Lightning Risk Assessment — help

Overview

The Lightning Risk Assessment calculator evaluates the need for lightning protection systems (LPS) per IEC 62305-2 — Protection against lightning: Risk management. It calculates risk R1 (loss of human life) and determines whether a lightning protection system is required, and if so, at which protection level (LPL I–IV).

The calculator provides:

Collection area — equivalent area attracting lightning strikes
Expected strikes — annual frequency of dangerous lightning events (N_d)
Risk assessment — R1 broken into RA (touch/step), RB (fire/damage), RC (system failure)
Protection decision — whether LPS is required
Protection level — LPL I, II, III, or IV with rolling sphere radius and mesh size

Input Parameters

Structure

Parameter	Default	Range	Description
`structure_length`	40 m	1 – 1000	Structure length
`structure_width`	20 m	1 – 1000	Structure width
`structure_height`	10 m	1 – 300	Structure height

Lightning Environment

Parameter	Default	Description
`flash_density`	2 fl/km²/yr	Ground flash density N_g (from local lightning data)
`location_factor`	flat	Relative location, C_d per IEC 62305-2 Table A.1: surrounded by taller objects (0.25), flat = surrounded by objects of the same height or smaller (0.5), moderate = isolated, no objects in the vicinity (1.0), exposed = isolated on a hilltop or knoll (2.0)

Structure Properties

Parameter	Default	Description
`structure_type`	non_metal_roof	Roof and structure material → PB probability
`occupancy`	occupied	Occupancy level → LA loss factor
`fire_risk`	ordinary	Fire/explosion risk → LB loss factor

Systems & Protection

Parameter	Default	Description
`internal_systems`	low_voltage	Service lines connected to the internal systems (none, LV power, telecom, LV power + telecom) → number of lines n in P_C
`consequence_of_failure`	standard	Consequence of system failure → LC factor
`touch_step_protection`	none	Touch/step voltage measures → PA factor
`surge_protection`	none	Coordinated SPD system on every connected line → P_SPD (IEC 62305-2 Table B.3)
`existing_lps`	none	Existing LPS level → reduces PB by efficiency

Output Results

Output	Symbol	Unit	Description
Collection Area	A_d	m²	Equivalent area attracting direct strikes
Expected Strikes	N_d	/yr	Annual expected dangerous lightning events
Risk RA	R_A	—	Injury from touch/step voltages
Risk RB	R_B	—	Physical damage (fire, explosion)
Risk RC	R_C	—	Failure of internal systems
Total Risk	R₁	—	R_A + R_B + R_C
Tolerable Risk	R_T	—	10^-5 for loss of human life
Protection Required	—	Yes / No	Whether R1 > RT
Protection Level	LPL	I – IV	Required lightning protection level
Rolling Sphere	—	m	Rolling sphere radius for LPL (20 / 30 / 45 / 60 m)
Mesh Size	—	m	Maximum mesh size (5 / 10 / 15 / 20 m)

Formulas

Collection Area (IEC 62305-2 eq. A.2)

A_d = L×W + 2×(3H)×(L+W) + π×(3H)²

The 3H factor accounts for the attractive radius of the structure. For a 40×20×10 m building: A_d = 800 + 3,600 + 2,827 ≈ 7,227 m².

Expected Dangerous Events (IEC 62305-2 Annex A)

N_d = N_g × A_d × C_d × 10^-6

Risk R1 Components

R_A = N_d × P_A × L_A
R_B = N_d × P_B × L_B
R_C = N_d × P_C × L_C,  P_C = 1 − (1 − P_SPD × C_LD)ⁿ
R₁ = R_A + R_B + R_C

The probabilities and losses are category values chosen by the inputs (a simplification of the IEC 62305-2 Annex B/C factor products). An existing LPS multiplies P_B by (1 − efficiency).

P_C follows IEC 62305-2 B.4: each connected service line contributes P_C,i = P_SPD × C_LD, and the lines combine as P_C = 1 − (1 − P_C,1)(1 − P_C,2)…, so connecting more lines raises P_C. The calculator simplifies this to one category: every connected line is taken as an unshielded aerial or buried line (C_LD = 1, Table B.4) and the selected SPD level is applied to all of them. With no connected line (stand-alone systems) C_LD = 0 and P_C = 0. Shielded or bonded lines, isolating interfaces and SPDs better than LPL I (P_SPD 0.005–0.001) are not modelled.

Factor	Input	Values
C_d	`location_factor`	surrounded by higher objects 0.25, flat (same height or smaller) 0.5, moderate (isolated) 1, exposed (isolated on a hilltop) 2 — Table A.1
P_A	`touch_step_protection`	none 1, warning notices 0.1, electrical insulation 0.01, equipotential bonding 0.01
P_B	`structure_type`	metal roof + metal structure 0.001, non-metal roof + metal structure 0.01, non-metal roof 0.1, thatched roof 0.3
P_B multiplier	`existing_lps`	none 1, IV 0.2, III 0.1, II 0.05, I 0.02
n (lines)	`internal_systems`	none 0 (P_C = 0), low voltage 1, telecom 1, LV and telecom 2
C_LD	—	1 (unshielded line, Table B.4)
P_SPD	`surge_protection`	none 1, spd_1 (LPL III–IV) 0.05, spd_2 (LPL II) 0.02, spd_3 (LPL I) 0.01 — Table B.3
L_A	`occupancy`	occupied 0.01, high occupancy 0.1
L_B	`fire_risk`	no fire risk 0, ordinary 0.1, high fire risk 0.5, explosion risk 1
L_C	`consequence_of_failure`	no consequence 0, standard 0.01, critical 0.1

Protection Level Determination

If R₁ > R_T (10^-5), lightning protection is required. The minimum LPL is the level whose PB reduction factor (efficiency) brings R₁ ≤ R_T.

LPL	Efficiency	Rolling Sphere	Mesh Size
I	0.98	20 m	5 × 5 m
II	0.95	30 m	10 × 10 m
III	0.90	45 m	15 × 15 m
IV	0.80	60 m	20 × 20 m

Worked Examples

The 25 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_lightning_risk; worked examples for every calculation).

#	Case	A_D (m²)	N_D (/yr)	R₁ (/yr)	LPS	R₁ with LPS	Result
1	Small building among taller ones	1,406.9	3.52 × 10⁻⁴	1.06 × 10⁻⁵	class IV	7.74 × 10⁻⁶	FAIL
2	40 × 20 × 10 m building, all defaults	7,227.4	7.23 × 10⁻³	2.17 × 10⁻⁴	class I	1.46 × 10⁻⁴	FAIL
3	Hilltop warehouse with high fire risk	34,309.7	0.343	0.024	class I	7.21 × 10⁻³	FAIL
4	Bonded building needing class IV	3,087.9	3.09 × 10⁻³	3.18 × 10⁻⁵	class IV	7.10 × 10⁻⁶	FAIL
5	Bonded building needing class III	7,227.4	7.23 × 10⁻³	7.44 × 10⁻⁵	class III	9.40 × 10⁻⁶	FAIL
6	Bonded building needing class II	7,227.4	0.0108	1.12 × 10⁻⁴	class II	8.67 × 10⁻⁶	FAIL
7	Bonded building needing class I	7,227.4	0.0217	2.21 × 10⁻⁴	class I	8.67 × 10⁻⁶	FAIL
8	Existing class III LPS already adequate	7,227.4	7.23 × 10⁻³	9.40 × 10⁻⁶	none	–	PASS
9	Existing class IV LPS needs upgrading	7,227.4	0.0108	2.49 × 10⁻⁵	class II	8.67 × 10⁻⁶	FAIL
10	Isolated building (C_D 1)	2,649.9	1.32 × 10⁻³	1.52 × 10⁻⁵	class IV	4.64 × 10⁻⁶	FAIL
11	Small hut isolated on a hilltop (C_D 2)	458.5	9.17 × 10⁻⁴	1.83 × 10⁻⁷	none	–	PASS
12	Metal roof and metal frame	12,351.5	0.0124	4.94 × 10⁻⁶	none	–	PASS
13	Non-metal roof on a metal frame	12,351.5	0.0185	2.41 × 10⁻⁵	class IV	9.26 × 10⁻⁶	FAIL
14	Thatched-roof cottage	1,833.9	3.67 × 10⁻³	1.14 × 10⁻⁴	class II	9.90 × 10⁻⁶	FAIL
15	High-occupancy hall	11,331.5	8.50 × 10⁻³	1.72 × 10⁻⁴	class I	8.84 × 10⁻⁵	FAIL
16	Structure with no fire risk	20,361.7	0.0407	2.44 × 10⁻⁵	class I	2.44 × 10⁻⁵	FAIL
17	Explosion-risk process building	6,427.4	0.0225	2.29 × 10⁻⁴	class I	9.00 × 10⁻⁶	FAIL
18	Telecom equipment with critical consequence	1,372.4	2.06 × 10⁻³	2.06 × 10⁻⁴	class I	2.06 × 10⁻⁴	FAIL
19	Same telecom building with LPL III–IV SPDs	1,372.4	2.06 × 10⁻³	1.07 × 10⁻⁵	class I	1.05 × 10⁻⁵	FAIL
20	Same telecom building with SPD level 3	1,372.4	2.06 × 10⁻³	2.47 × 10⁻⁶	none	–	PASS
21	LV and telecom lines combined	7,227.4	7.23 × 10⁻³	4.31 × 10⁻⁶	none	–	PASS
22	LV + telecom with no life consequence	4,809.6	4.81 × 10⁻³	9.62 × 10⁻⁷	none	–	PASS
23	No connected service lines	554.5	8.32 × 10⁻⁴	1.66 × 10⁻⁷	none	–	PASS
24	300 m tower on a hilltop	2,617,090.0	10.5	0.21	class I	0.209	FAIL
25	Smallest structure at the lowest flash density	41.3	2.06 × 10⁻⁶	6.19 × 10⁻⁸	none	–	PASS

Example 1 — Small building among taller ones

A 10 × 10 × 5 m building surrounded by higher structures (C_D 0.25) at N_G 1: with its unprotected LV line (P_C 1) R1 lands just above R_T and a class IV LPS is enough.

