Load Cable Sizing (1-Phase) — help

Edition and voltage-change convention: The calculation uses the AS/NZS 3008.1.1:2017 tables, the only supported edition; any other edition is rejected with a validation error. For lagging power factor the effective term is \(R PF + X\sqrt{1-PF^2}\); for leading power factor it is \(R PF - X\sqrt{1-PF^2}\). The signed result reports voltage drop or rise, while compliance uses its absolute magnitude.

Overview

Performs comprehensive single-phase load cable sizing per AS/NZS 3008.1.1:2017 and AS/NZS 3000:2018. The calculator verifies cable suitability through six checks:

Current Carrying Capacity (CCC) — Base ampacity with derating for ambient temperature, cable grouping, installation method, and burial conditions.
Voltage Drop — Single-phase voltage drop using the factor-of-2 formula for go-and-return path.
Short Circuit Withstand — Adiabatic equation verifying the cable can withstand prospective fault current for the protection device clearing time.
Earth Fault Loop Impedance — Verifies sufficient earth fault current to operate the protection device within required disconnection time.
Earth Conductor Size — The protective earth conductor is not smaller than the AS/NZS 3000:2018 Table 5.1 minimum for the phase conductor size.
Earth Conductor Withstand — Adiabatic equation verifying the earth conductor can carry the largest (near-end) earth fault current \(I_{ef} = V / Z_{source}\) for the fault clearing time.

Intended for single-phase non-motor loads: lighting, small power, single-phase HVAC, heating, UPS, control panels, and domestic circuits. For three-phase loads use the Load Cable Sizing (3-Phase) calculator (c0030). For motor loads use the Motor Cable Sizing calculators (c0006 / c0032).

Input Parameters

Load Parameters

Parameter	Type	Default	Range	Description
`specify_by`	Enum: power / current	power	—	Specify load by power rating or current rating
`power`	Number	5	0.1 – 10000	Load rated power (hidden if specify_by = current)
`powertype`	Enum: kW / watt / HP	kW	—	Power unit (hidden if specify_by = current)
`voltage`	Enum	230 V	100 – 300 V	Single-phase supply voltage (110, 120, 220, 230, 240, 277 V)
`powerfactor`	Number	0.85	0.5 – 1.0	Load power factor cos(φ)
`load_current`	Number	30 A	0.1 – 10000 A	Full load current (hidden if specify_by = power)
`load_type`	Enum	General Load	—	Type of load: General Load, Lighting, Small Power, HVAC, Heating, UPS, Control Panel, Domestic
`design_factor`	Number	1.0	0.8 – 2.0	Multiplier applied to load current for design margin

Cable

Single-phase cables are always multicore — no cable formation selector is shown.

Parameter	Type	Default	Range	Description
`cable_type`	Enum: Fixed / Flexible / MIMS	Fixed	—	Cable construction type
`conductor`	Enum	16 mm²	1 – 630 mm²	Phase conductor cross-sectional area
`multicore_arrangement`	Enum: Circular / Shaped	Circular	—	Multicore cable arrangement (always visible for 1ph)
`cable_insulation`	Enum: XLPE / PVC / EPR	XLPE	—	Insulation material type
`metal`	Enum: Cu / Al	Cu	—	Conductor material (hidden when cable_type = MIMS)
`earth_conductor`	Enum	16 mm²	1 – 630 mm²	Protective earth conductor size. Checked against the AS/NZS 3000 Table 5.1 minimum (Check 5) and for adiabatic withstand (Check 6). Auto-size mode uses the Table 5.1 minimum for each trial size.

Cable Installation

Fields in this section are conditionally visible based on the selected installation method. Singlecore-specific fields are not available for single-phase circuits.

