (k₁₂ = -1.742) = 29.226 J/cm²; 14 300 V (Eq 5, I* = I_arc = 19.205 kA): exponent = k₁ 3.6443 + k₂·lg 104 0.4337 + k₃·19.205/P_E(20) (-0.5960) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.9658) + k₁₃·lg 19.205 1.3604 + lg(1/1.2224) (-0.0872) = -0.2106; E = 12.552/50 × 250 × 10^-0.2106 (k₁₂ = -1.677) = 38.643 J/cm²
Interpolated full-current energy (Eq 19–21)	At 6.6 kV: E₁ = (29.226 − 17.360)/2.1 × (6.6 − 2.7) + 29.226 = 51.262; E₂ = (38.643 − 29.226)/11.6 × (6.6 − 14.3) + 38.643 = 32.392 → V_oc > 2.7 kV so E = E₂ = 32.392 J/cm² = 7.742 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 15.939 kA, T_min = 300 ms): exponent = k₁ 3.0685 + k₂·lg 104 0.5244 + k₃·15.939/P_E(20) (-0.0690) + k₁₁·lg 20 (-0.0781) + k₁₂·lg 914.4 (-5.3567) + k₁₃·lg 15.939 1.4309 + lg(1/1.2224) (-0.0872) = -0.5671; E = 12.552/50 × 300 × 10^-0.5671 (k₁₂ = -1.809) = 20.405 J/cm²; 2700 V (I_arc,min = 17.302 kA, T_min = 300 ms): exponent = k₁ 3.8706 + k₂·lg 104 0.3732 + k₃·17.302/P_E(20) (-0.6755) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-5.1583) + k₁₃·lg 17.302 1.3495 + lg(1/1.2224) (-0.0872) = -0.3277; E = 12.552/50 × 300 × 10^-0.3277 (k₁₂ = -1.742) = 35.413 J/cm²; 14 300 V (I_arc,min = 18.822 kA, T_min = 300 ms): exponent = k₁ 3.6443 + k₂·lg 104 0.4337 + k₃·18.822/P_E(20) (-0.5841) + k₁₁·lg 20 0.0000 + k₁₂·lg 914.4 (-4.9658) + k₁₃·lg 18.822 1.3511 + lg(1/1.2224) (-0.0872) = -0.2080; E = 12.552/50 × 300 × 10^-0.2080 (k₁₂ = -1.677) = 46.652 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 6.6 kV: E₁ = (35.413 − 20.405)/2.1 × (6.6 − 2.7) + 35.413 = 63.284; E₂ = (46.652 − 35.413)/11.6 × (6.6 − 14.3) + 46.652 = 39.191 → V_oc > 2.7 kV so E = E₂ = 39.191 J/cm² = 9.367 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 914.4 × (5.0208/17.360)^1/(-1.809) = 1,815 mm; 2700 V 914.4 × (5.0208/29.226)^1/(-1.742) = 2,514 mm; 14 300 V 914.4 × (5.0208/38.643)^1/(-1.677) = 3,088 mm; reduced: 600 V 914.4 × (5.0208/20.405)^1/(-1.809) = 1,985 mm; 2700 V 914.4 × (5.0208/35.413)^1/(-1.742) = 2,806 mm; 14 300 V 914.4 × (5.0208/46.652)^1/(-1.677) = 3,455 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (2,514 − 1,815)/2.1 × (6.6 − 2.7) + 2,514 = 3,810; AFB₂ = (3,088 − 2,514)/11.6 × (6.6 − 14.3) + 3,088 = 2,707 → V_oc > 2.7 kV so AFB = AFB₂ = 2,707 mm; reduced: AFB₁ = (2,806 − 1,985)/2.1 × (6.6 − 2.7) + 2,806 = 4,332; AFB₂ = (3,455 − 2,806)/11.6 × (6.6 − 14.3) + 3,455 = 3,024 → V_oc > 2.7 kV so AFB = AFB₂ = 3,024 mm
Governing case	max(full 7.742, reduced 9.367 cal/cm²) → the reduced arcing-current case: E = 9.367 cal/cm² (39.191 J/cm²), AFB = max(2,707, 3,024) = 3,024 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 9.367 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 9.4 cal/cm² (category-equivalent 3, informational) — informational, not a pass/fail check → 9.367 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 9.367 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(250, 300) = 300 ms → 300 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 9.37 cal/cm² at 914.4 mm, AFB 3,024 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases): Iarc,600/2700/14300 = 16.263/17.654/19.205 kA (full), 15.939/17.302/18.822 kA (reduced); E600/2700/14300 = 17.360/29.226/38.643 J/cm² (full, 250 ms), 20.405/35.413/46.652 J/cm² (reduced, 300 ms); Iarc = 18.176 kA, Iarc,min = 17.813 kA, VarCf = 0.0399, typical box CF = 1.2224 (EES 33.954 in); E = 32.392 / 39.191 J/cm², AFB = 2707 / 3024 mm (full / reduced); reduced case governs: 9.367 cal/cm², AFB 3024 mm. (validation case `c0007-6.6kv-switchgear-vcbb-20ka-idmt`)

Example 26 — 11 kV switchgear, 25 kA (15 kV switchgear preset)

11 kV switchgear at a normal 25 kA fault level with relay-plus-breaker clearing — the commonest Australian distribution voltage at a realistic fault level, unlike the 1 kA weak-source case.

Given: V_oc = 11,000 V, I_bf = 25 kA, VCB (vertical conductors in a box), T = 100 ms at I_arc and T_min = 120 ms at I_arc,min; gap G = 152 mm, working distance D = 914.4 mm, enclosure 1,143 H × 762 W × 762 D mm (from the 15kV_Switchgear preset where not given; MCP 15kv_switchgear).