Given: Structure 10 × 10 × 5 m (L × W × H), ground flash density N_G = 1 flashes/km²/yr, located surrounded by higher objects; non-metallic roof and structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: none; surge protection: no coordinated SPDs; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 10 × 10 + 2 × 15 × (10 + 10) + π × 15² = 100.0 + 600.0 + 706.9 = 1,406.9 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 1 × 1,406.9 × 0.25 × 10⁻⁶ = 3.517 × 10⁻⁴ /yr
Probabilities	P_A = 1 (none); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 1 × 1)¹ = 1 (LV power line, n = 1, unshielded C_LD = 1; no coordinated SPDs, P_SPD = 1, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 3.517 × 10⁻⁴ × 1 × 0.01 = 3.517 × 10⁻⁶; R_B = N_D·P_B·L_B = 3.517 × 10⁻⁴ × 0.1 × 0.1 = 3.517 × 10⁻⁶; R_C = N_D·P_C·L_C = 3.517 × 10⁻⁴ × 1 × 0.01 = 3.517 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 3.517 × 10⁻⁶ + 3.517 × 10⁻⁶ + 3.517 × 10⁻⁶ → 1.055 × 10⁻⁵ > R_T = 10⁻⁵/yr (105.5 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 3.517 × 10⁻⁶): class IV: 3.517 × 10⁻⁶ + 3.517 × 10⁻⁶ × 0.2 + 3.517 × 10⁻⁶ = 7.738 × 10⁻⁶ ≤ R_T → class IV; rolling sphere 60 m, mesh 20 × 20 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class IV LPS → 7.738 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (77.4 %) PASS
Result	1/2 checks pass → FAIL; R₁ = 1.055 × 10⁻⁵/yr; recommended LPS: class IV; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 10 × 10 + 6 × 5 × (10 + 10) + 9π × 5² = 1406.9 m²; N_D = 1 × 1406.9 × 0.25 × 1e-6 = 0.0003517/yr; R_A = N_D × 1 × 0.01 = 3.517e-06, R_B = N_D × 0.1 × 0.1 = 3.517e-06, P_C = 1 − (1 − 1 × 1)^1 = 1 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 1, Table B.3); R_C = N_D × 1 × 0.01 = 3.517e-06; R1 = 1.055e-05 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): IV, residual R1 = 7.738e-06; rolling sphere 60 m, mesh 20 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-10x10x5m-ng1-surrounded`)

Example 2 — 40 × 20 × 10 m building, all defaults

With every factor at its default the touch/step component R_A alone exceeds R_T, so even a class I LPS leaves R1 above the limit.

Given: Structure 40 × 20 × 10 m (L × W × H), ground flash density N_G = 2 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof and structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: none; surge protection: no coordinated SPDs; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 40 × 20 + 2 × 30 × (40 + 20) + π × 30² = 800.0 + 3,600.0 + 2,827.4 = 7,227.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 2 × 7,227.4 × 0.5 × 10⁻⁶ = 7.227 × 10⁻³ /yr
Probabilities	P_A = 1 (none); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 1 × 1)¹ = 1 (LV power line, n = 1, unshielded C_LD = 1; no coordinated SPDs, P_SPD = 1, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 7.227 × 10⁻³ × 1 × 0.01 = 7.227 × 10⁻⁵; R_B = N_D·P_B·L_B = 7.227 × 10⁻³ × 0.1 × 0.1 = 7.227 × 10⁻⁵; R_C = N_D·P_C·L_C = 7.227 × 10⁻³ × 1 × 0.01 = 7.227 × 10⁻⁵
R1 check	R₁ = R_A + R_B + R_C = 7.227 × 10⁻⁵ + 7.227 × 10⁻⁵ + 7.227 × 10⁻⁵ → 2.168 × 10⁻⁴ > R_T = 10⁻⁵/yr (2,168.2 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 7.227 × 10⁻⁵): class IV: 7.227 × 10⁻⁵ + 7.227 × 10⁻⁵ × 0.2 + 7.227 × 10⁻⁵ = 1.590 × 10⁻⁴ > R_T; class III: 7.227 × 10⁻⁵ + 7.227 × 10⁻⁵ × 0.1 + 7.227 × 10⁻⁵ = 1.518 × 10⁻⁴ > R_T; class II: 7.227 × 10⁻⁵ + 7.227 × 10⁻⁵ × 0.05 + 7.227 × 10⁻⁵ = 1.482 × 10⁻⁴ > R_T; class I: 7.227 × 10⁻⁵ + 7.227 × 10⁻⁵ × 0.02 + 7.227 × 10⁻⁵ = 1.460 × 10⁻⁴ > R_T — no class achieves R_T, class I recommended as the ceiling; rolling sphere 20 m, mesh 5 × 5 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class I LPS → 1.460 × 10⁻⁴ > R_T = 10⁻⁵/yr (1,459.9 %) FAIL
Result	0/2 checks pass → FAIL; R₁ = 2.168 × 10⁻⁴/yr; recommended LPS: class I; governing: risk r1 with recommended lps. Even an LPS of class I leaves R1 = 0.000146 > 1e-05; the remaining risk is dominated by RA, which an LPS does not reduce in this engine — add touch/step protection measures (RA) or coordinated SPDs (RC).
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 40 × 20 + 6 × 10 × (40 + 20) + 9π × 10² = 7227.4 m²; N_D = 2 × 7227.4 × 0.5 × 1e-6 = 0.007227/yr; R_A = N_D × 1 × 0.01 = 7.227e-05, R_B = N_D × 0.1 × 0.1 = 7.227e-05, P_C = 1 − (1 − 1 × 1)^1 = 1 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 1, Table B.3); R_C = N_D × 1 × 0.01 = 7.227e-05; R1 = 0.0002168 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): I (none suffices, I is the ceiling), residual R1 = 0.000146; rolling sphere 20 m, mesh 5 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-40x20x10m-ng2-flat`)

Example 3 — Hilltop warehouse with high fire risk

A large exposed warehouse (C_D 2, L_B 0.5) is far above R_T; class I is recommended but R_A keeps the residual risk above the limit.

Given: Structure 100 × 50 × 20 m (L × W × H), ground flash density N_G = 5 flashes/km²/yr, located isolated on a hilltop or knoll (exposed); non-metallic roof and structure, high fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: none; surge protection: no coordinated SPDs; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 100 × 50 + 2 × 60 × (100 + 50) + π × 60² = 5,000.0 + 18,000.0 + 11,309.7 = 34,309.7 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 5 × 34,309.7 × 2 × 10⁻⁶ = 0.3431 /yr
Probabilities	P_A = 1 (none); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 1 × 1)¹ = 1 (LV power line, n = 1, unshielded C_LD = 1; no coordinated SPDs, P_SPD = 1, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.5 (high fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 0.3431 × 1 × 0.01 = 3.431 × 10⁻³; R_B = N_D·P_B·L_B = 0.3431 × 0.1 × 0.5 = 0.01715; R_C = N_D·P_C·L_C = 0.3431 × 1 × 0.01 = 3.431 × 10⁻³
R1 check	R₁ = R_A + R_B + R_C = 3.431 × 10⁻³ + 0.01715 + 3.431 × 10⁻³ → 0.02402 > R_T = 10⁻⁵/yr (240,168.1 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 0.01715): class IV: 3.431 × 10⁻³ + 0.01715 × 0.2 + 3.431 × 10⁻³ = 0.01029 > R_T; class III: 3.431 × 10⁻³ + 0.01715 × 0.1 + 3.431 × 10⁻³ = 8.577 × 10⁻³ > R_T; class II: 3.431 × 10⁻³ + 0.01715 × 0.05 + 3.431 × 10⁻³ = 7.720 × 10⁻³ > R_T; class I: 3.431 × 10⁻³ + 0.01715 × 0.02 + 3.431 × 10⁻³ = 7.205 × 10⁻³ > R_T — no class achieves R_T, class I recommended as the ceiling; rolling sphere 20 m, mesh 5 × 5 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class I LPS → 7.205 × 10⁻³ > R_T = 10⁻⁵/yr (72,050.4 %) FAIL
Result	0/2 checks pass → FAIL; R₁ = 0.02402/yr; recommended LPS: class I; governing: risk r1 with recommended lps. Even an LPS of class I leaves R1 = 0.00721 > 1e-05; the remaining risk is dominated by RA, which an LPS does not reduce in this engine — add touch/step protection measures (RA) or coordinated SPDs (RC).
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 100 × 50 + 6 × 20 × (100 + 50) + 9π × 20² = 34309.7 m²; N_D = 5 × 34309.7 × 2 × 1e-6 = 0.3431/yr; R_A = N_D × 1 × 0.01 = 0.003431, R_B = N_D × 0.1 × 0.5 = 0.01715, P_C = 1 − (1 − 1 × 1)^1 = 1 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 1, Table B.3); R_C = N_D × 1 × 0.01 = 0.003431; R1 = 0.02402 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): I (none suffices, I is the ceiling), residual R1 = 0.007205; rolling sphere 20 m, mesh 5 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-100x50x20m-ng5-exposed-high-fire`)

Example 4 — Bonded building needing class IV

With equipotential bonding and coordinated SPDs only R_B matters, and a class IV LPS (P_B × 0.2) is the lowest class that meets R_T.

Given: Structure 30 × 15 × 6 m (L × W × H), ground flash density N_G = 2 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof and structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: equipotential bonding; surge protection: coordinated SPDs for LPL II; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 30 × 15 + 2 × 18 × (30 + 15) + π × 18² = 450.0 + 1,620.0 + 1,017.9 = 3,087.9 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 2 × 3,087.9 × 0.5 × 10⁻⁶ = 3.088 × 10⁻³ /yr
Probabilities	P_A = 0.01 (equipotential bonding); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.02 × 1)¹ = 0.02 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL II, P_SPD = 0.02, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 3.088 × 10⁻³ × 0.01 × 0.01 = 3.088 × 10⁻⁷; R_B = N_D·P_B·L_B = 3.088 × 10⁻³ × 0.1 × 0.1 = 3.088 × 10⁻⁵; R_C = N_D·P_C·L_C = 3.088 × 10⁻³ × 0.02 × 0.01 = 6.176 × 10⁻⁷
R1 check	R₁ = R_A + R_B + R_C = 3.088 × 10⁻⁷ + 3.088 × 10⁻⁵ + 6.176 × 10⁻⁷ → 3.181 × 10⁻⁵ > R_T = 10⁻⁵/yr (318.1 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 3.088 × 10⁻⁵): class IV: 3.088 × 10⁻⁷ + 3.088 × 10⁻⁵ × 0.2 + 6.176 × 10⁻⁷ = 7.102 × 10⁻⁶ ≤ R_T → class IV; rolling sphere 60 m, mesh 20 × 20 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class IV LPS → 7.102 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (71.0 %) PASS
Result	1/2 checks pass → FAIL; R₁ = 3.181 × 10⁻⁵/yr; recommended LPS: class IV; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 30 × 15 + 6 × 6 × (30 + 15) + 9π × 6² = 3087.9 m²; N_D = 2 × 3087.9 × 0.5 × 1e-6 = 0.003088/yr; R_A = N_D × 0.01 × 0.01 = 3.088e-07, R_B = N_D × 0.1 × 0.1 = 3.088e-05, P_C = 1 − (1 − 0.02 × 1)^1 = 0.02 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.02, Table B.3); R_C = N_D × 0.02 × 0.01 = 6.176e-07; R1 = 3.181e-05 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): IV, residual R1 = 7.102e-06; rolling sphere 60 m, mesh 20 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-lpl-iv-selected`)

Example 5 — Bonded building needing class III

The same protection measures on a larger building: class IV is not enough and class III (P_B × 0.1) is selected.