Parameter	Type	Default	Visible When	Description
`installation_method`	Enum	Unenclosed	Always	Unenclosed, DirectBuried, Enclosed, Conduit, BuriedConduit, ThermalInsulation
`unenclosed_type_mc`	Enum	Spaced from Surface	Unenclosed	Exposed To Sun, Spaced from Surface, Touching Surface
`unenclosed_in_air`	Enum	Perforated Trays Horizontal	Unenclosed (not touching)	Tray/ladder/catenary arrangement
`unenclosed_catinerary`	Enum	Bunched on Catinerary Wire	Air = On Catinerary Wire	Spaced or Bunched on catenary
`cables_per_tier`	Enum: 1–9	1	Unenclosed + not bunched	Number of cables per tier
`ladder_spacing`	Enum: Touching / Spaced / Bunched	Spaced	Unenclosed + not catenary	Spacing on ladder/tray
`ladder_tiers`	Enum: 1Tier / 2Tier / 3Tier	1Tier	Ladder spacing ≠ Bunched	Number of ladder tiers
`bunched_circuits_cables`	Enum: 1–>18	1	Unenclosed	Number of bunched cables/circuits
`bunched_unenclosed_type`	Enum	Bunched In Air	Unenclosed	Bunched arrangement type
`thermal_ins_type1`	Enum: Completely / Partial	Completely	ThermalInsulation	Thermal insulation coverage
`thermal_ins_type2`	Enum: Unenclosed / Enclosed	Enclosed	ThermalInsulation	Thermal insulation method
`enclosed_install_type`	Enum	Wiring Enclosure in Air	Enclosed	Wiring Enclosure in Air, Metalic Enclosure in Air
`conduit_spacing`	Enum	Touching	Conduit	Touching, Spaced 0.3m, 0.45m, 0.6m
`direct_buried_spacing`	Enum	Touching	DirectBuried	Touching, Spaced 0.15m, 0.3m, 0.45m, 0.6m
`buried_circuits_cables`	Enum: 1–12	3	Conduit or DirectBuried	Number of buried circuits/cables
`ambient_temp`	Enum: 15–85 °C	40 °C	Not DirectBuried, not Conduit	Air ambient temperature for derating
`burial_depth`	Enum: 0.5–3+ m	0.8	DirectBuried or Conduit	Depth of burial for underground cables
`soil_ambient`	Enum: 10–40 °C	25 °C	DirectBuried or Conduit	Soil ambient temperature
`soil_resistivity`	Enum: 0.8–3 K·m/W	1	DirectBuried or Conduit	Soil thermal resistivity
`num_circuits`	Integer	1	Always	Number of grouped circuits for derating (1–20)

Protection Parameters

Parameter	Type	Default	Range	Description
`fault_current`	Number	10000 A	100 – 100000 A	Prospective short circuit fault current at load
`protection_time`	Number	0.1 s	0.01 – 5.0 s	Maximum clearing time for protection device, used for the phase short circuit withstand check (Check 3)
`earth_fault_clearing_time`	Number	0.04 s	0.005 – 5.0 s	Earth-fault clearing time \(t_{ef}\) for the earth conductor withstand check (Check 6). A fault at the cable origin draws far more than the device's instantaneous threshold, so this is the device's instantaneous operating time; enter the upstream backup time instead if that device is relied on to clear the fault.
`trip_current`	Number	32 A	1 – 10000 A	Circuit breaker or fuse rating
`trip_multiplier`	Number	5	3 – 15	Instantaneous magnetic trip multiplier (typically 5–10× rating)
`source_impedance`	Number	0.1 Ω	0.001 – 10.0 Ω	Impedance of source (transformer + upstream cables). Sets the earth fault loop impedance and the near-end earth fault current \(I_{ef} = V / Z_{source}\) for the earth withstand check.

Calculation Settings

Parameter	Type	Default	Range	Description
`voltagedropmax`	Number	5%	1 – 10%	Maximum acceptable voltage drop percentage

Output Results

Calculated Currents

Output	Unit	Description
`full_load_current`	A	Calculated or user-specified load current
`design_current`	A	Full load current × design factor

Check 1: Current Carrying Capacity

Output	Unit	Description
`base_current`	A	Base cable ampacity from AS/NZS 3008 tables
`derated_current`	A	Base current after applying all derating factors
`derating_factor`	—	Combined derating factor (temperature × grouping)
`margin`	A	Spare capacity: derated current − design current
`passes`	Boolean	Whether derated capacity ≥ design current

Check 2: Voltage Drop

Output	Unit	Description
`rc`	Ω/km	Cable resistance per km (from AS/NZS 3008 lookup)
`xc`	Ω/km	Cable reactance per km (from AS/NZS 3008 lookup)
`impedance`	Ω/km	Cable impedance \(Z_c = \sqrt{R_c^2 + X_c^2}\)
`voltage_drop`	V	Absolute voltage drop
`voltage_drop_percent`	%	Voltage drop as percentage of supply
`margin_percent`	%	Remaining margin: max allowed − actual
`passes`	Boolean	Whether \(V_{d\%} \leq V_{d,max\%}\)

Check 3: Short Circuit Withstand

Output	Unit	Description
`k_factor`	—	Material/insulation factor from AS/NZS 3008 Table 52
`max_withstand_time`	s	Maximum time cable can withstand fault current
`protection_time`	s	Protection device operating time
`passes`	Boolean	Whether \(t_{max} \geq t_{protection}\)

