Short Circuit Calculator — BS 7671:2018+A2:2022 🇬🇧
BS 7671:2018+A2:2022, the IET Wiring Regulations, provides a comprehensive framework for short-circuit protection in UK electrical installations. The standard addresses two distinct but related requirements: protection against fault currents to prevent cable damage (Regulation 434.5.2) and automatic disconnection of supply to prevent electric shock (Regulation 411.3.2). Both requirements hinge on understanding fault current magnitudes and disconnection times at every point in an installation.
A distinctive feature of BS 7671 is its extensive use of earth fault loop impedance (Zs) tables. Rather than requiring engineers to calculate exact fault currents, the standard provides maximum permissible Zs values for each combination of protective device type and rating. If the measured or calculated Zs is below the tabulated maximum, both automatic disconnection and fault current protection are satisfied simultaneously.
This calculator implements the full BS 7671 verification methodology, including the adiabatic equation for cable thermal withstand, Zs table lookups with temperature correction, and protective device breaking capacity checks against prospective fault levels.
How Short Circuit Works Under BS 7671:2018+A2:2022
The Dual Protection Requirement
BS 7671 requires short-circuit protection to satisfy two independent criteria. First, Regulation 434.5.2 requires that the cable can withstand the thermal effects of fault current for the duration of the protective device's operation (cable thermal withstand). Second, Regulation 411.3.2 requires automatic disconnection within specified times to provide protection against electric shock: 0.4 seconds for final circuits not exceeding 32A, and 5 seconds for distribution circuits (Regulation 411.3.2.2 and 411.3.2.3). Both must be verified.
Step 1: Determine Prospective Fault Current
Regulation 313.1 requires the prospective fault current (both short-circuit and earth fault) to be determined at every relevant point. The regional electricity company (DNO) provides the external earth fault loop impedance Ze and prospective fault current at the origin. For downstream points, the total earth fault loop impedance Zs = Ze + (R1 + R2), where R1 is the line conductor resistance and R2 is the circuit protective conductor (CPC) resistance, both from Appendix 3 tables.
Step 2: The Adiabatic Equation (Regulation 434.5.2)
The adiabatic equation verifies that fault current energy does not exceed the cable's thermal capacity:
t ≤ (k2S2) / I2
The k values are obtained from Table 43.1 of BS 7671. For thermoplastic (PVC) insulated copper conductors, k = 115. For thermosetting (XLPE) insulated copper conductors, k = 143. For aluminium conductors, the values are 76 (PVC) and 94 (XLPE) respectively. These values assume initial temperatures at the conductor's maximum operating temperature and final temperatures at the short-circuit withstand limit.
Step 3: Earth Fault Loop Impedance Verification
BS 7671 Tables 41.2 through 41.6 provide maximum Zs values for different protective device types (Type B, C, and D MCBs, BS 88 fuses, BS 3036 semi-enclosed fuses). The measured or calculated Zs must not exceed the tabulated value. Critically, the tabulated values are at the reference temperature, but installed cables operate at higher temperatures. Regulation 411.3.2 Note 2 requires applying a correction factor; in practice the IET Guidance Note 3 recommends multiplying the measured Zs by a factor of 1.20 (for thermoplastic cables operating at 70°C) to account for conductor resistance increase with temperature.
Step 4: Verify Protective Device Breaking Capacity
Regulation 432.1 states the rated short-circuit breaking capacity of each protective device must be not less than the prospective fault current at its point of installation. Standard domestic MCBs are typically rated at 6kA or 10kA. Where the prospective fault current exceeds the device rating, Regulation 432.3 permits the use of back-up protection (a coordinated upstream device that limits fault current), provided the combination is verified by the manufacturer.
Step 5: Document the Results
BS 7671 Part 6 (Inspection and Testing) requires the prospective fault current to be recorded on the Electrical Installation Certificate (EIC) or Minor Works Certificate. Regulation 643.7 specifies that the prospective fault current must be measured or calculated at the origin and at every distribution board. This calculator produces results suitable for direct inclusion in certification documentation.