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.042870) + 1.035·lg 25 − 0.083·lg 152} × P_I(25) = 10^1.2229 × 1.0562 = 17.646 kA; 2700 V: 10^{0.006500 + 1.001·lg 25 − 0.024·lg 152} × P_I(25) = 10^1.3535 × 0.9281 = 20.945 kA; 14 300 V: 10^{0.005795 + 1.015·lg 25 − 0.011·lg 152} × P_I(25) = 10^1.4007 × 0.9281 = 23.352 kA (VCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 11 kV: I_arc,1 = (20.945 − 17.646)/2.1 × (11 − 2.7) + 20.945 = 33.986; I_arc,2 = (23.352 − 20.945)/11.6 × (11 − 14.3) + 23.352 = 22.667 → V_oc > 2.7 kV so I_arc = I_arc,2 = 22.667 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 11⁵ = (-0.2298); k₃V_oc⁴ = 8.3137×10⁻⁵ × 11⁴ = 1.2172; k₄V_oc³ = −0.0019382 × 11³ = (-2.5797); k₅V_oc² = 0.022366 × 11² = 2.7063; k₆V_oc = −0.12645 × 11 = (-1.3910); k₇ = 0.3023; sum = 0.0253; applied to each reference current, I_arc,min = 17.646/20.945/23.352 × (1 − 0.5 × 0.0253) = 17.423/20.681/23.057 kA, interpolated as above to 22.381 kA
Enclosure correction (Eq 11–15)	1,143 H × 762 W × 762 D mm → typical box, Table 7 (typical, VCB). W₁ = [660.4 + (762 − 660.4) × (11 + 4)/20]/25.4 (Eq 11) = 29.000 in; H₁ = 1,143/25.4 (VCB height stays actual size) = 45.000 in; EES = (45.000 + 29.000)/2 = 37.000 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 37.000² + 0.03441 × 37.000 + 0.4325 = 1.2922 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 17.646 kA): exponent = k₁ 0.7534 + k₂·lg 152 1.2349 + k₃·17.646/P_E(25) 1.1713 + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 17.646 1.1930 + lg(1/1.2922) (-0.1113) = -0.4906; E = 12.552/50 × 100 × 10^-0.4906 (k₁₂ = -1.598) = 8.112 J/cm²; 2700 V (Eq 4, I* = I_arc = 20.945 kA): exponent = k₁ 2.4002 + k₂·lg 152 0.3600 + k₃·20.945/P_E(25) 0.3197 + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.6460) + k₁₃·lg 20.945 1.2918 + lg(1/1.2922) (-0.1113) = -0.3857; E = 12.552/50 × 100 × 10^-0.3857 (k₁₂ = -1.569) = 10.330 J/cm²; 14 300 V (Eq 5, I* = I_arc = 23.352 kA): exponent = k₁ 3.8259 + k₂·lg 152 0.2400 + k₃·23.352/P_E(25) (-1.0061) + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.6431) + k₁₃·lg 23.352 1.3546 + lg(1/1.2922) (-0.1113) = -0.3400; E = 12.552/50 × 100 × 10^-0.3400 (k₁₂ = -1.568) = 11.475 J/cm²
Interpolated full-current energy (Eq 19–21)	At 11 kV: E₁ = (10.330 − 8.112)/2.1 × (11 − 2.7) + 10.330 = 19.097; E₂ = (11.475 − 10.330)/11.6 × (11 − 14.3) + 11.475 = 11.149 → V_oc > 2.7 kV so E = E₂ = 11.149 J/cm² = 2.665 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 17.423 kA, T_min = 120 ms): exponent = k₁ 0.7534 + k₂·lg 152 1.2349 + k₃·17.423/P_E(25) 1.1565 + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 17.423 1.1878 + lg(1/1.2922) (-0.1113) = -0.5107; E = 12.552/50 × 120 × 10^-0.5107 (k₁₂ = -1.598) = 9.294 J/cm²; 2700 V (I_arc,min = 20.681 kA, T_min = 120 ms): exponent = k₁ 2.4002 + k₂·lg 152 0.3600 + k₃·20.681/P_E(25) 0.3157 + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.6460) + k₁₃·lg 20.681 1.2864 + lg(1/1.2922) (-0.1113) = -0.3951; E = 12.552/50 × 120 × 10^-0.3951 (k₁₂ = -1.569) = 12.129 J/cm²; 14 300 V (I_arc,min = 23.057 kA, T_min = 120 ms): exponent = k₁ 3.8259 + k₂·lg 152 0.2400 + k₃·23.057/P_E(25) (-0.9934) + k₁₁·lg 25 0.0000 + k₁₂·lg 914.4 (-4.6431) + k₁₃·lg 23.057 1.3492 + lg(1/1.2922) (-0.1113) = -0.3327; E = 12.552/50 × 120 × 10^-0.3327 (k₁₂ = -1.568) = 14.002 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 11 kV: E₁ = (12.129 − 9.294)/2.1 × (11 − 2.7) + 12.129 = 23.334; E₂ = (14.002 − 12.129)/11.6 × (11 − 14.3) + 14.002 = 13.469 → V_oc > 2.7 kV so E = E₂ = 13.469 J/cm² = 3.219 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 914.4 × (5.0208/8.112)^1/(-1.598) = 1,235 mm; 2700 V 914.4 × (5.0208/10.330)^1/(-1.569) = 1,448 mm; 14 300 V 914.4 × (5.0208/11.475)^1/(-1.568) = 1,549 mm; reduced: 600 V 914.4 × (5.0208/9.294)^1/(-1.598) = 1,344 mm; 2700 V 914.4 × (5.0208/12.129)^1/(-1.569) = 1,604 mm; 14 300 V 914.4 × (5.0208/14.002)^1/(-1.568) = 1,759 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,448 − 1,235)/2.1 × (11 − 2.7) + 1,448 = 2,293; AFB₂ = (1,549 − 1,448)/11.6 × (11 − 14.3) + 1,549 = 1,520 → V_oc > 2.7 kV so AFB = AFB₂ = 1,520 mm; reduced: AFB₁ = (1,604 − 1,344)/2.1 × (11 − 2.7) + 1,604 = 2,632; AFB₂ = (1,759 − 1,604)/11.6 × (11 − 14.3) + 1,759 = 1,715 → V_oc > 2.7 kV so AFB = AFB₂ = 1,715 mm
Governing case	max(full 2.665, reduced 3.219 cal/cm²) → the reduced arcing-current case: E = 3.219 cal/cm² (13.469 J/cm²), AFB = max(1,520, 1,715) = 1,715 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 3.219 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 3.3 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 3.219 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 3.219 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 120) = 120 ms → 120 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 3.22 cal/cm² at 914.4 mm, AFB 1,715 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases): Iarc,600/2700/14300 = 17.646/20.945/23.352 kA (full), 17.423/20.681/23.057 kA (reduced); E600/2700/14300 = 8.112/10.330/11.475 J/cm² (full, 100 ms), 9.294/12.129/14.002 J/cm² (reduced, 120 ms); Iarc = 22.667 kA, Iarc,min = 22.381 kA, VarCf = 0.0253, typical box CF = 1.2922 (EES 37.000 in); E = 11.149 / 13.469 J/cm², AFB = 1520 / 1715 mm (full / reduced); reduced case governs: 3.219 cal/cm², AFB 1715 mm. (validation case `c0007-11kv-switchgear-preset-25ka`)

Example 27 — 415 V panel, MCCB: 25 ms at Iarc but 3 s at Iarc,min

The full arcing current trips the MCCB instantaneously but the reduced current falls below the instantaneous pickup and clears on the thermal curve in 3 s. T ≤ 2 s and T_min > 2 s, so the 2 s check must use max(T, T_min) — and the reduced case dominates.

Given: V_oc = 415 V, I_bf = 10 kA, VCB (vertical conductors in a box), T = 25 ms at I_arc and T_min = 3,000 ms at I_arc,min; gap G = 25 mm, working distance D = 457.2 mm, enclosure 355.6 H × 304.8 W × 254 D mm (from the LV_MCC_Panel_Deep preset where not given; MCP lv_mcc_panel_deep).