Check 4: Earth Fault Loop Impedance

Output	Unit	Description
`z_source`	Ω	Source impedance (transformer + upstream)
`z_phase`	Ω	Phase conductor impedance for cable length
`z_earth`	Ω	Earth conductor impedance \(L_{km}\sqrt{R_e^2 + X_e^2}\)
`rc_earth`	Ω/km	Earth conductor AC resistance at the insulation's operating temperature
`xc_earth`	Ω/km	Earth conductor reactance: AS/NZS 3008 Table 30 at the earth size, phase-cable arrangement
`z_loop`	Ω	Total earth fault loop impedance
`fault_current`	A	Prospective earth fault current
`voltage_phase`	V	Phase voltage (equals supply voltage for single-phase)
`passes`	Boolean	Whether fault current ≥ trip threshold

Check 5: Earth Conductor Size

Result key check_earth_size.

Output	Unit	Description
`earth_area`	mm²	Earth conductor used (the Table 5.1 minimum in auto-size mode)
`minimum_earth_area`	mm²	AS/NZS 3000:2018 Table 5.1 minimum for the phase conductor size
`passes`	Boolean	Whether \(S_e \geq S_{e,min}\)

Check 6: Earth Conductor Withstand

Result key check_earth_withstand.

Output	Unit	Description
`fault_current`	A	Near-end earth fault current \(I_{ef} = V / Z_{source}\)
`k_factor`	—	AS/NZS 3008 Table 52 k, shared with the phase conductor
`min_csa`	mm²	Adiabatic minimum earth conductor \(I_{ef}\sqrt{t_{ef}}/k\)
`max_withstand_time`	s	Time the earth conductor can carry \(I_{ef}\): \((k S_e / I_{ef})^2\)
`passes`	Boolean	Whether \(S_e \geq S_{e,min}\)

Overall Result

Output	Unit	Description
`all_checks_pass`	Boolean	True only when all six checks pass
`status`	text	"PASS" or "FAIL"
`num_checks_passed`	Integer	Count of checks passed (0–6)
`num_checks`	Integer	Number of checks run (6)
`failure_reasons`	list	List of failure reason strings (empty if all pass)

Formulas

Load Current (Single-Phase)

\[ I_{load} = \frac{P \times 1000}{V \times \cos\phi} \]

Where \(P\) is load power in kW, \(V\) is supply voltage, and \(\cos\phi\) is power factor. Unlike three-phase, there is no \(\sqrt{3}\) factor and no efficiency term (non-motor load).

Design Current

\[ I_{design} = I_{load} \times k_{design} \]

Where \(k_{design}\) is the design factor (default 1.0). Increase to account for load growth or safety margin. The design current is used for current-carrying capacity and for voltage drop.

Check 1: Current Carrying Capacity

\[ I_{rated} = I_{base} \times k_{derating} \] \[ \text{Check: } I_{rated} \geq I_{design} \]

\(I_{base}\) is the base ampacity from AS/NZS 3008 Tables 4–21. \(k_{derating}\) is the product of derating factors for ambient temperature, cable grouping, installation method, and burial conditions (AS/NZS 3008 Tables 22–29).

Cable Impedance

\[ Z_c = \sqrt{R_c^2 + X_c^2} \quad (\Omega/\text{km}) \]

Where \(R_c\) and \(X_c\) are looked up from AS/NZS 3008 tables based on conductor material, size, insulation, and temperature.

Check 2: Voltage Drop (Single-Phase)

\[ V_d = 2 \, I_B \, L_{km} \left(R_c \cos\phi \pm X_c \sin\phi\right), \qquad I_B = I_{load} \times k_{design} \]

The factor of 2 accounts for the go-and-return path in a single-phase circuit. In three-phase calculations, \(\sqrt{3}\) is used instead. Voltage drop is evaluated at the design current \(I_B\), the current the cable and its protective device are sized for, not at the load current. \(L_{km}\) is the cable length in km; the sign is + for a lagging and − for a leading power factor, and compliance uses the magnitude.