Key Reference Tables
BS 7671 Table 43.1
Values of k for common combinations of conductor and insulation materials, used in the adiabatic equation
Obtain k values: Cu/PVC = 115, Cu/XLPE = 143, Al/PVC = 76, Al/XLPE = 94 for calculating cable thermal withstand capacity k²S²
BS 7671 Table 41.2–41.6
Maximum earth fault loop impedance Zₛ for automatic disconnection within required times, listed by protective device type and rating
Look up the maximum permissible Zₛ for the specific protective device (e.g., Table 41.3 for Type B MCBs, Table 41.4 for Type C MCBs) to verify automatic disconnection
BS 7671 Appendix 3, Tables 3A–3F
Cable impedance data: resistance and reactance per metre for various cable types at 20°C and operating temperature
Calculate R₁ + R₂ values for the line and CPC conductors to determine total earth fault loop impedance Zₛ = Zₑ + (R₁ + R₂)
BS 7671 Regulation 434.5.2
The adiabatic equation requirement: fault duration must not cause conductor temperature to exceed the limiting value
The governing regulation for cable short-circuit thermal withstand verification: t ≤ k²S²/I²
BS 7671 Regulation 411.3.2
Maximum disconnection times for TN systems: 0.4s for final circuits ≤32A, 5s for distribution circuits
Determine the required disconnection time for the circuit type, which drives the maximum permissible earth fault loop impedance
IET Guidance Note 3, Table 3A
Correction factors for measured earth fault loop impedance to account for conductor temperature rise from ambient to operating temperature
Apply the 1.20 correction factor (thermoplastic cables) to measured Zₛ values before comparing against BS 7671 table maximums
Worked Example — BS 7671:2018+A2:2022 Short Circuit
Scenario
A 6mm² Cu PVC/PVC flat twin and earth cable supplies a 32A final circuit. The external earth fault loop impedance Zₑ = 0.35Ω (from DNO). The cable is 30m long with a 2.5mm² CPC. Protective device is a 32A Type B MCB rated at 6kA. Verify short-circuit protection per BS 7671:2018+A2.
Determine R₁ + R₂ from Appendix 3
From BS 7671 Appendix 3 Table 3A, for 6mm² line conductor and 2.5mm² CPC in flat twin and earth cable: (R₁ + R₂) at 20°C = (3.08 + 7.41) mΩ/m = 10.49 mΩ/m. Apply temperature correction factor of 1.20 for PVC at operating temperature: (R₁ + R₂) = 10.49 × 1.20 = 12.59 mΩ/m.
(R₁ + R₂) at operating temp = 10.49 × 1.20 = 12.59 mΩ/m(R₁ + R₂) = 12.59 mΩ/m
Calculate total earth fault loop impedance Zₛ
Total Zₛ is the sum of external impedance from the DNO and the cable impedance for the circuit length.
Zₛ = Zₑ + [(R₁ + R₂) × L] = 0.35 + (0.01259 × 30) = 0.35 + 0.378 = 0.728ΩZₛ = 0.728Ω
Verify Zₛ against BS 7671 Table 41.3
From BS 7671 Table 41.3, for a 32A Type B MCB with 0.4s disconnection time (final circuit ≤32A per Regulation 411.3.2.2), the maximum permissible Zₛ = 1.37Ω.
Zₛ measured (0.728Ω) ≤ Zₛ max (1.37Ω)PASS — Earth fault loop impedance is within limits for automatic disconnection in 0.4s
Calculate prospective earth fault current
The earth fault current is derived from the supply voltage and the total earth fault loop impedance.
Iₑf = U₀ / Zₛ = 230 / 0.728 = 316AProspective earth fault current = 316A
Verify cable thermal withstand (adiabatic equation)
For 6mm² Cu PVC cable, k = 115 from Table 43.1. Check that the fault energy does not exceed the cable's withstand for the CPC (2.5mm² is the weakest link).
k²S² (CPC) = 115² × 2.5² = 13,225 × 6.25 = 82,656 A²s
t_max = k²S² / I² = 82,656 / 316² = 82,656 / 99,856 = 0.828sPASS — The CPC can withstand the fault for 0.828s, which exceeds the 0.4s disconnection time. The line conductor (6mm²) has even greater withstand capacity.