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VCB 600 V coefficients of Table 1 = 10^{(-0.042870) + 1.035·lg 10 − 0.083·lg 25} × P_I(10) = 10^0.8761 × 1.1024 = 8.288 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.415)² × (1/8.288² − (0.6² − 0.415²)/(0.6² × 10²))] = 1/√[2.0903 × (0.014558 − 0.005216)] = 7.156 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 0.415⁵ = 0.0000; k₃V_oc⁴ = 8.3137×10⁻⁵ × 0.415⁴ = 0.0000; k₄V_oc³ = −0.0019382 × 0.415³ = (-0.0001); k₅V_oc² = 0.022366 × 0.415² = 0.0039; k₆V_oc = −0.12645 × 0.415 = (-0.0525); k₇ = 0.3023; sum = 0.2535; I_arc,min = I_arc(1 − 0.5 VarC_f) = 7.156 × (1 − 0.5 × 0.2535) = 6.249 kA
Enclosure correction (Eq 11–15)	355.6 H × 304.8 W × 254 D mm → typical box, Table 7 (typical, VCB). W₁ = 304.8 mm (below 508 mm → 20 in) = 20.000 in; H₁ = 355.6 mm (below 508 mm → 20 in) = 20.000 in; EES = (20.000 + 20.000)/2 = 20.000 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 20.000² + 0.03441 × 20.000 + 0.4325 = 0.9999 (Eq 14)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 8.288 kA in the k₃ term, I_arc = 7.156 kA in the k₁₃ term, T = 25 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 0.7534 + k₂·lg 25 0.7912 + k₃·8.288/P_E(10) 1.3176 + k₁₁·lg 10 0.0000 + k₁₂·lg 457.2 (-4.2508) + k₁₃·lg 7.156 0.8179 + lg(1/0.9999) 0.0000 = -0.5707; E = 12.552/50 × 25 × 10^-0.5707 (k₁₂ = -1.598) = 1.687 J/cm² = 0.403 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 6.249 kA in the k₁₃ term, T_min = 3,000 ms; the k₃ term keeps the full I_arc,600 = 8.288 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 0.7534 + k₂·lg 25 0.7912 + k₃·8.288/P_E(10) 1.3176 + k₁₁·lg 10 0.0000 + k₁₂·lg 457.2 (-4.2508) + k₁₃·lg 6.249 0.7616 + lg(1/0.9999) 0.0000 = -0.6270; E = 12.552/50 × 3,000 × 10^-0.6270 (k₁₂ = -1.598) = 177.779 J/cm² = 42.490 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 457.2 × (5.0208/1.687)^1/(-1.598) = 231 mm; reduced 457.2 × (5.0208/177.779)^1/(-1.598) = 4,261 mm
Governing case	max(full 0.403, reduced 42.490 cal/cm²) → the reduced arcing-current case: E = 42.490 cal/cm² (177.779 J/cm²), AFB = max(231, 4,261) = 4,261 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 42.490 cal/cm² > 1.2 cal/cm² → arc-flash suit, minimum arc rating 42.5 cal/cm² (beyond category 4 — de-energise). Caveat: the clearing time exceeds 2 s, so the exposure assumption behind this energy is invalid — fix the clearing time before relying on the PPE result — informational, not a pass/fail check → 42.490 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E exceeds 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 42.490 vs limit 40.000 cal/cm² FAIL
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(25, 3,000) = 3,000 ms; sensitivity with both times capped at 2 s: incident energy 42.49 → 28.33 cal/cm² (the uncapped figure is reported) — most other tools report the capped figure → 3,000 vs limit 2,000 ms FAIL
Result	0/2 checks pass → FAIL; E = 42.49 cal/cm² at 457.2 mm, AFB 4,261 mm, arc-flash suit; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first). Arc duration exceeds 2 s. IEEE 1584-2018 suggests 2 s as a reasonable maximum exposure where a worker can move away; the energy here uses the full time entered.
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases): Iarc,600 = 8.288 kA; Iarc = 7.156 kA, Iarc,min = 6.249 kA, VarCf = 0.2535, typical box CF = 0.9999 (EES 20.000 in); E = 1.687 / 177.779 J/cm², AFB = 231 / 4261 mm (full / reduced); reduced case governs: 42.490 cal/cm², AFB 4261 mm. (validation case `c0007-415v-mccb-reduced-current-beyond-2s`)

Example 28 — 6.6 kV cable termination box narrower than 4 × the gap

A 500 mm wide box with a 152 mm gap is narrower than 4G = 608 mm, outside the boxes the enclosure correction was derived from: the result is calculated and carries the width warning.