Voltage Drop Percentage

\[ V_{d\%} = \frac{V_d}{V_{supply}} \times 100 \] \[ \text{Check: } V_{d\%} \leq V_{d,max\%} \]

Check 3: Short Circuit Withstand (Adiabatic Equation)

\[ t_{max} = \frac{k^2 \times S^2}{I_f^2} \] \[ \text{Check: } t_{max} \geq t_{protection} \]

Where \(k\) is the material/insulation factor (AS/NZS 3008 Table 52), \(S\) is conductor cross-sectional area in mm², and \(I_f\) is prospective fault current in amps. The cable must withstand the fault for at least the protection device clearing time.

k-Factor Values (AS/NZS 3008 Table 52)

Material	PVC (70/160 °C)	XLPE (90/250 °C)	EPR (90/250 °C)
Copper	115	143	143
Aluminium	76	94	94

Check 4: Earth Fault Loop Impedance (Single-Phase)

\[ Z_{loop} = Z_{source} + Z_{phase} + Z_{earth}, \qquad Z_{earth} = L_{km}\sqrt{R_e^2 + X_e^2} \] \[ I_{fault} = \frac{V_{ph}}{Z_{loop}} \] \[ \text{Check: } I_{fault} \geq I_{trip} \times k_{mag} \] \[ L_{max} = \frac{V_{ph} / I_a - Z_{source}}{|z_{phase}| + |z_{earth}|} \times 1000 \quad (\text{m}) \]

For single-phase circuits, \(V_{ph} = V_{supply}\) because the supply voltage is already the phase-to-neutral voltage. This differs from three-phase where \(V_{ph} = V / \sqrt{3}\). The fault current must exceed the protection device magnetic trip threshold (\(I_{trip} \times k_{mag}\)) to ensure disconnection within the required time.

The earth conductor impedance includes its reactance: \(Z_{earth} = L_{km}\sqrt{R_e^2 + X_e^2}\), where \(R_e\) is the earth conductor's AC resistance at the insulation's operating temperature and \(X_e\) is its AS/NZS 3008 Table 30 reactance at the earth conductor size, in the same arrangement as the phase cable. Leaving \(X_e\) out understates the loop impedance and overstates the fault current, most for large earth conductors where \(X_e\) approaches \(R_e\). The maximum length uses the same model: \(|z_{phase}|\) and \(|z_{earth}|\) are per-kilometre impedance magnitudes, and adding magnitudes gives a loop impedance no smaller than the phasor sum.

Check 5: Earth Conductor Size (AS/NZS 3000 Table 5.1)

\[ \text{Check: } S_e \geq S_{e,min} \]

\(S_{e,min}\) is the AS/NZS 3000:2018 Table 5.1 minimum protective earth conductor for the phase conductor size (for example 4 mm² for 16 mm², 16 mm² for 50 mm²). In manual mode an earth conductor below the minimum fails the calculation. In auto-size mode each trial size carries the Table 5.1 minimum, so this check always passes there.

Check 6: Earth Conductor Withstand (Adiabatic Equation)

\[ I_{ef} = \frac{V}{Z_{source}} \] \[ S_{e,min} = \frac{I_{ef} \times \sqrt{t_{ef}}}{k} \] \[ t_{max,e} = \left(\frac{k \times S_e}{I_{ef}}\right)^2 \] \[ \text{Check: } S_e \geq S_{e,min} \]

The largest earth fault current flows for a fault at the cable origin (near end), where only the source impedance limits it. For single-phase \(V_{ph} = V\). \(t_{ef}\) is the earth-fault clearing time (earth_fault_clearing_time, default 0.04 s), not the CB clearance time used for Check 3: a fault at the cable origin draws far more than the protective device's instantaneous threshold, so it clears in the instantaneous operating time. If an upstream device is relied on to clear that fault instead, enter its clearing time. The earth is an integral core of the same cable, so it starts at the insulation operating temperature and ends at the same final temperature as the phase conductor: it shares the phase conductor's AS/NZS 3008 Table 52 k. A stiff source (small \(Z_{source}\)) with a long clearing time can make the Table 5.1 earth too small; auto-size then steps up to a phase size whose Table 5.1 earth is large enough.

\(I_{ef}\) comes from the upstream loop impedance, while Check 3 uses the prospective fault current input. If \(V_{ph} / Z_{source}\) exceeds the prospective fault current, the calculation warns that the two inputs are inconsistent: check the upstream loop impedance against the fault level.