Given: Structure 40 × 20 × 10 m (L × W × H), ground flash density N_G = 2 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof and structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: equipotential bonding; surge protection: coordinated SPDs for LPL II; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 40 × 20 + 2 × 30 × (40 + 20) + π × 30² = 800.0 + 3,600.0 + 2,827.4 = 7,227.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 2 × 7,227.4 × 0.5 × 10⁻⁶ = 7.227 × 10⁻³ /yr
Probabilities	P_A = 0.01 (equipotential bonding); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.02 × 1)¹ = 0.02 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL II, P_SPD = 0.02, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 7.227 × 10⁻³ × 0.01 × 0.01 = 7.227 × 10⁻⁷; R_B = N_D·P_B·L_B = 7.227 × 10⁻³ × 0.1 × 0.1 = 7.227 × 10⁻⁵; R_C = N_D·P_C·L_C = 7.227 × 10⁻³ × 0.02 × 0.01 = 1.445 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 7.227 × 10⁻⁷ + 7.227 × 10⁻⁵ + 1.445 × 10⁻⁶ → 7.444 × 10⁻⁵ > R_T = 10⁻⁵/yr (744.4 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 7.227 × 10⁻⁵): class IV: 7.227 × 10⁻⁷ + 7.227 × 10⁻⁵ × 0.2 + 1.445 × 10⁻⁶ = 1.662 × 10⁻⁵ > R_T; class III: 7.227 × 10⁻⁷ + 7.227 × 10⁻⁵ × 0.1 + 1.445 × 10⁻⁶ = 9.396 × 10⁻⁶ ≤ R_T → class III; rolling sphere 45 m, mesh 15 × 15 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class III LPS → 9.396 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (94.0 %) PASS
Result	1/2 checks pass → FAIL; R₁ = 7.444 × 10⁻⁵/yr; recommended LPS: class III; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 40 × 20 + 6 × 10 × (40 + 20) + 9π × 10² = 7227.4 m²; N_D = 2 × 7227.4 × 0.5 × 1e-6 = 0.007227/yr; R_A = N_D × 0.01 × 0.01 = 7.227e-07, R_B = N_D × 0.1 × 0.1 = 7.227e-05, P_C = 1 − (1 − 0.02 × 1)^1 = 0.02 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.02, Table B.3); R_C = N_D × 0.02 × 0.01 = 1.445e-06; R1 = 7.444e-05 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): III, residual R1 = 9.396e-06; rolling sphere 45 m, mesh 15 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-lpl-iii-selected`)

Example 6 — Bonded building needing class II

Higher flash density (N_G 3) pushes the recommendation to class II (P_B × 0.05, 30 m rolling sphere).

Given: Structure 40 × 20 × 10 m (L × W × H), ground flash density N_G = 3 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof and structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: equipotential bonding; surge protection: coordinated SPDs for LPL II; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 40 × 20 + 2 × 30 × (40 + 20) + π × 30² = 800.0 + 3,600.0 + 2,827.4 = 7,227.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 3 × 7,227.4 × 0.5 × 10⁻⁶ = 0.01084 /yr
Probabilities	P_A = 0.01 (equipotential bonding); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.02 × 1)¹ = 0.02 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL II, P_SPD = 0.02, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 0.01084 × 0.01 × 0.01 = 1.084 × 10⁻⁶; R_B = N_D·P_B·L_B = 0.01084 × 0.1 × 0.1 = 1.084 × 10⁻⁴; R_C = N_D·P_C·L_C = 0.01084 × 0.02 × 0.01 = 2.168 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 1.084 × 10⁻⁶ + 1.084 × 10⁻⁴ + 2.168 × 10⁻⁶ → 1.117 × 10⁻⁴ > R_T = 10⁻⁵/yr (1,116.6 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 1.084 × 10⁻⁴): class IV: 1.084 × 10⁻⁶ + 1.084 × 10⁻⁴ × 0.2 + 2.168 × 10⁻⁶ = 2.493 × 10⁻⁵ > R_T; class III: 1.084 × 10⁻⁶ + 1.084 × 10⁻⁴ × 0.1 + 2.168 × 10⁻⁶ = 1.409 × 10⁻⁵ > R_T; class II: 1.084 × 10⁻⁶ + 1.084 × 10⁻⁴ × 0.05 + 2.168 × 10⁻⁶ = 8.673 × 10⁻⁶ ≤ R_T → class II; rolling sphere 30 m, mesh 10 × 10 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class II LPS → 8.673 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (86.7 %) PASS
Result	1/2 checks pass → FAIL; R₁ = 1.117 × 10⁻⁴/yr; recommended LPS: class II; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 40 × 20 + 6 × 10 × (40 + 20) + 9π × 10² = 7227.4 m²; N_D = 3 × 7227.4 × 0.5 × 1e-6 = 0.01084/yr; R_A = N_D × 0.01 × 0.01 = 1.084e-06, R_B = N_D × 0.1 × 0.1 = 0.0001084, P_C = 1 − (1 − 0.02 × 1)^1 = 0.02 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.02, Table B.3); R_C = N_D × 0.02 × 0.01 = 2.168e-06; R1 = 0.0001117 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): II, residual R1 = 8.673e-06; rolling sphere 30 m, mesh 10 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-lpl-ii-selected`)

Example 7 — Bonded building needing class I

At N_G 6 only a class I LPS (P_B × 0.02, 20 m sphere, 5 m mesh) brings R1 within R_T.

Given: Structure 40 × 20 × 10 m (L × W × H), ground flash density N_G = 6 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof and structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: electrical insulation; surge protection: coordinated SPDs for LPL I; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 40 × 20 + 2 × 30 × (40 + 20) + π × 30² = 800.0 + 3,600.0 + 2,827.4 = 7,227.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 6 × 7,227.4 × 0.5 × 10⁻⁶ = 0.02168 /yr
Probabilities	P_A = 0.01 (electrical insulation); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.01 × 1)¹ = 0.01 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL I, P_SPD = 0.01, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 0.02168 × 0.01 × 0.01 = 2.168 × 10⁻⁶; R_B = N_D·P_B·L_B = 0.02168 × 0.1 × 0.1 = 2.168 × 10⁻⁴; R_C = N_D·P_C·L_C = 0.02168 × 0.01 × 0.01 = 2.168 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 2.168 × 10⁻⁶ + 2.168 × 10⁻⁴ + 2.168 × 10⁻⁶ → 2.212 × 10⁻⁴ > R_T = 10⁻⁵/yr (2,211.6 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 2.168 × 10⁻⁴): class IV: 2.168 × 10⁻⁶ + 2.168 × 10⁻⁴ × 0.2 + 2.168 × 10⁻⁶ = 4.770 × 10⁻⁵ > R_T; class III: 2.168 × 10⁻⁶ + 2.168 × 10⁻⁴ × 0.1 + 2.168 × 10⁻⁶ = 2.602 × 10⁻⁵ > R_T; class II: 2.168 × 10⁻⁶ + 2.168 × 10⁻⁴ × 0.05 + 2.168 × 10⁻⁶ = 1.518 × 10⁻⁵ > R_T; class I: 2.168 × 10⁻⁶ + 2.168 × 10⁻⁴ × 0.02 + 2.168 × 10⁻⁶ = 8.673 × 10⁻⁶ ≤ R_T → class I; rolling sphere 20 m, mesh 5 × 5 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class I LPS → 8.673 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (86.7 %) PASS
Result	1/2 checks pass → FAIL; R₁ = 2.212 × 10⁻⁴/yr; recommended LPS: class I; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 40 × 20 + 6 × 10 × (40 + 20) + 9π × 10² = 7227.4 m²; N_D = 6 × 7227.4 × 0.5 × 1e-6 = 0.02168/yr; R_A = N_D × 0.01 × 0.01 = 2.168e-06, R_B = N_D × 0.1 × 0.1 = 0.0002168, P_C = 1 − (1 − 0.01 × 1)^1 = 0.01 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.01, Table B.3); R_C = N_D × 0.01 × 0.01 = 2.168e-06; R1 = 0.0002212 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): I, residual R1 = 8.673e-06; rolling sphere 20 m, mesh 5 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-lpl-i-selected`)

Example 8 — Existing class III LPS already adequate

An installed class III LPS reduces P_B to 0.01 and the building passes as it stands; no further LPS is recommended.