Given: V_oc = 6,600 V, I_bf = 10 kA, VCB (vertical conductors in a box), T = 100 ms at I_arc and T_min = 100 ms at I_arc,min (same clearing time); gap G = 152 mm, working distance D = 914.4 mm, enclosure 600 H × 500 W × 400 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.042870) + 1.035·lg 10 − 0.083·lg 152} × P_I(10) = 10^0.8110 × 1.1024 = 7.135 kA; 2700 V: 10^{0.006500 + 1.001·lg 10 − 0.024·lg 152} × P_I(10) = 10^0.9551 × 0.9469 = 8.540 kA; 14 300 V: 10^{0.005795 + 1.015·lg 10 − 0.011·lg 152} × P_I(10) = 10^0.9968 × 0.9469 = 9.400 kA (VCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 6.6 kV: I_arc,1 = (8.540 − 7.135)/2.1 × (6.6 − 2.7) + 8.540 = 11.149; I_arc,2 = (9.400 − 8.540)/11.6 × (6.6 − 14.3) + 9.400 = 8.829 → V_oc > 2.7 kV so I_arc = I_arc,2 = 8.829 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 6.6⁵ = (-0.0179); k₃V_oc⁴ = 8.3137×10⁻⁵ × 6.6⁴ = 0.1578; k₄V_oc³ = −0.0019382 × 6.6³ = (-0.5572); k₅V_oc² = 0.022366 × 6.6² = 0.9743; k₆V_oc = −0.12645 × 6.6 = (-0.8346); k₇ = 0.3023; sum = 0.0246; applied to each reference current, I_arc,min = 7.135/8.540/9.400 × (1 − 0.5 × 0.0246) = 7.047/8.435/9.284 kA, interpolated as above to 8.720 kA
Enclosure correction (Eq 11–15)	600 H × 500 W × 400 D mm → typical box, Table 7 (typical, VCB). W₁ = 500 mm (below 508 mm → 20 in) = 20.000 in; H₁ = 600/25.4 (508–660.4 mm: actual size) = 23.622 in; EES = (23.622 + 20.000)/2 = 21.811 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 21.811² + 0.03441 × 21.811 + 0.4325 = 1.0393 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 7.135 kA): exponent = k₁ 0.7534 + k₂·lg 152 1.2349 + k₃·7.135/P_E(10) 1.1343 + k₁₁·lg 10 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 7.135 0.8167 + lg(1/1.0393) (-0.0168) = -0.8094; E = 12.552/50 × 100 × 10^-0.8094 (k₁₂ = -1.598) = 3.894 J/cm²; 2700 V (Eq 4, I* = I_arc = 8.540 kA): exponent = k₁ 2.4002 + k₂·lg 152 0.3600 + k₃·8.540/P_E(10) 0.3194 + k₁₁·lg 10 0.0000 + k₁₂·lg 914.4 (-4.6460) + k₁₃·lg 8.540 0.9108 + lg(1/1.0393) (-0.0168) = -0.6724; E = 12.552/50 × 100 × 10^-0.6724 (k₁₂ = -1.569) = 5.338 J/cm²; 14 300 V (Eq 5, I* = I_arc = 9.400 kA): exponent = k₁ 3.8259 + k₂·lg 152 0.2400 + k₃·9.400/P_E(10) (-0.9924) + k₁₁·lg 10 0.0000 + k₁₂·lg 914.4 (-4.6431) + k₁₃·lg 9.400 0.9634 + lg(1/1.0393) (-0.0168) = -0.6229; E = 12.552/50 × 100 × 10^-0.6229 (k₁₂ = -1.568) = 5.982 J/cm²
Interpolated full-current energy (Eq 19–21)	At 6.6 kV: E₁ = (5.338 − 3.894)/2.1 × (6.6 − 2.7) + 5.338 = 8.021; E₂ = (5.982 − 5.338)/11.6 × (6.6 − 14.3) + 5.982 = 5.554 → V_oc > 2.7 kV so E = E₂ = 5.554 J/cm² = 1.328 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 7.047 kA, T_min = 100 ms): exponent = k₁ 0.7534 + k₂·lg 152 1.2349 + k₃·7.047/P_E(10) 1.1203 + k₁₁·lg 10 0.0000 + k₁₂·lg 914.4 (-4.7319) + k₁₃·lg 7.047 0.8115 + lg(1/1.0393) (-0.0168) = -0.8285; E = 12.552/50 × 100 × 10^-0.8285 (k₁₂ = -1.598) = 3.726 J/cm²; 2700 V (I_arc,min = 8.435 kA, T_min = 100 ms): exponent = k₁ 2.4002 + k₂·lg 152 0.3600 + k₃·8.435/P_E(10) 0.3155 + k₁₁·lg 10 0.0000 + k₁₂·lg 914.4 (-4.6460) + k₁₃·lg 8.435 0.9055 + lg(1/1.0393) (-0.0168) = -0.6815; E = 12.552/50 × 100 × 10^-0.6815 (k₁₂ = -1.569) = 5.226 J/cm²; 14 300 V (I_arc,min = 9.284 kA, T_min = 100 ms): exponent = k₁ 3.8259 + k₂·lg 152 0.2400 + k₃·9.284/P_E(10) (-0.9802) + k₁₁·lg 10 0.0000 + k₁₂·lg 914.4 (-4.6431) + k₁₃·lg 9.284 0.9581 + lg(1/1.0393) (-0.0168) = -0.6160; E = 12.552/50 × 100 × 10^-0.6160 (k₁₂ = -1.568) = 6.077 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 6.6 kV: E₁ = (5.226 − 3.726)/2.1 × (6.6 − 2.7) + 5.226 = 8.012; E₂ = (6.077 − 5.226)/11.6 × (6.6 − 14.3) + 6.077 = 5.512 → V_oc > 2.7 kV so E = E₂ = 5.512 J/cm² = 1.318 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 914.4 × (5.0208/3.894)^1/(-1.598) = 780 mm; 2700 V 914.4 × (5.0208/5.338)^1/(-1.569) = 951 mm; 14 300 V 914.4 × (5.0208/5.982)^1/(-1.568) = 1,022 mm; reduced: 600 V 914.4 × (5.0208/3.726)^1/(-1.598) = 759 mm; 2700 V 914.4 × (5.0208/5.226)^1/(-1.569) = 938 mm; 14 300 V 914.4 × (5.0208/6.077)^1/(-1.568) = 1,033 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (951 − 780)/2.1 × (6.6 − 2.7) + 951 = 1,268; AFB₂ = (1,022 − 951)/11.6 × (6.6 − 14.3) + 1,022 = 975 → V_oc > 2.7 kV so AFB = AFB₂ = 975 mm; reduced: AFB₁ = (938 − 759)/2.1 × (6.6 − 2.7) + 938 = 1,271; AFB₂ = (1,033 − 938)/11.6 × (6.6 − 14.3) + 1,033 = 970 → V_oc > 2.7 kV so AFB = AFB₂ = 970 mm
Governing case	max(full 1.328, reduced 1.318 cal/cm²) → the full arcing-current case: E = 1.328 cal/cm² (5.554 J/cm²), AFB = max(975, 970) = 975 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 1.328 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 1.4 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 1.328 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 1.328 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 100) = 100 ms → 100 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 1.33 cal/cm² at 914.4 mm, AFB 975 mm, arc-rated clothing; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first). Enclosure width is less than four times the conductor gap; the enclosure correction factor was not derived for such narrow boxes.
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases; its width ≥ 4G input guard bypassed, the equations are unchanged): Iarc,600/2700/14300 = 7.135/8.540/9.400 kA (full), 7.047/8.435/9.284 kA (reduced); E600/2700/14300 = 3.894/5.338/5.982 J/cm² (full, 100 ms), 3.726/5.226/6.077 J/cm² (reduced, 100 ms); Iarc = 8.829 kA, Iarc,min = 8.720 kA, VarCf = 0.0246, typical box CF = 1.0393 (EES 21.811 in); E = 5.554 / 5.512 J/cm², AFB = 975 / 970 mm (full / reduced); full case governs: 1.328 cal/cm², AFB 975 mm. (validation case `c0007-6.6kv-narrow-termination-box-width-under-4g`)

Example 29 — 600 V, VCB, 20 kA: the low-voltage side of the reduced-case step

At exactly 600 V the low-voltage form applies and the k3 term of the reduced-current energy keeps the full Iarc,600. Paired with the 601 V example to pin the 600 → 601 V step in the reduced-current energy (8.90 → 6.24 J/cm²) the standard and the official calculator both produce.

Given: V_oc = 600 V, I_bf = 20 kA, VCB (vertical conductors in a box), T = 100 ms at I_arc and T_min = 100 ms at I_arc,min (same clearing time); gap G = 32 mm, working distance D = 609.6 mm, enclosure 610 H × 610 W × 610 D mm.