Single-Phase vs Three-Phase: Key Differences

Formula	Single-Phase (this calc)	Three-Phase (c0030)
Load Current	\( I = \frac{P \times 1000}{V \times PF} \)	\( I = \frac{P \times 1000}{\sqrt{3} \times V \times PF} \)
Voltage Drop	\( V_d = \frac{2 \times I \times L \times Z_c}{1000} \)	\( V_d = \frac{\sqrt{3} \times I \times L \times Z_c}{1000} \)
Phase Voltage	\( V_{ph} = V \)	\( V_{ph} = V / \sqrt{3} \)
Near-End Earth Fault	\( I_{ef} = V / Z_{source} \)	\( I_{ef} = (V / \sqrt{3}) / Z_{source} \)
Cable Core	2 Core	3 Core

Length Conversion Factors

From	To Meters
1 Kilometer	1000 m
1 Foot	0.3048 m
1 Mile	1609.34 m
1 Yard	0.9144 m

Worked Examples

The 2 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_cable_size; worked examples for every calculation).

#	Case	Cable	I_design (A)	I_derated (A)	V_d (%)	Governing	Result
1	5 kW single-phase load, 30 m, 3 kA fault: phase withstand sets 10 mm²	10 mm² Cu XLPE (auto)	25.6	78.0	1.35	earth conductor thermal withstand	PASS
2	Check 4 mm² for a 20 A single-phase circuit over 40 m	4 mm² Cu XLPE	20.0	45.0	3.51	earth conductor thermal withstand	FAIL

Example 1 — 5 kW single-phase load, 30 m, 3 kA fault: phase withstand sets 10 mm²

Single-phase auto sizing: 6 mm² cannot withstand 3 kA for 0.1 s (minimum 6.63 mm²), so 10 mm² is selected; its 4 mm² Table 5.1 earth carries the 2.3 kA near-end earth fault (230 V / 0.1 Ω), cleared instantaneously in 0.04 s, with 3.22 mm² needed (80 %, the highest utilisation, so earth withstand governs).

Given: 5 kW single-phase load at 230 V, PF 0.85 (default) lagging, design factor 1 (default). Auto sizing of a copper XLPE (X-90) fixed two-core cable, route 30 m; unenclosed, spaced from surface, on perforated trays horizontal, 1 cable(s) per tier, 1 tier(s), spaced, air ambient 40 °C (default). Protection: prospective fault 3 kA cleared in 0.1 s (default), earth-fault clearing time 0.04 s (default), 32 A device with 5× instantaneous trip (default), upstream loop impedance 0.1 Ω (default), voltage-drop limit 5 % (default). AS/NZS 3008.1.1:2017 tables.

Load current	I_load = 5 kW × 1000 / (230 × 0.85) = 25.58 A; design factor 1.0 → I_design = 25.58 A
Sizes tried	Standard sizes tried smallest first with the AS/NZS 3000 Table 5.1 earth. Selected 10 mm² with a 4 mm² earth.
Check 1 — capacity	Base rating Table 11, column 2, row 10: 78 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_derated = 78 × 1.00 = 78.00 A vs I_design 25.58 A (loading 32.8 %) PASS
Check 2 — voltage drop	R_c = 2.33 Ω/km (Ref: Table 35, Column 5, Row: 10mm²), X_c = 0.0840 Ω/km (Ref: Table 30, Column 10, Row: 10mm²). At the design current: ΔV = 2 × 25.58 × 0.030 × (2.33 × 0.85 + 0.0840 × 0.527) = 3.11 V (drop) = 1.35 % of 230 V, limit 5 % PASS
Check 3 — short circuit	k = 143 (Table 52, Cu 90 → 250 °C). t_max = (143 × 10)² / 3,000² = 0.2272 s vs 0.1 s clearing; S_min = 3,000 × √0.1 / 143 = 6.63 mm² PASS
Check 4 — earth fault loop	Z_s = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 5.88 Ω/km and X_e = 0.0930 Ω/km (Table 30 at 4 mm²): Z_s = 0.1 + 0.0699 (phase) + 0.1764 (earth) = 0.3464 Ω vs Z_s,max = 230 / (32 × 5) = 1.4375 Ω; I_fault = 230.0 / 0.3464 = 664 A vs 160 A PASS. L_max = (1.4375 − 0.1) / 8.212 Ω/km = 162.9 m vs 30 m PASS
Check 5 — earth size	AS/NZS 3000 Table 5.1 minimum for a 10 mm² phase conductor: 4 mm²; earth 4 mm² PASS
Check 6 — earth withstand	Largest earth-fault current, a fault at the cable origin: I_ef = 230 / 0.1 = 2,300 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 2,300 × √0.04 / 143 = 3.22 mm² vs 4 mm² (t_max = (143 × 4 / 2,300)² = 0.0618 s) PASS
Result	7/7 checks pass → PASS; 10 mm² Cu with 4 mm² earth; power loss 91 W (1.83 %); governing: earth conductor withstand
Reference	Hand calculation: I = 5000 / (230 × 0.85) = 25.58 A (calcs/test_c0031 single-phase formula); phase adiabatic minimum S = I·√t/k = 3000·√0.1/143 = 6.63 mm² (k = 143, AS/NZS 3008.1.1:2017 Table 52, 90 °C row) so 6 mm² fails and 10 mm² withstands (143 × 10 / 3000)² = 0.2272 s; single-phase near-end earth fault I_ef = V/Z_source = 230/0.1 = 2300 A, cleared instantaneously in the default t_ef = 0.04 s, needs an earth of 2300·√0.04/143 = 3.22 mm², so the 4 mm² AS/NZS 3000 Table 5.1 earth of 10 mm² passes (80 %, the highest utilisation, governs); ΔV = 2·I·L·(R cosφ + X sinφ) = 2·25.58·0.03·(2.33·0.85 + 0.084·0.527) with Table 35/30 values for 10 mm² = 3.11 V = 1.35 %; Zs = 0.1 + 0.03·√(2.33² + 0.084²) + 0.03·√(5.88² + 0.093²) = 0.1 + 0.0700 + 0.1764 = 0.3464 Ω ≤ 230/(5 × 32 A) = 1.4375 Ω. (validation case `c0031-5kw-230v-30m-auto-3ka`)