Given: Structure 40 × 20 × 10 m (L × W × H), ground flash density N_G = 2 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof and structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: equipotential bonding; surge protection: coordinated SPDs for LPL II; existing LPS: class III.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 40 × 20 + 2 × 30 × (40 + 20) + π × 30² = 800.0 + 3,600.0 + 2,827.4 = 7,227.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 2 × 7,227.4 × 0.5 × 10⁻⁶ = 7.227 × 10⁻³ /yr
Probabilities	P_A = 0.01 (equipotential bonding); P_B = 0.1 (non-metallic roof and structure) × 0.1 (existing class III LPS) = 0.01; P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.02 × 1)¹ = 0.02 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL II, P_SPD = 0.02, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 7.227 × 10⁻³ × 0.01 × 0.01 = 7.227 × 10⁻⁷; R_B = N_D·P_B·L_B = 7.227 × 10⁻³ × 0.01 × 0.1 = 7.227 × 10⁻⁶; R_C = N_D·P_C·L_C = 7.227 × 10⁻³ × 0.02 × 0.01 = 1.445 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 7.227 × 10⁻⁷ + 7.227 × 10⁻⁶ + 1.445 × 10⁻⁶ → 9.396 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (94.0 %) PASS
LPS selection	R₁ ≤ R_T: no (further) lightning protection system is required
Result	1/1 checks pass → PASS; R₁ = 9.396 × 10⁻⁶/yr; recommended LPS: none; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 40 × 20 + 6 × 10 × (40 + 20) + 9π × 10² = 7227.4 m²; N_D = 2 × 7227.4 × 0.5 × 1e-6 = 0.007227/yr; R_A = N_D × 0.01 × 0.01 = 7.227e-07, R_B = N_D × 0.01 × 0.1 = 7.227e-06, P_C = 1 − (1 − 0.02 × 1)^1 = 0.02 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.02, Table B.3); R_C = N_D × 0.02 × 0.01 = 1.445e-06; R1 = 9.396e-06 ≤ R_T 1e-5 (Table 4). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-existing-lps-iii-passes`)

Example 9 — Existing class IV LPS needs upgrading

An installed class IV LPS leaves R1 above R_T, so the tool recommends the class that does meet it.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 40 × 20 + 2 × 30 × (40 + 20) + π × 30² = 800.0 + 3,600.0 + 2,827.4 = 7,227.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 3 × 7,227.4 × 0.5 × 10⁻⁶ = 0.01084 /yr
Probabilities	P_A = 0.01 (equipotential bonding); P_B = 0.1 (non-metallic roof and structure) × 0.2 (existing class IV LPS) = 0.02; P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.02 × 1)¹ = 0.02 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL II, P_SPD = 0.02, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 0.01084 × 0.01 × 0.01 = 1.084 × 10⁻⁶; R_B = N_D·P_B·L_B = 0.01084 × 0.02 × 0.1 = 2.168 × 10⁻⁵; R_C = N_D·P_C·L_C = 0.01084 × 0.02 × 0.01 = 2.168 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 1.084 × 10⁻⁶ + 2.168 × 10⁻⁵ + 2.168 × 10⁻⁶ → 2.493 × 10⁻⁵ > R_T = 10⁻⁵/yr (249.3 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 1.084 × 10⁻⁴): class IV: 1.084 × 10⁻⁶ + 1.084 × 10⁻⁴ × 0.2 + 2.168 × 10⁻⁶ = 2.493 × 10⁻⁵ > R_T; class III: 1.084 × 10⁻⁶ + 1.084 × 10⁻⁴ × 0.1 + 2.168 × 10⁻⁶ = 1.409 × 10⁻⁵ > R_T; class II: 1.084 × 10⁻⁶ + 1.084 × 10⁻⁴ × 0.05 + 2.168 × 10⁻⁶ = 8.673 × 10⁻⁶ ≤ R_T → class II; rolling sphere 30 m, mesh 10 × 10 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class II LPS → 8.673 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (86.7 %) PASS
Result	1/2 checks pass → FAIL; R₁ = 2.493 × 10⁻⁵/yr; recommended LPS: class II; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 40 × 20 + 6 × 10 × (40 + 20) + 9π × 10² = 7227.4 m²; N_D = 3 × 7227.4 × 0.5 × 1e-6 = 0.01084/yr; R_A = N_D × 0.01 × 0.01 = 1.084e-06, R_B = N_D × 0.02 × 0.1 = 2.168e-05, P_C = 1 − (1 − 0.02 × 1)^1 = 0.02 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.02, Table B.3); R_C = N_D × 0.02 × 0.01 = 2.168e-06; R1 = 2.493e-05 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): II, residual R1 = 8.673e-06; rolling sphere 30 m, mesh 10 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-existing-lps-iv-upgrade`)

Example 10 — Isolated building (C_D 1)

An isolated structure with no neighbours (location 'moderate', C_D 1) doubles N_D compared with the 'flat' case.

Given: Structure 25 × 12 × 6 m (L × W × H), ground flash density N_G = 0.5 flashes/km²/yr, located isolated, no other objects nearby (moderate); non-metallic roof and structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: warning notices; surge protection: coordinated SPDs for LPL III–IV; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 25 × 12 + 2 × 18 × (25 + 12) + π × 18² = 300.0 + 1,332.0 + 1,017.9 = 2,649.9 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 0.5 × 2,649.9 × 1 × 10⁻⁶ = 1.325 × 10⁻³ /yr
Probabilities	P_A = 0.1 (warning notices); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.05 × 1)¹ = 0.05 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL III–IV, P_SPD = 0.05, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 1.325 × 10⁻³ × 0.1 × 0.01 = 1.325 × 10⁻⁶; R_B = N_D·P_B·L_B = 1.325 × 10⁻³ × 0.1 × 0.1 = 1.325 × 10⁻⁵; R_C = N_D·P_C·L_C = 1.325 × 10⁻³ × 0.05 × 0.01 = 6.625 × 10⁻⁷
R1 check	R₁ = R_A + R_B + R_C = 1.325 × 10⁻⁶ + 1.325 × 10⁻⁵ + 6.625 × 10⁻⁷ → 1.524 × 10⁻⁵ > R_T = 10⁻⁵/yr (152.4 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 1.325 × 10⁻⁵): class IV: 1.325 × 10⁻⁶ + 1.325 × 10⁻⁵ × 0.2 + 6.625 × 10⁻⁷ = 4.637 × 10⁻⁶ ≤ R_T → class IV; rolling sphere 60 m, mesh 20 × 20 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class IV LPS → 4.637 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (46.4 %) PASS
Result	1/2 checks pass → FAIL; R₁ = 1.524 × 10⁻⁵/yr; recommended LPS: class IV; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 25 × 12 + 6 × 6 × (25 + 12) + 9π × 6² = 2649.9 m²; N_D = 0.5 × 2649.9 × 1 × 1e-6 = 0.001325/yr; R_A = N_D × 0.1 × 0.01 = 1.325e-06, R_B = N_D × 0.1 × 0.1 = 1.325e-05, P_C = 1 − (1 − 0.05 × 1)^1 = 0.05 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.05, Table B.3); R_C = N_D × 0.05 × 0.01 = 6.625e-07; R1 = 1.524e-05 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): IV, residual R1 = 4.637e-06; rolling sphere 60 m, mesh 20 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-moderate-location`)

Example 11 — Small hut isolated on a hilltop (C_D 2)

An isolated structure on a hilltop or knoll takes C_D 2 (Table A.1), four times the 'flat' (same-height neighbours) value of 0.5 used by default.

Given: Structure 6 × 4 × 3 m (L × W × H), ground flash density N_G = 1 flashes/km²/yr, located isolated on a hilltop or knoll (exposed); metal roof on a metal structure, ordinary fire risk, occupied; internal systems: no connected lines (standard consequence); touch/step measures: electrical insulation; surge protection: no coordinated SPDs; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 6 × 4 + 2 × 9 × (6 + 4) + π × 9² = 24.0 + 180.0 + 254.5 = 458.5 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 1 × 458.5 × 2 × 10⁻⁶ = 9.169 × 10⁻⁴ /yr
Probabilities	P_A = 0.01 (electrical insulation); P_B = 0.001 (metal roof on a metal structure); P_C = 0 (no connected lines: C_LD = 0, Table B.4)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 9.169 × 10⁻⁴ × 0.01 × 0.01 = 9.169 × 10⁻⁸; R_B = N_D·P_B·L_B = 9.169 × 10⁻⁴ × 0.001 × 0.1 = 9.169 × 10⁻⁸; R_C = N_D·P_C·L_C = 9.169 × 10⁻⁴ × 0 × 0.01 = 0
R1 check	R₁ = R_A + R_B + R_C = 9.169 × 10⁻⁸ + 9.169 × 10⁻⁸ + 0 → 1.834 × 10⁻⁷ ≤ R_T = 10⁻⁵/yr (1.8 %) PASS
LPS selection	R₁ ≤ R_T: no (further) lightning protection system is required
Result	1/1 checks pass → PASS; R₁ = 1.834 × 10⁻⁷/yr; recommended LPS: none; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 6 × 4 + 6 × 3 × (6 + 4) + 9π × 3² = 458.5 m²; N_D = 1 × 458.5 × 2 × 1e-6 = 0.0009169/yr; R_A = N_D × 0.01 × 0.01 = 9.169e-08, R_B = N_D × 0.001 × 0.1 = 9.169e-08, P_C = 0 (no connected line, C_LD = 0, Table B.4); R_C = N_D × 0 × 0.01 = 0; R1 = 1.834e-07 ≤ R_T 1e-5 (Table 4). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-hilltop-hut`)

Example 12 — Metal roof and metal frame

A metal-clad steel-frame building has P_B 0.001, so R_B is negligible and the building passes without an LPS.

Given: Structure 60 × 30 × 12 m (L × W × H), ground flash density N_G = 2 flashes/km²/yr, located among objects of the same height or smaller (flat); metal roof on a metal structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: electrical insulation; surge protection: coordinated SPDs for LPL II; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 60 × 30 + 2 × 36 × (60 + 30) + π × 36² = 1,800.0 + 6,480.0 + 4,071.5 = 12,351.5 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 2 × 12,351.5 × 0.5 × 10⁻⁶ = 0.01235 /yr
Probabilities	P_A = 0.01 (electrical insulation); P_B = 0.001 (metal roof on a metal structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.02 × 1)¹ = 0.02 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL II, P_SPD = 0.02, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 0.01235 × 0.01 × 0.01 = 1.235 × 10⁻⁶; R_B = N_D·P_B·L_B = 0.01235 × 0.001 × 0.1 = 1.235 × 10⁻⁶; R_C = N_D·P_C·L_C = 0.01235 × 0.02 × 0.01 = 2.470 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 1.235 × 10⁻⁶ + 1.235 × 10⁻⁶ + 2.470 × 10⁻⁶ → 4.941 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (49.4 %) PASS
LPS selection	R₁ ≤ R_T: no (further) lightning protection system is required
Result	1/1 checks pass → PASS; R₁ = 4.941 × 10⁻⁶/yr; recommended LPS: none; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 60 × 30 + 6 × 12 × (60 + 30) + 9π × 12² = 12351.5 m²; N_D = 2 × 12351.5 × 0.5 × 1e-6 = 0.01235/yr; R_A = N_D × 0.01 × 0.01 = 1.235e-06, R_B = N_D × 0.001 × 0.1 = 1.235e-06, P_C = 1 − (1 − 0.02 × 1)^1 = 0.02 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.02, Table B.3); R_C = N_D × 0.02 × 0.01 = 2.47e-06; R1 = 4.941e-06 ≤ R_T 1e-5 (Table 4). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-metal-structure`)

Example 13 — Non-metal roof on a metal frame

P_B 0.01 for a non-metallic roof on a steel frame: R1 is above R_T and a class IV LPS is enough.