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VCB 600 V coefficients of Table 1 = 10^{(-0.042870) + 1.035·lg 20 − 0.083·lg 32} × P_I(20) = 10^1.1788 × 1.0782 = 16.272 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.6)² × (1/16.272² − (0.6² − 0.6²)/(0.6² × 20²))] = 1/√[1.0000 × (0.003777 − 0.000000)] = 16.272 kA (at 600 V exactly, Eq 25 returns I_arc,600)
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 0.6⁵ = 0.0000; k₃V_oc⁴ = 8.3137×10⁻⁵ × 0.6⁴ = 0.0000; k₄V_oc³ = −0.0019382 × 0.6³ = (-0.0004); k₅V_oc² = 0.022366 × 0.6² = 0.0081; k₆V_oc = −0.12645 × 0.6 = (-0.0759); k₇ = 0.3023; sum = 0.2340; I_arc,min = I_arc(1 − 0.5 VarC_f) = 16.272 × (1 − 0.5 × 0.2340) = 14.368 kA
Enclosure correction (Eq 11–15)	610 H × 610 W × 610 D mm → typical box, Table 7 (typical, VCB). W₁ = 610/25.4 (508–660.4 mm: actual size) = 24.016 in; H₁ = 610/25.4 (508–660.4 mm: actual size) = 24.016 in; EES = (24.016 + 24.016)/2 = 24.016 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 24.016² + 0.03441 × 24.016 + 0.4325 = 1.0847 (Eq 14)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 16.272 kA in the k₃ term, I_arc = 16.272 kA in the k₁₃ term, T = 100 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 0.7534 + k₂·lg 32 0.8519 + k₃·16.272/P_E(20) 1.3226 + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 16.272 1.1594 + lg(1/1.0847) (-0.0353) = -0.3986; E = 12.552/50 × 100 × 10^-0.3986 (k₁₂ = -1.598) = 10.027 J/cm² = 2.397 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 14.368 kA in the k₁₃ term, T_min = 100 ms; the k₃ term keeps the full I_arc,600 = 16.272 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 0.7534 + k₂·lg 32 0.8519 + k₃·16.272/P_E(20) 1.3226 + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 14.368 1.1076 + lg(1/1.0847) (-0.0353) = -0.4503; E = 12.552/50 × 100 × 10^-0.4503 (k₁₂ = -1.598) = 8.901 J/cm² = 2.127 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 609.6 × (5.0208/10.027)^1/(-1.598) = 940 mm; reduced 609.6 × (5.0208/8.901)^1/(-1.598) = 872 mm
Governing case	max(full 2.397, reduced 2.127 cal/cm²) → the full arcing-current case: E = 2.397 cal/cm² (10.027 J/cm²), AFB = max(940, 872) = 940 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 2.397 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 2.4 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 2.397 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 2.397 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 100) = 100 ms → 100 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 2.40 cal/cm² at 609.6 mm, AFB 940 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases): Iarc,600 = 16.272 kA; Iarc = 16.272 kA, Iarc,min = 14.368 kA, VarCf = 0.2340, typical box CF = 1.0847 (EES 24.016 in); E = 10.027 / 8.901 J/cm², AFB = 940 / 872 mm (full / reduced); full case governs: 2.397 cal/cm², AFB 940 mm. (validation case `c0007-600v-vcb-reduced-case-lv-side-of-step`)

Example 30 — 601 V, VCB, 20 kA: the interpolated side of the reduced-case step

One volt higher the Eq 16–24 interpolation applies and each reduced reference current replaces Iarc,600 in the k3 term too, so the reduced-current energy drops to 6.24 J/cm² while the full-current energy carries on almost unchanged.

Given: V_oc = 601 V, I_bf = 20 kA, VCB (vertical conductors in a box), T = 100 ms at I_arc and T_min = 100 ms at I_arc,min (same clearing time); gap G = 32 mm, working distance D = 609.6 mm, enclosure 610 H × 610 W × 610 D mm.