Example 2 — Check 4 mm² for a 20 A single-phase circuit over 40 m

Single-phase voltage drop uses the factor 2 instead of √3 (3.51 %), and the near-end earth fault uses V rather than V/√3: 230 V / 0.1 Ω = 2.3 kA, cleared instantaneously in 0.04 s, needs a 3.22 mm² earth, so the 2.5 mm² earth fails its withstand (129 %) and governs.

Given: single-phase load of 20 A at 230 V, PF 0.85 (default) lagging (for voltage drop), design factor 1 (default). Check 4 mm² copper XLPE (X-90) fixed two-core cable with a 2.5 mm² earth, route 40 m; unenclosed, spaced from surface, on perforated trays horizontal, 1 cable(s) per tier, 1 tier(s), spaced, air ambient 40 °C (default). Protection: prospective fault 1 kA cleared in 0.1 s (default), earth-fault clearing time 0.04 s (default), 20 A device with 5× instantaneous trip (default), upstream loop impedance 0.1 Ω (default), voltage-drop limit 5 % (default). AS/NZS 3008.1.1:2017 tables.

Load current	I_load = 20.00 A (given); design factor 1.0 → I_design = 20.00 A
Check 1 — capacity	Base rating Table 11, column 2, row 4: 45 A. Derating Table 24, row 1: 1.00; Table 27(1), 90 °C conductor column, row 40: 1.00 → F = 1.00. I_derated = 45 × 1.00 = 45.00 A vs I_design 20.00 A (loading 44.4 %) PASS
Check 2 — voltage drop	R_c = 5.88 Ω/km (Ref: Table 35, Column 5, Row: 4mm²), X_c = 0.0930 Ω/km (Ref: Table 30, Column 10, Row: 4mm²). At the design current: ΔV = 2 × 20.00 × 0.040 × (5.88 × 0.85 + 0.0930 × 0.527) = 8.08 V (drop) = 3.51 % of 230 V, limit 5 % PASS
Check 3 — short circuit	k = 143 (Table 52, Cu 90 → 250 °C). t_max = (143 × 4)² / 1,000² = 0.3272 s vs 0.1 s clearing; S_min = 1,000 × √0.1 / 143 = 2.21 mm² PASS
Check 4 — earth fault loop	Z_s = Z_ext + L·√(R_c² + X_c²) + L·√(R_e² + X_e²) with the earth's R_e = 9.45 Ω/km and X_e = 0.0988 Ω/km (Table 30 at 2.5 mm²): Z_s = 0.1 + 0.2352 (phase) + 0.3780 (earth) = 0.7133 Ω vs Z_s,max = 230 / (20 × 5) = 2.3000 Ω; I_fault = 230.0 / 0.7133 = 322 A vs 100 A PASS. L_max = (2.3000 − 0.1) / 15.331 Ω/km = 143.5 m vs 40 m PASS
Check 5 — earth size	AS/NZS 3000 Table 5.1 minimum for a 4 mm² phase conductor: 2.5 mm²; earth 2.5 mm² PASS
Check 6 — earth withstand	Largest earth-fault current, a fault at the cable origin: I_ef = 230 / 0.1 = 2,300 A, cleared in t_ef = 0.04 s (default: a fault at the origin is far above the device's instantaneous threshold, so it clears instantaneously). k = 143 (integral earth core: the phase conductor's Table 52 k). S_min = I_ef × √t_ef / k = 2,300 × √0.04 / 143 = 3.22 mm² vs 2.5 mm² (t_max = (143 × 2.5 / 2,300)² = 0.0242 s) FAIL
Result	6/7 checks pass → FAIL; 4 mm² Cu with 2.5 mm² earth; power loss 188 W (4.81 %); governing: earth conductor withstand. Power loss (4.81%) is significant The upstream earth-loop impedance (0.1 Ω) gives 2300 A of earth-fault current at the cable origin, more than the 1 kA prospective fault: the two inputs are inconsistent Consider larger conductor to reduce energy losses Check the upstream loop impedance against the prospective fault level; the earth withstand check uses the loop impedance