Given: Structure 60 × 30 × 12 m (L × W × H), ground flash density N_G = 3 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof on a metal structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: electrical insulation; surge protection: coordinated SPDs for LPL II; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 60 × 30 + 2 × 36 × (60 + 30) + π × 36² = 1,800.0 + 6,480.0 + 4,071.5 = 12,351.5 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 3 × 12,351.5 × 0.5 × 10⁻⁶ = 0.01853 /yr
Probabilities	P_A = 0.01 (electrical insulation); P_B = 0.01 (non-metallic roof on a metal structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.02 × 1)¹ = 0.02 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL II, P_SPD = 0.02, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 0.01853 × 0.01 × 0.01 = 1.853 × 10⁻⁶; R_B = N_D·P_B·L_B = 0.01853 × 0.01 × 0.1 = 1.853 × 10⁻⁵; R_C = N_D·P_C·L_C = 0.01853 × 0.02 × 0.01 = 3.705 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 1.853 × 10⁻⁶ + 1.853 × 10⁻⁵ + 3.705 × 10⁻⁶ → 2.409 × 10⁻⁵ > R_T = 10⁻⁵/yr (240.9 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 1.853 × 10⁻⁵): class IV: 1.853 × 10⁻⁶ + 1.853 × 10⁻⁵ × 0.2 + 3.705 × 10⁻⁶ = 9.264 × 10⁻⁶ ≤ R_T → class IV; rolling sphere 60 m, mesh 20 × 20 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class IV LPS → 9.264 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (92.6 %) PASS
Result	1/2 checks pass → FAIL; R₁ = 2.409 × 10⁻⁵/yr; recommended LPS: class IV; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 60 × 30 + 6 × 12 × (60 + 30) + 9π × 12² = 12351.5 m²; N_D = 3 × 12351.5 × 0.5 × 1e-6 = 0.01853/yr; R_A = N_D × 0.01 × 0.01 = 1.853e-06, R_B = N_D × 0.01 × 0.1 = 1.853e-05, P_C = 1 − (1 − 0.02 × 1)^1 = 0.02 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.02, Table B.3); R_C = N_D × 0.02 × 0.01 = 3.705e-06; R1 = 2.409e-05 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): IV, residual R1 = 9.264e-06; rolling sphere 60 m, mesh 20 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-non-metal-roof-metal-frame`)

Example 14 — Thatched-roof cottage

A thatched roof (P_B 0.3) makes R_B dominant even on a small house; the LPS class follows from R_B alone.

Given: Structure 12 × 8 × 6 m (L × W × H), ground flash density N_G = 2 flashes/km²/yr, located isolated, no other objects nearby (moderate); thatched roof, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: warning notices; surge protection: coordinated SPDs for LPL II; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 12 × 8 + 2 × 18 × (12 + 8) + π × 18² = 96.0 + 720.0 + 1,017.9 = 1,833.9 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 2 × 1,833.9 × 1 × 10⁻⁶ = 3.668 × 10⁻³ /yr
Probabilities	P_A = 0.1 (warning notices); P_B = 0.3 (thatched roof); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.02 × 1)¹ = 0.02 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL II, P_SPD = 0.02, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 3.668 × 10⁻³ × 0.1 × 0.01 = 3.668 × 10⁻⁶; R_B = N_D·P_B·L_B = 3.668 × 10⁻³ × 0.3 × 0.1 = 1.100 × 10⁻⁴; R_C = N_D·P_C·L_C = 3.668 × 10⁻³ × 0.02 × 0.01 = 7.336 × 10⁻⁷
R1 check	R₁ = R_A + R_B + R_C = 3.668 × 10⁻⁶ + 1.100 × 10⁻⁴ + 7.336 × 10⁻⁷ → 1.144 × 10⁻⁴ > R_T = 10⁻⁵/yr (1,144.3 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 1.100 × 10⁻⁴): class IV: 3.668 × 10⁻⁶ + 1.100 × 10⁻⁴ × 0.2 + 7.336 × 10⁻⁷ = 2.641 × 10⁻⁵ > R_T; class III: 3.668 × 10⁻⁶ + 1.100 × 10⁻⁴ × 0.1 + 7.336 × 10⁻⁷ = 1.540 × 10⁻⁵ > R_T; class II: 3.668 × 10⁻⁶ + 1.100 × 10⁻⁴ × 0.05 + 7.336 × 10⁻⁷ = 9.903 × 10⁻⁶ ≤ R_T → class II; rolling sphere 30 m, mesh 10 × 10 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class II LPS → 9.903 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (99.0 %) PASS
Result	1/2 checks pass → FAIL; R₁ = 1.144 × 10⁻⁴/yr; recommended LPS: class II; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 12 × 8 + 6 × 6 × (12 + 8) + 9π × 6² = 1833.9 m²; N_D = 2 × 1833.9 × 1 × 1e-6 = 0.003668/yr; R_A = N_D × 0.1 × 0.01 = 3.668e-06, R_B = N_D × 0.3 × 0.1 = 0.00011, P_C = 1 − (1 − 0.02 × 1)^1 = 0.02 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.02, Table B.3); R_C = N_D × 0.02 × 0.01 = 7.336e-07; R1 = 0.0001144 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): II, residual R1 = 9.903e-06; rolling sphere 30 m, mesh 10 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-thatched-roof`)

Example 15 — High-occupancy hall

High occupancy raises L_A to 0.1; warning notices (P_A 0.1) are not enough to keep R_A within R_T.

Given: Structure 50 × 30 × 12 m (L × W × H), ground flash density N_G = 1.5 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof and structure, ordinary fire risk, high occupancy; internal systems: LV power line (standard consequence); touch/step measures: warning notices; surge protection: coordinated SPDs for LPL II; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 50 × 30 + 2 × 36 × (50 + 30) + π × 36² = 1,500.0 + 5,760.0 + 4,071.5 = 11,331.5 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 1.5 × 11,331.5 × 0.5 × 10⁻⁶ = 8.499 × 10⁻³ /yr
Probabilities	P_A = 0.1 (warning notices); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.02 × 1)¹ = 0.02 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL II, P_SPD = 0.02, Table B.3)
Losses	L_A = 0.1 (high occupancy); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 8.499 × 10⁻³ × 0.1 × 0.1 = 8.499 × 10⁻⁵; R_B = N_D·P_B·L_B = 8.499 × 10⁻³ × 0.1 × 0.1 = 8.499 × 10⁻⁵; R_C = N_D·P_C·L_C = 8.499 × 10⁻³ × 0.02 × 0.01 = 1.700 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 8.499 × 10⁻⁵ + 8.499 × 10⁻⁵ + 1.700 × 10⁻⁶ → 1.717 × 10⁻⁴ > R_T = 10⁻⁵/yr (1,716.7 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 8.499 × 10⁻⁵): class IV: 8.499 × 10⁻⁵ + 8.499 × 10⁻⁵ × 0.2 + 1.700 × 10⁻⁶ = 1.037 × 10⁻⁴ > R_T; class III: 8.499 × 10⁻⁵ + 8.499 × 10⁻⁵ × 0.1 + 1.700 × 10⁻⁶ = 9.518 × 10⁻⁵ > R_T; class II: 8.499 × 10⁻⁵ + 8.499 × 10⁻⁵ × 0.05 + 1.700 × 10⁻⁶ = 9.094 × 10⁻⁵ > R_T; class I: 8.499 × 10⁻⁵ + 8.499 × 10⁻⁵ × 0.02 + 1.700 × 10⁻⁶ = 8.839 × 10⁻⁵ > R_T — no class achieves R_T, class I recommended as the ceiling; rolling sphere 20 m, mesh 5 × 5 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class I LPS → 8.839 × 10⁻⁵ > R_T = 10⁻⁵/yr (883.9 %) FAIL
Result	0/2 checks pass → FAIL; R₁ = 1.717 × 10⁻⁴/yr; recommended LPS: class I; governing: risk r1 with recommended lps. Even an LPS of class I leaves R1 = 8.84e-05 > 1e-05; the remaining risk is dominated by RA, which an LPS does not reduce in this engine — add touch/step protection measures (RA) or coordinated SPDs (RC).
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 50 × 30 + 6 × 12 × (50 + 30) + 9π × 12² = 11331.5 m²; N_D = 1.5 × 11331.5 × 0.5 × 1e-6 = 0.008499/yr; R_A = N_D × 0.1 × 0.1 = 8.499e-05, R_B = N_D × 0.1 × 0.1 = 8.499e-05, P_C = 1 − (1 − 0.02 × 1)^1 = 0.02 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.02, Table B.3); R_C = N_D × 0.02 × 0.01 = 1.7e-06; R1 = 0.0001717 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): I (none suffices, I is the ceiling), residual R1 = 8.839e-05; rolling sphere 20 m, mesh 5 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-high-occupancy`)

Example 16 — Structure with no fire risk

L_B 0 removes R_B entirely, so R1 = R_A + R_C stays above R_T and the recommended class I LPS cannot change it.