Arcing current at the reference voltages (Eq 1)	600 V: 10^{(-0.042870) + 1.035·lg 20 − 0.083·lg 32} × P_I(20) = 10^1.1788 × 1.0782 = 16.272 kA; 2700 V: 10^{0.006500 + 1.001·lg 20 − 0.024·lg 32} × P_I(20) = 10^1.2727 × 0.9323 = 17.470 kA; 14 300 V: 10^{0.005795 + 1.015·lg 20 − 0.011·lg 32} × P_I(20) = 10^1.3098 × 0.9323 = 19.027 kA (VCB coefficients of Table 1; P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 16–18)	Interpolated to 0.601 kV: I_arc,1 = (17.470 − 16.272)/2.1 × (0.601 − 2.7) + 17.470 = 16.273; I_arc,2 = (19.027 − 17.470)/11.6 × (0.601 − 14.3) + 19.027 = 17.188; I_arc,3 = 16.273 × (2.7 − 0.601)/2.1 + 17.188 × (0.601 − 0.6)/2.1 = 16.273 kA (0.6 < V_oc ≤ 2.7 kV)
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 0.601⁵ = 0.0000; k₃V_oc⁴ = 8.3137×10⁻⁵ × 0.601⁴ = 0.0000; k₄V_oc³ = −0.0019382 × 0.601³ = (-0.0004); k₅V_oc² = 0.022366 × 0.601² = 0.0081; k₆V_oc = −0.12645 × 0.601 = (-0.0760); k₇ = 0.3023; sum = 0.2339; applied to each reference current, I_arc,min = 16.272/17.470/19.027 × (1 − 0.5 × 0.2339) = 14.369/15.426/16.801 kA, interpolated as above to 14.370 kA
Enclosure correction (Eq 11–15)	610 H × 610 W × 610 D mm → typical box, Table 7 (typical, VCB). W₁ = 610/25.4 (508–660.4 mm: actual size) = 24.016 in; H₁ = 610/25.4 (508–660.4 mm: actual size) = 24.016 in; EES = (24.016 + 24.016)/2 = 24.016 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 24.016² + 0.03441 × 24.016 + 0.4325 = 1.0847 (Eq 14)
Incident energy, full current (Eq 3–5)	P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I. 600 V (Eq 3, I* = I_arc = 16.272 kA): exponent = k₁ 0.7534 + k₂·lg 32 0.8519 + k₃·16.272/P_E(20) 1.3226 + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 16.272 1.1594 + lg(1/1.0847) (-0.0353) = -0.3986; E = 12.552/50 × 100 × 10^-0.3986 (k₁₂ = -1.598) = 10.027 J/cm²; 2700 V (Eq 4, I* = I_arc = 17.470 kA): exponent = k₁ 2.4002 + k₂·lg 32 0.2483 + k₃·17.470/P_E(20) 0.3318 + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.3697) + k₁₃·lg 17.470 1.2147 + lg(1/1.0847) (-0.0353) = -0.2099; E = 12.552/50 × 100 × 10^-0.2099 (k₁₂ = -1.569) = 15.481 J/cm²; 14 300 V (Eq 5, I* = I_arc = 19.027 kA): exponent = k₁ 3.8259 + k₂·lg 32 0.1656 + k₃·19.027/P_E(20) (-1.0201) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.3670) + k₁₃·lg 19.027 1.2666 + lg(1/1.0847) (-0.0353) = -0.1643; E = 12.552/50 × 100 × 10^-0.1643 (k₁₂ = -1.568) = 17.196 J/cm²
Interpolated full-current energy (Eq 19–21)	At 0.601 kV: E₁ = (15.481 − 10.027)/2.1 × (0.601 − 2.7) + 15.481 = 10.030; E₂ = (17.196 − 15.481)/11.6 × (0.601 − 14.3) + 17.196 = 15.171; E₃ = 10.030 × (2.7 − 0.601)/2.1 + 15.171 × (0.601 − 0.6)/2.1 = 10.032 J/cm² (0.6 < V_oc ≤ 2.7 kV) = 2.398 cal/cm²
Incident energy, reduced current (Eq 3–5)	Above 600 V the reduced reference current I_arc,min replaces I_arc in both the k₃ and k₁₃ terms at each reference voltage (at or below 600 V the k₃ term keeps the full I_arc,600). 600 V (I_arc,min = 14.369 kA, T_min = 100 ms): exponent = k₁ 0.7534 + k₂·lg 32 0.8519 + k₃·14.369/P_E(20) 1.1679 + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.4505) + k₁₃·lg 14.369 1.1077 + lg(1/1.0847) (-0.0353) = -0.6050; E = 12.552/50 × 100 × 10^-0.6050 (k₁₂ = -1.598) = 6.234 J/cm²; 2700 V (I_arc,min = 15.426 kA, T_min = 100 ms): exponent = k₁ 2.4002 + k₂·lg 32 0.2483 + k₃·15.426/P_E(20) 0.2930 + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.3697) + k₁₃·lg 15.426 1.1619 + lg(1/1.0847) (-0.0353) = -0.3016; E = 12.552/50 × 100 × 10^-0.3016 (k₁₂ = -1.569) = 12.536 J/cm²; 14 300 V (I_arc,min = 16.801 kA, T_min = 100 ms): exponent = k₁ 3.8259 + k₂·lg 32 0.1656 + k₃·16.801/P_E(20) (-0.9008) + k₁₁·lg 20 0.0000 + k₁₂·lg 609.6 (-4.3670) + k₁₃·lg 16.801 1.2131 + lg(1/1.0847) (-0.0353) = -0.0985; E = 12.552/50 × 100 × 10^-0.0985 (k₁₂ = -1.568) = 20.011 J/cm²
Interpolated reduced-current energy (Eq 19–21)	At 0.601 kV: E₁ = (12.536 − 6.234)/2.1 × (0.601 − 2.7) + 12.536 = 6.237; E₂ = (20.011 − 12.536)/11.6 × (0.601 − 14.3) + 20.011 = 11.184; E₃ = 6.237 × (2.7 − 0.601)/2.1 + 11.184 × (0.601 − 0.6)/2.1 = 6.239 J/cm² (0.6 < V_oc ≤ 2.7 kV) = 1.491 cal/cm²
Arc-flash boundary (Eq 7–9)	AFB = D × (5.0208/E)^1/k₁₂ at each reference voltage — full: 600 V 609.6 × (5.0208/10.027)^1/(-1.598) = 940 mm; 2700 V 609.6 × (5.0208/15.481)^1/(-1.569) = 1,249 mm; 14 300 V 609.6 × (5.0208/17.196)^1/(-1.568) = 1,337 mm; reduced: 600 V 609.6 × (5.0208/6.234)^1/(-1.598) = 698 mm; 2700 V 609.6 × (5.0208/12.536)^1/(-1.569) = 1,092 mm; 14 300 V 609.6 × (5.0208/20.011)^1/(-1.568) = 1,472 mm
Interpolated boundary (Eq 22–24)	Full: AFB₁ = (1,249 − 940)/2.1 × (0.601 − 2.7) + 1,249 = 940; AFB₂ = (1,337 − 1,249)/11.6 × (0.601 − 14.3) + 1,337 = 1,234; AFB₃ = 940 × (2.7 − 0.601)/2.1 + 1,234 × (0.601 − 0.6)/2.1 = 940 mm (0.6 < V_oc ≤ 2.7 kV); reduced: AFB₁ = (1,092 − 698)/2.1 × (0.601 − 2.7) + 1,092 = 698; AFB₂ = (1,472 − 1,092)/11.6 × (0.601 − 14.3) + 1,472 = 1,023; AFB₃ = 698 × (2.7 − 0.601)/2.1 + 1,023 × (0.601 − 0.6)/2.1 = 698 mm (0.6 < V_oc ≤ 2.7 kV)
Governing case	max(full 2.398, reduced 1.491 cal/cm²) → the full arcing-current case: E = 2.398 cal/cm² (10.032 J/cm²), AFB = max(940, 698) = 940 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 2.398 cal/cm² > 1.2 cal/cm² → arc-rated clothing, minimum arc rating 2.4 cal/cm² (category-equivalent 1, informational) — informational, not a pass/fail check → 2.398 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 2.398 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(100, 100) = 100 ms → 100 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 2.40 cal/cm² at 609.6 mm, AFB 940 mm, arc-rated clothing; governing: De-energise threshold (40 cal/cm²) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases): Iarc,600/2700/14300 = 16.272/17.470/19.027 kA (full), 14.369/15.426/16.801 kA (reduced); E600/2700/14300 = 10.027/15.481/17.196 J/cm² (full, 100 ms), 6.234/12.536/20.011 J/cm² (reduced, 100 ms); Iarc = 16.273 kA, Iarc,min = 14.370 kA, VarCf = 0.2339, typical box CF = 1.0847 (EES 24.016 in); E = 10.032 / 6.239 J/cm², AFB = 940 / 698 mm (full / reduced); full case governs: 2.398 cal/cm², AFB 940 mm. (validation case `c0007-601v-vcb-reduced-case-hv-side-of-step`)

Example 31 — 240 V panel at exactly 2 kA: no sustained-arc note

IEEE 1584-2018 notes that a sustained arc is less likely at 240 V or below with less than 2 kA available. At exactly 2 kA that note does not apply, so the result carries no warnings — the threshold is pinned here; 1999 A gets the note (unit tests).

Given: V_oc = 240 V, I_bf = 2 kA, VCB (vertical conductors in a box), T = 500 ms at I_arc and T_min = 500 ms at I_arc,min (same clearing time); gap G = 25 mm, working distance D = 457.2 mm, enclosure 355.6 H × 304.8 W × 254 D mm (from the LV_MCC_Panel_Deep preset where not given; MCP lv_mcc_panel_deep).