Reference	Hand calculation with AS/NZS 3008.1.1:2017 Table 35/30 values for 4 mm² (2.5 mm² earth, its reactance from Table 30 at 2.5 mm²): ΔV = 2·20·0.04·(5.88·0.85 + 0.093·0.527) = 8.08 V = 3.51 %; Zs = 0.1 + \|Z4\|·0.04 + \|Z2.5\|·0.04 = 0.1 + 0.04·√(5.88² + 0.093²) + 0.04·√(9.45² + 0.0988²) = 0.1 + 0.2352 + 0.3780 = 0.7133 Ω ≤ 230/(5 × 20 A) = 2.3 Ω; Lmax = (2.3 − 0.1)/(5.8807 + 9.4505 Ω/km) = 143.5 m; withstand t = (143 × 4 / 1000)² = 0.3272 s; earth: 2.5 mm² meets the AS/NZS 3000 Table 5.1 minimum for 4 mm², but the single-phase near-end earth fault I_ef = 230/0.1 = 2300 A cleared in the default t_ef = 0.04 s needs S_min = 2300·√0.04/143 = 3.22 mm² > 2.5 mm² (129 %), so the circuit fails and earth withstand governs. (validation case `c0031-check-4mm2-20a-40m`)

Standards & References

AS/NZS 3008.1.1:2017 — Electrical installations — Selection of cables — Cables for alternating voltages up to and including 0.6/1 kV
- Tables 4–21: Current carrying capacity by installation method
- Tables 22–29: Derating factors (temperature, grouping, burial)
- Tables 30–34: Cable reactance values
- Tables 35–42: Cable resistance values
- Table 52: k-factors for short circuit and earth conductor withstand
AS/NZS 3000:2018 — Electrical installations (Wiring Rules)
- Clause 3.6: Voltage drop limits (typically 5%)
- Clause 5.5: Earth fault loop impedance requirements
- Table 5.1: Minimum protective earth conductor size
- Table 8.2: Maximum disconnection times
IEC 60364 — Low-voltage electrical installations — Part 4-41: Protection against electric shock

Tips & Best Practices

Tips

The single-phase voltage drop factor of 2 produces a higher drop than the three-phase factor of \(\sqrt{3}\) for the same current and cable — expect roughly 15% more voltage drop.
For single-phase circuits at 230 V, the earth fault current is higher than three-phase at the same voltage because \(V_{ph} = V\) instead of \(V / \sqrt{3}\). This makes earth fault checks easier to pass.
Use the design factor to account for future load growth. A factor of 1.2 provides 20% growth allowance.
When specifying by current, set power factor to a reasonable value as it is still used in some display outputs.
For long domestic circuits (e.g., shed or garage feeds), voltage drop is typically the limiting factor — check this first.
Short circuit withstand often fails for small conductors (1 – 6 mm²) at high fault levels. Consider the actual fault current at the load point, which may be much lower than the switchboard fault level.
The calculator uses 2-core cable configuration (active + neutral) which is correct for single-phase circuits.

Limitations

Steady-state only — inrush current from motors, transformers, or capacitive loads is NOT considered.
No starting current analysis — for motor loads use the Motor Cable Sizing calculators (c0006 / c0032).
Cable resistance is taken at the insulation's operating temperature (PVC 75 °C, XLPE 90 °C, EPR 110 °C; aluminium at most 90 °C), the same temperature as the current rating, not at the actual load temperature.
Only Multicore Circular cable arrangement is supported for impedance table lookups.
Earth fault loop calculation assumes a simple radial circuit. Ring circuits or circuits with multiple earth paths require separate analysis.
The adiabatic short circuit equation assumes no heat dissipation during the fault. This is conservative for short durations (< 5 s) but unconservative for longer durations — keep protection times short.