Given: Structure 80 × 40 × 15 m (L × W × H), ground flash density N_G = 4 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof and structure, no fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: electrical insulation; surge protection: coordinated SPDs for LPL III–IV; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 80 × 40 + 2 × 45 × (80 + 40) + π × 45² = 3,200.0 + 10,800.0 + 6,361.7 = 20,361.7 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 4 × 20,361.7 × 0.5 × 10⁻⁶ = 0.04072 /yr
Probabilities	P_A = 0.01 (electrical insulation); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.05 × 1)¹ = 0.05 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL III–IV, P_SPD = 0.05, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0 (no fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 0.04072 × 0.01 × 0.01 = 4.072 × 10⁻⁶; R_B = N_D·P_B·L_B = 0.04072 × 0.1 × 0 = 0; R_C = N_D·P_C·L_C = 0.04072 × 0.05 × 0.01 = 2.036 × 10⁻⁵
R1 check	R₁ = R_A + R_B + R_C = 4.072 × 10⁻⁶ + 0 + 2.036 × 10⁻⁵ → 2.443 × 10⁻⁵ > R_T = 10⁻⁵/yr (244.3 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 0): class IV: 4.072 × 10⁻⁶ + 0 × 0.2 + 2.036 × 10⁻⁵ = 2.443 × 10⁻⁵ > R_T; class III: 4.072 × 10⁻⁶ + 0 × 0.1 + 2.036 × 10⁻⁵ = 2.443 × 10⁻⁵ > R_T; class II: 4.072 × 10⁻⁶ + 0 × 0.05 + 2.036 × 10⁻⁵ = 2.443 × 10⁻⁵ > R_T; class I: 4.072 × 10⁻⁶ + 0 × 0.02 + 2.036 × 10⁻⁵ = 2.443 × 10⁻⁵ > R_T — no class achieves R_T, class I recommended as the ceiling; rolling sphere 20 m, mesh 5 × 5 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class I LPS → 2.443 × 10⁻⁵ > R_T = 10⁻⁵/yr (244.3 %) FAIL
Result	0/2 checks pass → FAIL; R₁ = 2.443 × 10⁻⁵/yr; recommended LPS: class I; governing: risk r1 with recommended lps. Even an LPS of class I leaves R1 = 2.44e-05 > 1e-05; the remaining risk is dominated by RC, which an LPS does not reduce in this engine — add touch/step protection measures (RA) or coordinated SPDs (RC).
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 80 × 40 + 6 × 15 × (80 + 40) + 9π × 15² = 20361.7 m²; N_D = 4 × 20361.7 × 0.5 × 1e-6 = 0.04072/yr; R_A = N_D × 0.01 × 0.01 = 4.072e-06, R_B = N_D × 0.1 × 0 = 0, P_C = 1 − (1 − 0.05 × 1)^1 = 0.05 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.05, Table B.3); R_C = N_D × 0.05 × 0.01 = 2.036e-05; R1 = 2.443e-05 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): I (none suffices, I is the ceiling), residual R1 = 2.443e-05; rolling sphere 20 m, mesh 5 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-no-fire-risk`)

Example 17 — Explosion-risk process building

L_B 1 for explosion risk on a steel-framed building (P_B 0.01): class II leaves R1 above R_T and class I is required.

Given: Structure 30 × 20 × 10 m (L × W × H), ground flash density N_G = 7 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof on a metal structure, explosion risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: equipotential bonding; surge protection: coordinated SPDs for LPL I; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 30 × 20 + 2 × 30 × (30 + 20) + π × 30² = 600.0 + 3,000.0 + 2,827.4 = 6,427.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 7 × 6,427.4 × 0.5 × 10⁻⁶ = 0.0225 /yr
Probabilities	P_A = 0.01 (equipotential bonding); P_B = 0.01 (non-metallic roof on a metal structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.01 × 1)¹ = 0.01 (LV power line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL I, P_SPD = 0.01, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 1 (explosion risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 0.0225 × 0.01 × 0.01 = 2.250 × 10⁻⁶; R_B = N_D·P_B·L_B = 0.0225 × 0.01 × 1 = 2.250 × 10⁻⁴; R_C = N_D·P_C·L_C = 0.0225 × 0.01 × 0.01 = 2.250 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 2.250 × 10⁻⁶ + 2.250 × 10⁻⁴ + 2.250 × 10⁻⁶ → 2.295 × 10⁻⁴ > R_T = 10⁻⁵/yr (2,294.6 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 2.250 × 10⁻⁴): class IV: 2.250 × 10⁻⁶ + 2.250 × 10⁻⁴ × 0.2 + 2.250 × 10⁻⁶ = 4.949 × 10⁻⁵ > R_T; class III: 2.250 × 10⁻⁶ + 2.250 × 10⁻⁴ × 0.1 + 2.250 × 10⁻⁶ = 2.700 × 10⁻⁵ > R_T; class II: 2.250 × 10⁻⁶ + 2.250 × 10⁻⁴ × 0.05 + 2.250 × 10⁻⁶ = 1.575 × 10⁻⁵ > R_T; class I: 2.250 × 10⁻⁶ + 2.250 × 10⁻⁴ × 0.02 + 2.250 × 10⁻⁶ = 8.998 × 10⁻⁶ ≤ R_T → class I; rolling sphere 20 m, mesh 5 × 5 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class I LPS → 8.998 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (90.0 %) PASS
Result	1/2 checks pass → FAIL; R₁ = 2.295 × 10⁻⁴/yr; recommended LPS: class I; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 30 × 20 + 6 × 10 × (30 + 20) + 9π × 10² = 6427.4 m²; N_D = 7 × 6427.4 × 0.5 × 1e-6 = 0.0225/yr; R_A = N_D × 0.01 × 0.01 = 2.25e-06, R_B = N_D × 0.01 × 1 = 0.000225, P_C = 1 − (1 − 0.01 × 1)^1 = 0.01 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.01, Table B.3); R_C = N_D × 0.01 × 0.01 = 2.25e-06; R1 = 0.0002295 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): I, residual R1 = 8.998e-06; rolling sphere 20 m, mesh 5 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-explosion-risk`)

Example 18 — Telecom equipment with critical consequence

One unshielded telecom line with no SPDs (P_C 1) and a critical failure consequence (L_C 0.1): R_C dominates and an LPS cannot fix it.

Given: Structure 20 × 10 × 4 m (L × W × H), ground flash density N_G = 6 flashes/km²/yr, located surrounded by higher objects; metal roof on a metal structure, ordinary fire risk, occupied; internal systems: telecom line (critical consequence); touch/step measures: electrical insulation; surge protection: no coordinated SPDs; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 20 × 10 + 2 × 12 × (20 + 10) + π × 12² = 200.0 + 720.0 + 452.4 = 1,372.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 6 × 1,372.4 × 0.25 × 10⁻⁶ = 2.059 × 10⁻³ /yr
Probabilities	P_A = 0.01 (electrical insulation); P_B = 0.001 (metal roof on a metal structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 1 × 1)¹ = 1 (telecom line, n = 1, unshielded C_LD = 1; no coordinated SPDs, P_SPD = 1, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.1 (critical consequence)
Risk components	R_A = N_D·P_A·L_A = 2.059 × 10⁻³ × 0.01 × 0.01 = 2.059 × 10⁻⁷; R_B = N_D·P_B·L_B = 2.059 × 10⁻³ × 0.001 × 0.1 = 2.059 × 10⁻⁷; R_C = N_D·P_C·L_C = 2.059 × 10⁻³ × 1 × 0.1 = 2.059 × 10⁻⁴
R1 check	R₁ = R_A + R_B + R_C = 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ + 2.059 × 10⁻⁴ → 2.063 × 10⁻⁴ > R_T = 10⁻⁵/yr (2,062.7 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 2.059 × 10⁻⁷): class IV: 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ × 0.2 + 2.059 × 10⁻⁴ = 2.061 × 10⁻⁴ > R_T; class III: 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ × 0.1 + 2.059 × 10⁻⁴ = 2.061 × 10⁻⁴ > R_T; class II: 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ × 0.05 + 2.059 × 10⁻⁴ = 2.061 × 10⁻⁴ > R_T; class I: 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ × 0.02 + 2.059 × 10⁻⁴ = 2.061 × 10⁻⁴ > R_T — no class achieves R_T, class I recommended as the ceiling; rolling sphere 20 m, mesh 5 × 5 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class I LPS → 2.061 × 10⁻⁴ > R_T = 10⁻⁵/yr (2,060.7 %) FAIL
Result	0/2 checks pass → FAIL; R₁ = 2.063 × 10⁻⁴/yr; recommended LPS: class I; governing: risk r1 with recommended lps. Even an LPS of class I leaves R1 = 0.000206 > 1e-05; the remaining risk is dominated by RC, which an LPS does not reduce in this engine — add touch/step protection measures (RA) or coordinated SPDs (RC).
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 20 × 10 + 6 × 4 × (20 + 10) + 9π × 4² = 1372.4 m²; N_D = 6 × 1372.4 × 0.25 × 1e-6 = 0.002059/yr; R_A = N_D × 0.01 × 0.01 = 2.059e-07, R_B = N_D × 0.001 × 0.1 = 2.059e-07, P_C = 1 − (1 − 1 × 1)^1 = 1 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 1, Table B.3); R_C = N_D × 1 × 0.1 = 0.0002059; R1 = 0.0002063 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): I (none suffices, I is the ceiling), residual R1 = 0.0002061; rolling sphere 20 m, mesh 5 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-telecom-critical`)

Example 19 — Same telecom building with LPL III–IV SPDs

SPDs designed for LPL III–IV (P_SPD 0.05, Table B.3) leave R_C = N_D × 0.05 × 0.1 just above R_T; an LPS cannot remove it, so better-coordinated SPDs are needed.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 20 × 10 + 2 × 12 × (20 + 10) + π × 12² = 200.0 + 720.0 + 452.4 = 1,372.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 6 × 1,372.4 × 0.25 × 10⁻⁶ = 2.059 × 10⁻³ /yr
Probabilities	P_A = 0.01 (electrical insulation); P_B = 0.001 (metal roof on a metal structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.05 × 1)¹ = 0.05 (telecom line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL III–IV, P_SPD = 0.05, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.1 (critical consequence)
Risk components	R_A = N_D·P_A·L_A = 2.059 × 10⁻³ × 0.01 × 0.01 = 2.059 × 10⁻⁷; R_B = N_D·P_B·L_B = 2.059 × 10⁻³ × 0.001 × 0.1 = 2.059 × 10⁻⁷; R_C = N_D·P_C·L_C = 2.059 × 10⁻³ × 0.05 × 0.1 = 1.029 × 10⁻⁵
R1 check	R₁ = R_A + R_B + R_C = 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ + 1.029 × 10⁻⁵ → 1.070 × 10⁻⁵ > R_T = 10⁻⁵/yr (107.0 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 2.059 × 10⁻⁷): class IV: 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ × 0.2 + 1.029 × 10⁻⁵ = 1.054 × 10⁻⁵ > R_T; class III: 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ × 0.1 + 1.029 × 10⁻⁵ = 1.052 × 10⁻⁵ > R_T; class II: 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ × 0.05 + 1.029 × 10⁻⁵ = 1.051 × 10⁻⁵ > R_T; class I: 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ × 0.02 + 1.029 × 10⁻⁵ = 1.050 × 10⁻⁵ > R_T — no class achieves R_T, class I recommended as the ceiling; rolling sphere 20 m, mesh 5 × 5 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class I LPS → 1.050 × 10⁻⁵ > R_T = 10⁻⁵/yr (105.0 %) FAIL
Result	0/2 checks pass → FAIL; R₁ = 1.070 × 10⁻⁵/yr; recommended LPS: class I; governing: risk r1 with recommended lps. Even an LPS of class I leaves R1 = 1.05e-05 > 1e-05; the remaining risk is dominated by RC, which an LPS does not reduce in this engine — add touch/step protection measures (RA) or coordinated SPDs (RC).
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 20 × 10 + 6 × 4 × (20 + 10) + 9π × 4² = 1372.4 m²; N_D = 6 × 1372.4 × 0.25 × 1e-6 = 0.002059/yr; R_A = N_D × 0.01 × 0.01 = 2.059e-07, R_B = N_D × 0.001 × 0.1 = 2.059e-07, P_C = 1 − (1 − 0.05 × 1)^1 = 0.05 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.05, Table B.3); R_C = N_D × 0.05 × 0.1 = 1.029e-05; R1 = 1.07e-05 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): I (none suffices, I is the ceiling), residual R1 = 1.05e-05; rolling sphere 20 m, mesh 5 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-telecom-critical-spd1`)