Arcing current (Eq 1)	I_arc,600 = 10^{k₁ + k₂·lg I_bf + k₃·lg G} × P_I(I_bf) with the VCB 600 V coefficients of Table 1 = 10^{(-0.042870) + 1.035·lg 2 − 0.083·lg 25} × P_I(2) = 10^0.1527 × 1.0974 = 1.560 kA (P_I(I_bf) = k₄I_bf⁶ + k₅I_bf⁵ + … + k₉I_bf + k₁₀, the Eq 1 current polynomial with the Table 1 coefficients)
Final arcing current (Eq 25)	I_arc = 1/√[(0.6/0.24)² × (1/1.560² − (0.6² − 0.24²)/(0.6² × 2²))] = 1/√[6.2500 × (0.411103 − 0.210000)] = 0.892 kA
Variation factor and reduced current (Eq 2)	VarC_f = k₁V_oc⁶ + … + k₆V_oc + k₇ (Table 2, VCB): k₂V_oc⁵ = −1.4269×10⁻⁶ × 0.24⁵ = 0.0000; k₃V_oc⁴ = 8.3137×10⁻⁵ × 0.24⁴ = 0.0000; k₄V_oc³ = −0.0019382 × 0.24³ = 0.0000; k₅V_oc² = 0.022366 × 0.24² = 0.0013; k₆V_oc = −0.12645 × 0.24 = (-0.0303); k₇ = 0.3023; sum = 0.2732; I_arc,min = I_arc(1 − 0.5 VarC_f) = 0.892 × (1 − 0.5 × 0.2732) = 0.770 kA
Enclosure correction (Eq 11–15)	355.6 H × 304.8 W × 254 D mm → typical box, Table 7 (typical, VCB). W₁ = 304.8 mm (below 508 mm → 20 in) = 20.000 in; H₁ = 355.6 mm (below 508 mm → 20 in) = 20.000 in; EES = (20.000 + 20.000)/2 = 20.000 in (Eq 13); CF = b₁EES² + b₂EES + b₃ = (-0.0003020) × 20.000² + 0.03441 × 20.000 + 0.4325 = 0.9999 (Eq 14)
Incident energy, full current (Eq 6)	I* = I_arc,600 = 1.560 kA in the k₃ term, I_arc = 0.892 kA in the k₁₃ term, T = 500 ms (P_E(I_bf) = k₄I_bf⁷ + k₅I_bf⁶ + … + k₁₀I_bf, the energy-equation denominator with the Tables 3–5 coefficients — a different polynomial from P_I): exponent = k₁ 0.7534 + k₂·lg 25 0.7912 + k₃·1.560/P_E(2) 1.2455 + k₁₁·lg 2 0.0000 + k₁₂·lg 457.2 (-4.2508) + k₁₃·lg 0.892 (-0.0475) + lg(1/0.9999) 0.0000 = -1.5083; E = 12.552/50 × 500 × 10^-1.5083 (k₁₂ = -1.598) = 3.894 J/cm² = 0.931 cal/cm²
Incident energy, reduced current (Eq 6)	I_arc,min = 0.770 kA in the k₁₃ term, T_min = 500 ms; the k₃ term keeps the full I_arc,600 = 1.560 kA — at or below 600 V Eq 6 takes I_arc,600 from Eq 1, which has no reduced form (above 600 V each reference current is reduced instead): exponent = k₁ 0.7534 + k₂·lg 25 0.7912 + k₃·1.560/P_E(2) 1.2455 + k₁₁·lg 2 0.0000 + k₁₂·lg 457.2 (-4.2508) + k₁₃·lg 0.770 (-0.1086) + lg(1/0.9999) 0.0000 = -1.5693; E = 12.552/50 × 500 × 10^-1.5693 (k₁₂ = -1.598) = 3.384 J/cm² = 0.809 cal/cm²
Arc-flash boundary (Eq 10)	AFB = D × (5.0208/E)^1/k₁₂: full 457.2 × (5.0208/3.894)^1/(-1.598) = 390 mm; reduced 457.2 × (5.0208/3.384)^1/(-1.598) = 357 mm
Governing case	max(full 0.931, reduced 0.809 cal/cm²) → the full arcing-current case: E = 0.931 cal/cm² (3.894 J/cm²), AFB = max(390, 357) = 390 mm
Arc-rated PPE (NFPA 70E Table 130.5(G))	E = 0.931 cal/cm² ≤ 1.2 cal/cm² → arc-rated PPE not required (non-melting or untreated natural-fibre clothing is still required) — informational, not a pass/fail check → 0.931 vs limit 1.200 cal/cm² INFO
De-energise threshold (40 cal/cm²)	E is within 40 cal/cm², the arc rating of category 4 PPE — a practical de-energise threshold, not an NFPA 70E prohibition (NFPA 70E requires the hierarchy of risk controls before energised work) → 0.931 vs limit 40.000 cal/cm² PASS
Arc duration ≤ 2 s	longest clearing time max(T, T_min) = max(500, 500) = 500 ms → 500 vs limit 2,000 ms PASS
Result	2/2 checks pass → PASS; E = 0.93 cal/cm² at 457.2 mm, AFB 390 mm, arc-rated PPE not required; governing: Arc duration (2 s) (the pass/fail check with the highest value ÷ limit, failing checks first)
Reference	Independent recompute with github.com/LiaungYip/arcflash (MIT Python port of the IEEE 1584-2018 calculator, verified by its author against 144 000 official-spreadsheet cases): Iarc,600 = 1.560 kA; Iarc = 0.892 kA, Iarc,min = 0.770 kA, VarCf = 0.2732, typical box CF = 0.9999 (EES 20.000 in); E = 3.894 / 3.384 J/cm², AFB = 390 / 357 mm (full / reduced); full case governs: 0.931 cal/cm², AFB 390 mm. (validation case `c0007-240v-2ka-at-sustained-arc-threshold`)

Standards & References

IEEE 1584-2018 — IEEE Guide for Performing Arc-Flash Hazard Calculations. Eq 1–25; Tables 1–7 (model coefficients); Table 8 (typical gaps and enclosure sizes); Table 10 (typical working distances); 4.2 (range of the model); Annex D (worked examples D.1 and D.2).
IEEE 1584-2018 calculator spreadsheet (IEEE DataPort) — the official implementation of the model, used to verify this calculator.
NFPA 70E-2024 — Standard for Electrical Safety in the Workplace. 130.5(G) and Table 130.5(G): PPE for an incident-energy analysis; 130.5(H): equipment labelling; 130.7(C)(15): the separate PPE category method.
IEEE 1584.1-2022 — Guide for the Specification of Scope and Deliverable Requirements for an Arc-Flash Hazard Calculation Study.
ASTM F1506 / IEC 61482 — Arc-rated protective clothing.
ENA NENS 09 (Energy Networks Australia) — National guideline for the selection, use and maintenance of personal protective equipment for electrical arc hazards; the Australian network-industry practice for arc-flash PPE.
AS/NZS 4836 — Safe working on or near low-voltage and extra-low-voltage electrical installations and equipment.

The validation cases behind the worked examples can be downloaded and re-run: JSON · CSV. The validation scorecard shows the build and date of the latest run.

Tips & Limitations

Tips

Read both clearing times from the protective device’s time-current characteristic: \(T\) at \(I_{arc}\) and \(T_{min}\) at \(I_{arc,min}\). With inverse-time devices the reduced-current case often governs (Annex D.2).
Pick the equipment class to load the typical gap, working distance and enclosure of Tables 8 and 10, then override any value you have measured.
Choose the electrode configuration that matches the conductors where the arc would occur: vertical bus in switchgear is usually VCB; vertical conductors terminating in an insulating barrier (for example line-side terminals) VCBB; horizontal conductors in a box HCB.
Enclosure size matters: a smaller box focuses energy towards the opening (higher CF). Shallow low-voltage boxes use a separate correction (Eq 15).
Label equipment per NFPA 70E 130.5(H) with the incident energy and working distance, the arc-flash boundary and the nominal voltage.
Above 40 cal/cm², de-energise and look for ways to reduce the hazard: faster clearing, arc-flash relaying, maintenance switches, remote operation.
Current-limiting fuses also limit the let-through current; the model uses the prospective bolted current and ignores that, so results for fuse-protected equipment are conservative.
When the arc-flash boundary is under 305 mm (the shortest working distance the model is fitted for), the 1.2 cal/cm² boundary effectively sits at the equipment face; a warning is shown. A boundary between 305 mm and the working distance needs no warning: the energy at the working distance is already below 1.2 cal/cm².
Voltages of 22 kV and 33 kV are outside IEEE 1584-2018 and are rejected with that reason. The Lee theoretical model is grossly conservative above about 15 kV; a test-based study (arc-in-box modelling such as ArcPro, or EPRI-type data) or the network operator’s own arc-flash tables is the usual route.

