Max Zs Calculator (with 80% Temperature Rule)
Under BS 7671 Regulation 411.4.4, the earth fault loop impedance (Zs) must be low enough to ensure automatic disconnection of supply within the statutory time specified in Regulation 411.3.2. Because conductors are tested cold during on-site inspection, the 80% Rule (0.8 factor) per Appendix 3 and On-Site Guide Table B6 must be satisfied. This tool details every intermediate step, formula substitution, and regulatory margin.
Loop Impedance Summary
Why the 80% Rule is Mandatory for Testing: BS 7671 tabulated values are calculated for conductors at their maximum operating temperature (typically 70°C). When testing on cold, lightly-loaded circuits at ambient temperature (typically 10°C to 20°C), conductor resistance is lower. Multiplying tabulated Zs × 0.8 guarantees that when the circuit reaches full operating temperature under load, disconnection time will still be achieved.
Full 6-Step Max Zs Calculation Working
Supply Voltage & Nominal Device Rating
U0 = 230 V, Device In = 32 A
Standard single-phase nominal AC line voltage to earth and protective device nominal continuous current.
Statutory Disconnection Duration
Required disconnection time t = 0.40 s
Per BS 7671 Regulation 411.3.2.2, final circuits not exceeding 32 A in TN systems must disconnect within 0.4 seconds under earth fault conditions.
Instantaneous Tripping Current (Ia)
Ia = 5 × In
Ia = 5 × 32 = 160.0 A
Operating current causing automatic disconnection within the statutory time (e.g. Type B MCBs trip magnetically between 3x and 5x In; 5x guarantees disconnection).
Tabulated Maximum Zs at Conductor Operating Temperature (70°C)
Zs(tab) = U0 / Ia
Zs(tab) = 230 / 160.0 = 1.44 Ω
Theoretical maximum earth fault loop impedance per BS 7671 Chapter 41 Table 41.3 at full conductor operating temperature.
Ambient Temperature Correction (The 80% Rule)
Zs(max measured) = Zs(tab) × 0.80
Zs(max measured) = 1.37 × 0.80 = 1.10 Ω
Corrects for the temperature difference between ambient test conditions and maximum operating conductor temperature per BS 7671 Appendix 3 and On-Site Guide Table B6.
On-Site Measured Value Compliance Check
Enter a measured Zs value in Section 3 to test compliance.
Verifies whether on-site meter readings taken during periodic inspection or initial verification satisfy the corrected maximum impedance.
Worked Example & Calculation Breakdown
Scenario: A 230 V single-phase ring final socket circuit is protected by a 32 A Type B MCB (BS EN 60898). An electrician carries out periodic testing (EICR) at an ambient temperature of 18°C and measures Zs = 0.92 Ω at the furthest socket.
- Determine Tripping Current: Type B MCB requires
Ia = 5 × In = 5 × 32 = 160 Ato guarantee disconnection within 0.4 seconds. - Calculate Tabulated Maximum Zs:
Zs(tab) = (230 × 0.95) / 160 A = 218.5 / 160 = 1.37 Ω (Cmin corrected)(per BS 7671 Table 41.3). - Apply 80% Temperature Factor:
Zs(max measured) = 1.37 × 0.80 = 1.10 Ω(per On-Site Guide Table B6). - Compare Measured Reading:
Zs(measured) = 0.92 Ω ≤ 1.10 Ω ⇒ PASS ✔. The circuit provides 0.18 Ω (16%) impedance safety headroom.
BS 7671 Regulatory Framework & Boundaries
- Reg 411.3.2.2: Maximum disconnection time for AC final circuits not exceeding 32 A is 0.4 seconds in TN systems and 0.2 seconds in TT systems.
- Reg 411.3.2.3: Maximum disconnection time for distribution circuits and circuits exceeding 32 A is 5.0 seconds in TN systems and 1.0 second in TT systems.
- TT System Earthing Boundary (Reg 411.5.3): In TT installations, earth fault loop impedance is typically too high to operate overcurrent protective devices. Protection is achieved via RCDs where
RA × IΔn ≤ 50 V. For a standard 30 mA RCD, the regulatory maximum loop resistance is 1,667 Ω, though guidance recommendsRA ≤ 200 Ωto ensure electrode stability. - Cmin Voltage Factor: BS 7671 Table 41.3 values are computed incorporating the voltage factor
Cmin = 0.95in European harmonised standards, which is naturally satisfied by the 0.8 on-site temperature multiplier.
⚠️ Engineering design aid: Always verify results against published BS 7671 tables and manufacturer specific breaker curves. Not a compliance certificate or legal sign-off.
Frequently Asked Questions
Why do measured on-site Zs values use the 80% (0.8) rule of thumb?
Tabulated Max Zs values in BS 7671 Chapter 41 are calculated for conductors at maximum operating temperature (typically 70°C for thermoplastic PVC). When testing cold circuits on site (~20°C), conductor resistance is lower. Multiplying tabulated Max Zs by 0.8 compensates for the temperature rise that will occur during an earth fault (BS 7671 Appendix 3).
What is the Cmin voltage factor in BS 7671?
BS 7671 incorporates a voltage factor Cmin = 0.95 into earth fault loop impedance calculations (230 V × 0.95 = 218.5 V). This ensures protective devices disconnect within statutory disconnection times even when the UK national grid voltage drops to its minimum statutory tolerance.
What are the statutory disconnection times under Regulation 411.3.2.2?
For standard 230V TN systems, final circuits not exceeding 63A with socket-outlets, and 32A for fixed equipment, require a maximum disconnection time of 0.4 seconds. For TT systems, the maximum time is 0.2 seconds. Distribution circuits allow up to 5.0 seconds (TN) or 1.0 second (TT).
Built by a UK electrical engineer. If you spot a calculation discrepancy, want a specific breaker or fuse curve added, or have on-site test feedback, drop Adrian a line or email .