Verify MCB breaking capacity
The prospective short-circuit current (line-to-line or three-phase) at the point of installation will be higher than the earth fault current. Assuming the line-to-neutral prospective fault current at the origin is Iₛₑ = 230/0.35 = 657A (approximately), and accounting for line conductor impedance only: Iₛₑ at MCB = 230 / (0.35 + 2 × 0.00308 × 1.20 × 30) = 230 / (0.35 + 0.222) = 230 / 0.572 = 402A. The 6kA MCB is adequate.
Prospective fault current at MCB ≈ 402A << 6kA (MCB breaking capacity)PASS — MCB breaking capacity (6,000A) far exceeds the prospective fault current (402A)
The 6mm² Cu PVC cable with 2.5mm² CPC, protected by a 32A Type B MCB, fully complies with BS 7671:2018+A2. The earth fault loop impedance (0.728Ω) is well within the Table 41.3 maximum (1.37Ω), ensuring disconnection in under 0.4 seconds. The CPC thermal withstand (0.828s) exceeds the disconnection time. The MCB breaking capacity (6kA) is adequate for the prospective fault level. This is a typical result for a UK domestic final circuit.
Common Mistakes When Using BS 7671:2018+A2:2022
- 1
Not correcting Zₛ for conductor operating temperature — measured Zₛ values from a loop impedance tester reflect the cable temperature at the time of testing (typically near ambient). At full load, PVC conductors operate at 70°C, increasing resistance by approximately 20%. IET Guidance Note 3 recommends multiplying measured Zₛ by 1.20 before comparing against BS 7671 table values. Omitting this correction can make a non-compliant circuit appear to pass.
- 2
Confusing prospective short-circuit current with earth fault current — the prospective short-circuit current (line-to-line or line-to-neutral) is used for verifying protective device breaking capacity per Regulation 432.1. The earth fault current (line-to-earth via the CPC) is used for verifying automatic disconnection times per Regulation 411.3.2. These are different values with different impedance paths, and both must be checked independently.
- 3
Using the wrong disconnection time for the circuit type — BS 7671 Regulation 411.3.2.2 requires 0.4s for final circuits not exceeding 32A, while Regulation 411.3.2.3 allows 5s for distribution circuits. Using the 5s distribution time for a 32A final circuit would result in a dangerously high maximum Zₛ, potentially allowing inadequate earth fault protection.
- 4
Forgetting to verify BOTH overload and short-circuit protection independently — BS 7671 Section 432 to 434 treats overload protection (Section 433) and short-circuit protection (Section 434) as separate requirements. A cable may be correctly sized for overload via Regulation 433.1 but fail the short-circuit thermal withstand check, particularly for smaller CPCs in composite cables.
- 5
Not checking the CPC (circuit protective conductor) separately — in flat twin and earth cables, the CPC is typically smaller than the line conductor (e.g., 1.0mm² CPC with 2.5mm² line conductors). The CPC's thermal withstand (k²S²) is the limiting factor for earth fault conditions. BS 7671 Regulation 543.1.3 requires verification that the CPC can withstand the earth fault energy.
How Does BS 7671:2018+A2:2022 Compare?
BS 7671 is distinguished from other standards by its extensive Zₛ table system, which simplifies verification for standard installations by eliminating the need to calculate exact fault currents. The Zₛ approach is unique to the UK and directly links protective device selection to earth fault loop impedance. In contrast, IEC 60364 and AS/NZS 3008 require explicit fault current calculations. BS 7671's temperature correction factor (1.20) for measured Zₛ is another UK-specific practical consideration not found in other standards. The underlying adiabatic equation (Regulation 434.5.2) is identical to IEC 60364-4-43 and AS/NZS 3008.1.1 Clause 6.
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