Max Zs Table & Calculator (BS 7671:2018+A4:2026)
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.
Show Full Mathematical Derivation (AM2 Working Standard)BS 7671:2018+A4:2026
Maximum Allowable Measured Zs (80% Cold Rule)
Earth Fault Loop Impedance (Reg 411.4.4)
- U0 (Supply Voltage to Earth): 230 V (nominal single-phase voltage)
- Cmin (Voltage Tolerance Factor): 0.95 (BS 7671 Table 41.1 minimum grid tolerance)
- Ia (Tripping Operating Current): 160.0 A (instantaneous disconnection within 0.40 s)
Cold Circuit Testing Adjustment
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 (or not exceeding 63 A with socket-outlets) 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 final circuits exceeding 32 A supplying only fixed equipment, 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 disconnection time required by BS 7671s even when the UK national grid voltage drops to its minimum statutory tolerance.
What are the disconnection time required by BS 7671s 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).
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