Example 20 — Same telecom building with SPD level 3

Coordinated SPDs designed for LPL I (P_SPD 0.01, Table B.3) cut P_C to 0.01 and the building passes.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 20 × 10 + 2 × 12 × (20 + 10) + π × 12² = 200.0 + 720.0 + 452.4 = 1,372.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 6 × 1,372.4 × 0.25 × 10⁻⁶ = 2.059 × 10⁻³ /yr
Probabilities	P_A = 0.01 (electrical insulation); P_B = 0.001 (metal roof on a metal structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.01 × 1)¹ = 0.01 (telecom line, n = 1, unshielded C_LD = 1; coordinated SPDs for LPL I, P_SPD = 0.01, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.1 (critical consequence)
Risk components	R_A = N_D·P_A·L_A = 2.059 × 10⁻³ × 0.01 × 0.01 = 2.059 × 10⁻⁷; R_B = N_D·P_B·L_B = 2.059 × 10⁻³ × 0.001 × 0.1 = 2.059 × 10⁻⁷; R_C = N_D·P_C·L_C = 2.059 × 10⁻³ × 0.01 × 0.1 = 2.059 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 2.059 × 10⁻⁷ + 2.059 × 10⁻⁷ + 2.059 × 10⁻⁶ → 2.470 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (24.7 %) PASS
LPS selection	R₁ ≤ R_T: no (further) lightning protection system is required
Result	1/1 checks pass → PASS; R₁ = 2.470 × 10⁻⁶/yr; recommended LPS: none; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 20 × 10 + 6 × 4 × (20 + 10) + 9π × 4² = 1372.4 m²; N_D = 6 × 1372.4 × 0.25 × 1e-6 = 0.002059/yr; R_A = N_D × 0.01 × 0.01 = 2.059e-07, R_B = N_D × 0.001 × 0.1 = 2.059e-07, P_C = 1 − (1 − 0.01 × 1)^1 = 0.01 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.01, Table B.3); R_C = N_D × 0.01 × 0.1 = 2.059e-06; R1 = 2.47e-06 ≤ R_T 1e-5 (Table 4). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-telecom-critical-spd3`)

Example 21 — LV and telecom lines combined

Two connected lines with LPL II SPDs: P_C = 1 − (1 − 0.02)² = 0.0396, almost twice the single-line 0.02 — adding a line raises the internal-systems risk; R1 still meets R_T.

Given: Structure 40 × 20 × 10 m (L × W × H), ground flash density N_G = 2 flashes/km²/yr, located among objects of the same height or smaller (flat); metal roof on a metal structure, ordinary fire risk, occupied; internal systems: LV power and telecom lines (standard consequence); touch/step measures: equipotential bonding; surge protection: coordinated SPDs for LPL II; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 40 × 20 + 2 × 30 × (40 + 20) + π × 30² = 800.0 + 3,600.0 + 2,827.4 = 7,227.4 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 2 × 7,227.4 × 0.5 × 10⁻⁶ = 7.227 × 10⁻³ /yr
Probabilities	P_A = 0.01 (equipotential bonding); P_B = 0.001 (metal roof on a metal structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 0.02 × 1)² = 0.0396 (LV power and telecom lines, n = 2, unshielded C_LD = 1; coordinated SPDs for LPL II, P_SPD = 0.02, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 7.227 × 10⁻³ × 0.01 × 0.01 = 7.227 × 10⁻⁷; R_B = N_D·P_B·L_B = 7.227 × 10⁻³ × 0.001 × 0.1 = 7.227 × 10⁻⁷; R_C = N_D·P_C·L_C = 7.227 × 10⁻³ × 0.0396 × 0.01 = 2.862 × 10⁻⁶
R1 check	R₁ = R_A + R_B + R_C = 7.227 × 10⁻⁷ + 7.227 × 10⁻⁷ + 2.862 × 10⁻⁶ → 4.308 × 10⁻⁶ ≤ R_T = 10⁻⁵/yr (43.1 %) PASS
LPS selection	R₁ ≤ R_T: no (further) lightning protection system is required
Result	1/1 checks pass → PASS; R₁ = 4.308 × 10⁻⁶/yr; recommended LPS: none; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 40 × 20 + 6 × 10 × (40 + 20) + 9π × 10² = 7227.4 m²; N_D = 2 × 7227.4 × 0.5 × 1e-6 = 0.007227/yr; R_A = N_D × 0.01 × 0.01 = 7.227e-07, R_B = N_D × 0.001 × 0.1 = 7.227e-07, P_C = 1 − (1 − 0.02 × 1)^2 = 0.0396 (2 unshielded line(s), C_LD = 1, Table B.4; P_SPD 0.02, Table B.3); R_C = N_D × 0.0396 × 0.01 = 2.862e-06; R1 = 4.308e-06 ≤ R_T 1e-5 (Table 4). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-lv-and-telecom-spd2-combined`)

Example 22 — LV + telecom with no life consequence

LV and telecom lines without SPDs give P_C = 1, but no consequence of failure (L_C 0) makes R_C = 0.

Given: Structure 30 × 20 × 8 m (L × W × H), ground flash density N_G = 2 flashes/km²/yr, located among objects of the same height or smaller (flat); metal roof on a metal structure, ordinary fire risk, occupied; internal systems: LV power and telecom lines (no consequence for life); touch/step measures: equipotential bonding; surge protection: no coordinated SPDs; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 30 × 20 + 2 × 24 × (30 + 20) + π × 24² = 600.0 + 2,400.0 + 1,809.6 = 4,809.6 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 2 × 4,809.6 × 0.5 × 10⁻⁶ = 4.810 × 10⁻³ /yr
Probabilities	P_A = 0.01 (equipotential bonding); P_B = 0.001 (metal roof on a metal structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 1 × 1)² = 1 (LV power and telecom lines, n = 2, unshielded C_LD = 1; no coordinated SPDs, P_SPD = 1, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0 (no consequence for life)
Risk components	R_A = N_D·P_A·L_A = 4.810 × 10⁻³ × 0.01 × 0.01 = 4.810 × 10⁻⁷; R_B = N_D·P_B·L_B = 4.810 × 10⁻³ × 0.001 × 0.1 = 4.810 × 10⁻⁷; R_C = N_D·P_C·L_C = 4.810 × 10⁻³ × 1 × 0 = 0
R1 check	R₁ = R_A + R_B + R_C = 4.810 × 10⁻⁷ + 4.810 × 10⁻⁷ + 0 → 9.619 × 10⁻⁷ ≤ R_T = 10⁻⁵/yr (9.6 %) PASS
LPS selection	R₁ ≤ R_T: no (further) lightning protection system is required
Result	1/1 checks pass → PASS; R₁ = 9.619 × 10⁻⁷/yr; recommended LPS: none; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 30 × 20 + 6 × 8 × (30 + 20) + 9π × 8² = 4809.6 m²; N_D = 2 × 4809.6 × 0.5 × 1e-6 = 0.00481/yr; R_A = N_D × 0.01 × 0.01 = 4.81e-07, R_B = N_D × 0.001 × 0.1 = 4.81e-07, P_C = 1 − (1 − 1 × 1)^2 = 1 (2 unshielded line(s), C_LD = 1, Table B.4; P_SPD 1, Table B.3); R_C = N_D × 1 × 0 = 0; R1 = 9.619e-07 ≤ R_T 1e-5 (Table 4). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-lv-and-telecom-no-consequence`)

Example 23 — No connected service lines

A stand-alone shed with no incoming lines has C_LD 0 (Table B.4), so P_C = 0 and R_C = 0 even without SPDs.

Given: Structure 8 × 6 × 3 m (L × W × H), ground flash density N_G = 3 flashes/km²/yr, located among objects of the same height or smaller (flat); metal roof on a metal structure, ordinary fire risk, occupied; internal systems: no connected lines (standard consequence); touch/step measures: electrical insulation; surge protection: no coordinated SPDs; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 8 × 6 + 2 × 9 × (8 + 6) + π × 9² = 48.0 + 252.0 + 254.5 = 554.5 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 3 × 554.5 × 0.5 × 10⁻⁶ = 8.317 × 10⁻⁴ /yr
Probabilities	P_A = 0.01 (electrical insulation); P_B = 0.001 (metal roof on a metal structure); P_C = 0 (no connected lines: C_LD = 0, Table B.4)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 8.317 × 10⁻⁴ × 0.01 × 0.01 = 8.317 × 10⁻⁸; R_B = N_D·P_B·L_B = 8.317 × 10⁻⁴ × 0.001 × 0.1 = 8.317 × 10⁻⁸; R_C = N_D·P_C·L_C = 8.317 × 10⁻⁴ × 0 × 0.01 = 0
R1 check	R₁ = R_A + R_B + R_C = 8.317 × 10⁻⁸ + 8.317 × 10⁻⁸ + 0 → 1.663 × 10⁻⁷ ≤ R_T = 10⁻⁵/yr (1.7 %) PASS
LPS selection	R₁ ≤ R_T: no (further) lightning protection system is required
Result	1/1 checks pass → PASS; R₁ = 1.663 × 10⁻⁷/yr; recommended LPS: none; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 8 × 6 + 6 × 3 × (8 + 6) + 9π × 3² = 554.5 m²; N_D = 3 × 554.5 × 0.5 × 1e-6 = 0.0008317/yr; R_A = N_D × 0.01 × 0.01 = 8.317e-08, R_B = N_D × 0.001 × 0.1 = 8.317e-08, P_C = 0 (no connected line, C_LD = 0, Table B.4); R_C = N_D × 0 × 0.01 = 0; R1 = 1.663e-07 ≤ R_T 1e-5 (Table 4). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-no-internal-systems`)

Example 24 — 300 m tower on a hilltop

At the 300 m height limit the 3H collection radius dominates (A_D ≈ 2.6 km²): dozens of flashes a year, so class I is recommended and R_A and R_C still exceed R_T.