Developer Guide

Architecture

File layout:

components/c0031_load_cable_sizing_1ph/component.py — Component registration, parameter schema, equation builder, summary cards builder
components/c0031_load_cable_sizing_1ph/calculations.py — Pure calculation functions for single-phase load sizing
components/c0031_load_cable_sizing_1ph/equations.py — LaTeX equation builder for PDF report generation
components/c0031_load_cable_sizing_1ph/sidebar_form.html — Django template for sidebar input form

Shared dependencies:

From c0006_motor_cable_sizing/calculations.py: HP_TO_KW, SQRT_3, call_webcalcs_api, check_short_circuit, convert_length_to_meters, lookup_rc_xc, calculate_impedance
From c0030_load_cable_sizing/calculations.py: check_current_capacity_with_webcalcs_load
From core/mathjax_utils.py: multi_replace

The calculator class is LoadCableSizing1PhCalculator, extending ElectricalCalculator. It delegates all six checks to dedicated functions, with single-phase variants for voltage drop and earth fault loop calculations. The earth conductor checks are the shared check_earth_conductor_size and check_earth_conductor_withstand(..., phases=1) in core/cable_utils.py.

Relationship to c0030 (3-phase):

This calc mirrors c0030 structurally but differs in three formulas: load current (no √3), voltage drop (factor of 2 instead of √3), and earth fault (V_ph = V instead of V/√3). It also uses CableCore = '2 Core' when calling the webcalcs API. Check 1 (CCC) and Check 3 (short circuit) are shared with the three-phase version.

Code Paths

Key functions in calculations.py:

Function	Purpose
`calculate_load_current_1ph(power, voltage, pf, power_type)`	Single-phase load current: I = P1000 / (VPF)
`check_voltage_drop_with_webcalcs_1ph(data, webcalcs_results)`	Voltage drop with factor of 2 for go+return
`check_earth_fault_loop_1ph(data)`	Earth fault loop with V_ph = V
`map_calcs_to_webcalcs_params_load_1ph(data)`	Map inputs to webcalcs API format (CableCore = '2 Core')
`calculate_load_cable_sizing_1ph(data)`	Main orchestrator: runs all six checks

Key functions in equations.py:

Function	Purpose
`build_table_data(result)`	Build table rows for input and result parameters
`build_equations(result)`	Generate LaTeX equation articles for PDF report

Data flow:

User inputs arrive via PARAMETER_SCHEMA
LoadCableSizing1PhCalculator.calculate() assembles a data dict and calls calculate_load_cable_sizing_1ph(data)
Load current is computed (or user-specified value used)
Parameters are mapped to webcalcs format via map_calcs_to_webcalcs_params_load_1ph()
Webcalcs API is called to get CCC data and impedance values
Six checks run: CCC (shared), VD (1ph variant), SC (shared), EFL (1ph variant), earth size and earth withstand (shared, phases=1)
Results aggregated with overall pass/fail status

Testing

Running tests:

pytest calcs/test_c0031_load_cable_sizing_1ph.py -v

Worked examples: the examples above are generated from the MCP validation corpus (mcp_public/validation/cases/fe_calc_cable_size/) by python manage.py generate_help_examples --tool fe_calc_cable_size, which writes help/_load_cable_sizing_1ph_examples.html; calcs/test_help_examples.py fails if the committed fragment is stale.

Test classes:

TestCalculateLoadCurrent1Ph — Verifies load current formula for kW, watt, HP inputs; checks zero-input edge cases; confirms absence of √3 factor by comparing against three-phase result.
TestKnownCurrentMode1Ph — Verifies specify_by = current mode passes current through without modification.
TestDesignFactor1Ph — Verifies design factor multiplier is correctly applied (default 1.0, custom 1.25).
TestEarthFaultLoop1Ph — Confirms V_ph = V (not V/√3); verifies 1ph fault current is higher than 3ph for same inputs.
TestComponentRegistration1Ph — Verifies component registers with correct calc_type and display_name.

How to extend:

To add new insulation types, update the lookup table dicts in c0006_motor_cable_sizing/calculations.py and add the option to the cable_insulation enum in component.py.
To support additional voltage levels, add them to the voltage enum in PARAMETER_SCHEMA.
For new installation methods, update the installation_map in map_calcs_to_webcalcs_params_load_1ph().
Write tests covering new parameters and verify all six checks still produce correct results.