Limitations

Range of the model — three-phase AC, 50/60 Hz, 208 V to 15 kV; bolted fault current 500 A–106 kA (≤ 600 V) or 200 A–65 kA (> 600 V); gap 6.35–76.2 mm (≤ 600 V) or 19.05–254 mm (> 600 V); working distance ≥ 305 mm. Inputs outside this range are rejected, not extrapolated.
Single-phase and DC systems are outside IEEE 1584-2018.
Arc duration above 2 s — the standard suggests 2 s as a reasonable maximum where a worker can move away; a warning is shown and the full time entered is still used.
240 V or below with less than 2 kA — a sustained arc is possible but less likely; a warning is shown and the model still applies.
Enclosure width below four times the gap — outside the tested geometry for the correction factor; a warning is shown.
Enclosures above 1244.6 mm — treated as 1244.6 mm in the equivalent size; a warning is shown.
No protective device coordination — clearing times are inputs; the calculator does not model device characteristics.

Developer Guide

Architecture

File layout:

components/c0007_arc_flash_ieee1584/calculations.py — the IEEE 1584-2018 model equation by equation, coefficient tables, range-of-model validation and PPE guidance. Tables 1–7 are read from the database.
components/c0007_arc_flash_ieee1584/component.py — parameter schema, ArcFlashIEEE1584Calculator, equation builder, summary cards builder, registration.
components/c0007_arc_flash_ieee1584/excel_generator.py — Excel export following the same procedure.
components/c0007_arc_flash_ieee1584/fault_current.py — bolted fault current estimation utilities.
components/c0007_arc_flash_ieee1584/simplified.py — simplified front end.
components/c0007_arc_flash_ieee1584/templates/ — sidebar form template.
components/c0007_arc_flash_ieee1584/test_data/ieee1584_calculator_sample.json — reference cases from the IEEE 1584-2018 calculator spreadsheet.

The calculator class ArcFlashIEEE1584Calculator subclasses ElectricalCalculator from calcs.core.base_calculator. It fills blank inputs from EQUIPMENT_DEFAULTS and delegates to the pure function calculate_arc_flash_ieee1584(data). register_component() registers the calc type 'arc_flash_ieee1584' with the equation builder and summary cards builder.

Tables 1–7 live in the database (webcalcs.StandardTable, edition 2018), not in code: sheets IEEE1584_T1 … IEEE1584_T7, loaded from calcs/components/c0007_arc_flash_ieee1584/tables/ieee1584_2018.json by python manage.py load_standard_tables. calculations.py reads them through table_1() … table_7() (calcs.core.standard_tables, cached per process; restart after reloading). A missing table stops the calculation with a message naming the command. Staff can check every value at /mcp/admin/tables/arc_flash_ieee1584/.

Tables in calculations.py:

EQUIPMENT_DEFAULTS — Tables 8 and 10 equipment classes
MODEL_RANGE — range of the model (4.2)

Code Paths

Functions in calculations.py:

Function	Purpose
`calculate_arc_flash_ieee1584(data)`	Entry point. Validates, runs every step for both cases, returns the full results dict. Raises `ValueError` outside the range of the model.
`validate_inputs(data)`	List of range-of-model violations (empty when valid)
`intermediate_arcing_current(config, kv, ibf_ka, gap_mm)`	Eq 1 at one reference voltage (kA)
`arcing_current_variation_factor(config, voc_kv)`, `reduced_arcing_current(iarc_ka, var_cf)`	Eq 2
`final_arcing_current_lv(voc_kv, iarc_600_ka, ibf_ka)`	Eq 25 (≤ 600 V)
`interpolate_to_voltage(voc_kv, x_600, x_2700, x_14300)`	Eq 16–24 for current, energy or boundary (> 600 V only; raises at or below)
`enclosure_correction_factor(config, voc_kv, h, w, d)`	Eq 11–15: box type, equivalent sizes, EES, CF
`intermediate_incident_energy(...)`	Eq 3–5, or Eq 6 when `iarc_600_ka` is given (J/cm²)
`arc_flash_boundary(config, kv, energy_j_cm2, d_mm)`	Eq 7–10 solved for the 1.2 cal/cm² distance (mm)
`ppe_guidance(incident_energy_cal)`	NFPA 70E-2024 Table 130.5(G) tier, minimum arc rating, informational category

Request flow:

ArcFlashIEEE1584Calculator.validate_parameters() fills blanks from the equipment class and adds each validate_inputs message as an error.
calculate() calls calculate_arc_flash_ieee1584(data) and adds equipment_type to the results.
equation_builder() turns the results into report articles following the standard’s procedure; summary_cards_builder() produces the four dashboard cards.

Testing

Running tests:

pytest calcs/components/c0007_arc_flash_ieee1584 -q

Verification in test_calculation.py:

Annex D.1 and D.2 — every intermediate printed in the standard, within its rounding (±0.5 A, ±0.0005 J/cm², ±0.0005 in or CF, ±0.5 mm).
IEEE calculator spreadsheet — 300 cases (60 per electrode configuration, 208 V to 15 kV) compared on \(I_{arc}\), \(E\) and AFB for both the full and reduced cases at a relative tolerance of 0.1%. During development the engine was also checked against every valid row (105 120) of the full spreadsheet export. (The 144 000 quoted in the worked-example references is a different set: the cases the LiaungYip/arcflash port’s author generated from the spreadsheet to verify that port.)
Unit tests for each equation function, the PPE boundaries, every range-of-model rule, the warnings, the calculator class, the equation builder, the summary cards and the Excel report.
Worked examples — the examples above are generated from the MCP validation corpus (mcp_public/validation/cases/fe_calc_arc_flash/: 31 worked examples, each verified against an independent IEEE 1584-2018 hand calculation or the LiaungYip/arcflash port and, where available, the IEEE calculator sample, plus 9 rejection cases at the range-of-model limits that must be refused with the reason; all 40 are in the JSON/CSV downloads) by python manage.py generate_help_examples --tool fe_calc_arc_flash; the corpus check in calcs/test_help_examples.py fails if the committed fragment is stale.

How to extend:

Coefficients must be copied exactly from IEEE 1584-2018 Tables 1–7; any change must keep the Annex D and spreadsheet tests passing.
To add an equipment class, add an entry (with label) to EQUIPMENT_DEFAULTS and the matching <option> to the sidebar form; the schema enum picks it up automatically.
New result keys must be added to the equation builder, the Excel report and this page.