Given: Structure 20 × 20 × 300 m (L × W × H), ground flash density N_G = 2 flashes/km²/yr, located isolated on a hilltop or knoll (exposed); metal roof on a metal structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: none; surge protection: no coordinated SPDs; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 20 × 20 + 2 × 900 × (20 + 20) + π × 900² = 400.0 + 72,000.0 + 2,544,690.0 = 2,617,090.0 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 2 × 2,617,090.0 × 2 × 10⁻⁶ = 10.47 /yr
Probabilities	P_A = 1 (none); P_B = 0.001 (metal roof on a metal structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 1 × 1)¹ = 1 (LV power line, n = 1, unshielded C_LD = 1; no coordinated SPDs, P_SPD = 1, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 10.47 × 1 × 0.01 = 0.1047; R_B = N_D·P_B·L_B = 10.47 × 0.001 × 0.1 = 1.047 × 10⁻³; R_C = N_D·P_C·L_C = 10.47 × 1 × 0.01 = 0.1047
R1 check	R₁ = R_A + R_B + R_C = 0.1047 + 1.047 × 10⁻³ + 0.1047 → 0.2104 > R_T = 10⁻⁵/yr (2,104,140.4 %) FAIL
LPS selection	Try classes from IV, P_B × 0.2 / 0.1 / 0.05 / 0.02, R₁ = R_A + N_D·P_B·L_B × factor + R_C (unprotected N_D·P_B·L_B = 1.047 × 10⁻³): class IV: 0.1047 + 1.047 × 10⁻³ × 0.2 + 0.1047 = 0.2096 > R_T; class III: 0.1047 + 1.047 × 10⁻³ × 0.1 + 0.1047 = 0.2095 > R_T; class II: 0.1047 + 1.047 × 10⁻³ × 0.05 + 0.1047 = 0.2094 > R_T; class I: 0.1047 + 1.047 × 10⁻³ × 0.02 + 0.1047 = 0.2094 > R_T — no class achieves R_T, class I recommended as the ceiling; rolling sphere 20 m, mesh 5 × 5 m (IEC 62305-3 Table 2)
Residual R1	R₁ with class I LPS → 0.2094 > R_T = 10⁻⁵/yr (2,093,881.4 %) FAIL
Result	0/2 checks pass → FAIL; R₁ = 0.2104/yr; recommended LPS: class I; governing: risk r1 with recommended lps. Even an LPS of class I leaves R1 = 0.209 > 1e-05; the remaining risk is dominated by RA, which an LPS does not reduce in this engine — add touch/step protection measures (RA) or coordinated SPDs (RC).
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 20 × 20 + 6 × 300 × (20 + 20) + 9π × 300² = 2617090.0 m²; N_D = 2 × 2617090.0 × 2 × 1e-6 = 10.47/yr; R_A = N_D × 1 × 0.01 = 0.1047, R_B = N_D × 0.001 × 0.1 = 0.001047, P_C = 1 − (1 − 1 × 1)^1 = 1 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 1, Table B.3); R_C = N_D × 1 × 0.01 = 0.1047; R1 = 0.2104 > R_T 1e-5 (Table 4); lowest LPS class with R1 ≤ R_T (P_B × 0.2/0.1/0.05/0.02 for IV/III/II/I, Table B.2): I (none suffices, I is the ceiling), residual R1 = 0.2094; rolling sphere 20 m, mesh 5 m (IEC 62305-3 Table 2). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-tall-tower-300m`)

Example 25 — Smallest structure at the lowest flash density

A 1 × 1 × 1 m kiosk at N_G 0.1 (both at their input minimums) has a negligible risk.

Given: Structure 1 × 1 × 1 m (L × W × H), ground flash density N_G = 0.1 flashes/km²/yr, located among objects of the same height or smaller (flat); non-metallic roof and structure, ordinary fire risk, occupied; internal systems: LV power line (standard consequence); touch/step measures: none; surge protection: no coordinated SPDs; existing LPS: none.

Collection area	A_D = L·W + 2·(3H)·(L + W) + π·(3H)² = 1 × 1 + 2 × 3 × (1 + 1) + π × 3² = 1.0 + 12.0 + 28.3 = 41.3 m²
Dangerous events	N_D = N_G × A_D × C_D × 10⁻⁶ = 0.1 × 41.3 × 0.5 × 10⁻⁶ = 2.064 × 10⁻⁶ /yr
Probabilities	P_A = 1 (none); P_B = 0.1 (non-metallic roof and structure); P_C = 1 − (1 − P_SPD·C_LD)ⁿ = 1 − (1 − 1 × 1)¹ = 1 (LV power line, n = 1, unshielded C_LD = 1; no coordinated SPDs, P_SPD = 1, Table B.3)
Losses	L_A = 0.01 (occupied); L_B = 0.1 (ordinary fire risk); L_C = 0.01 (standard consequence)
Risk components	R_A = N_D·P_A·L_A = 2.064 × 10⁻⁶ × 1 × 0.01 = 2.064 × 10⁻⁸; R_B = N_D·P_B·L_B = 2.064 × 10⁻⁶ × 0.1 × 0.1 = 2.064 × 10⁻⁸; R_C = N_D·P_C·L_C = 2.064 × 10⁻⁶ × 1 × 0.01 = 2.064 × 10⁻⁸
R1 check	R₁ = R_A + R_B + R_C = 2.064 × 10⁻⁸ + 2.064 × 10⁻⁸ + 2.064 × 10⁻⁸ → 6.191 × 10⁻⁸ ≤ R_T = 10⁻⁵/yr (0.6 %) PASS
LPS selection	R₁ ≤ R_T: no (further) lightning protection system is required
Result	1/1 checks pass → PASS; R₁ = 6.191 × 10⁻⁸/yr; recommended LPS: none; governing: risk r1
Reference	Hand calculation, IEC 62305-2:2010 Annex A: A_D = 1 × 1 + 6 × 1 × (1 + 1) + 9π × 1² = 41.3 m²; N_D = 0.1 × 41.3 × 0.5 × 1e-6 = 2.064e-06/yr; R_A = N_D × 1 × 0.01 = 2.064e-08, R_B = N_D × 0.1 × 0.1 = 2.064e-08, P_C = 1 − (1 − 1 × 1)^1 = 1 (1 unshielded line(s), C_LD = 1, Table B.4; P_SPD 1, Table B.3); R_C = N_D × 1 × 0.01 = 2.064e-08; R1 = 6.191e-08 ≤ R_T 1e-5 (Table 4). P_A, P_B and L factors are the tool's published category values (help page factor table); P_C per IEC 62305-2 B.4 with unshielded lines (C_LD 1, Table B.4) and P_SPD from Table B.3. (validation case `c0038-minimum-inputs`)

Standards & References

IEC 62305-1:2010 — Protection against lightning: General principles
IEC 62305-2:2010 — Protection against lightning: Risk management. Primary reference for risk assessment methodology.
IEC 62305-3:2010 — Protection against lightning: Physical damage and life hazard
IEC 62305-4:2010 — Protection against lightning: Electrical and electronic systems
AS/NZS 1768:2007 — Lightning protection (Australian/NZ implementation)

Tips & Limitations

This calculator implements Risk R1 (loss of human life) only. R4 (economic loss) uses the same framework but with different tolerable risk (10^-3).
Ground flash density N_g should come from local meteorological data. In Australia, typical values range from 0.5 (Tasmania) to 12 (Darwin).
The location factor C_d significantly affects results. Use “moderate” (C_d = 1) for an isolated structure with no other objects nearby and “exposed” (C_d = 2) only for an isolated structure on a hilltop or knoll (IEC 62305-2 Table A.1).
An LPS reduces only R_B. When R_A (touch/step) or R_C (internal systems) alone exceeds 10^-5, even LPL I cannot achieve the tolerable risk: the calculator still reports LPL I and the residual risk check fails — add touch/step measures or coordinated SPDs.
Existing LPS reduces risk through the PB efficiency factor. If an existing LPS is already installed but the assessment still shows FAIL, a higher-level LPS is needed.
Surge protection devices (SPDs) reduce the PC component (internal system failures) but do not affect the physical damage risk RB. Even SPDs designed for LPL I only reduce P_C to 0.01 per line, so with a critical failure consequence R_C can still govern.
For structures with explosion risk, R1 is almost always above the tolerable threshold — LPL I is typically required.

Developer Guide — Architecture

This calculator follows the standard calcs component pattern:

components/c0038_lightning_risk_assessment/
├── __init__.py              # Docstring
├── apps.py                  # Django AppConfig
├── calculations.py          # Pure Python — IEC 62305-2 tables and formulas
├── component.py             # Schema, Calculator class, builders, registration
├── equations.py             # LaTeX equation templates
├── excel_generator.py       # Excel report generator
└── templates/.../sidebar_form.html  # Vue 3 sidebar form

This is the most table-heavy calc — calculations.py contains all IEC 62305-2 lookup tables as Python dictionaries.

Developer Guide — Code Paths

Purpose	File	Key Function / Class
Collection area	`calculations.py`	`calculate_collection_area(L, W, H)`
Expected strikes	`calculations.py`	`calculate_expected_strikes(Ng, Ad, Cd)`
Internal systems P_C	`calculations.py`	`calculate_internal_systems_probability(n_lines, P_SPD, C_LD)`
Risk components	`calculations.py`	`calculate_risk_components()`
Protection level	`calculations.py`	`determine_protection_level()`
Main entry	`calculations.py`	`calculate_lightning_risk(data)`
Validation	`component.py`	`LightningRiskCalculator.validate_parameters()`
Excel report	`excel_generator.py`	`create_c0038_excel_report(calculation)`
Registration	`component.py`	`register_component(registry)`

Developer Guide — Testing

# Run all tests for this component
pytest calcs/test_c0038_lightning_risk_assessment.py -v

Test coverage includes:

TestCollectionArea — geometric area calculation
TestExpectedStrikes — Nd calculation with various Ng and Cd
TestRiskComponents — individual risk component calculations
TestNoProtectionNeeded — small/sheltered structures
TestProtectionRequired — large/exposed structures
TestProtectionLevel — correct LPL determination
TestExistingLPS — risk reduction from existing protection
TestInternalSystemsProbability — P_C per IEC 62305-2 B.4 (P_SPD Table B.3, lines combined)
TestLocationFactors — C_D per IEC 62305-2 Table A.1
TestCalculateLightningRisk — end-to-end integration
TestCalculatorClass — validation, round-trip, registration