The maximum Zs values are in Chapter 41 of BS 7671. IET Wiring Matters (issue 105, May 2025) names Tables 41.2, 41.3 and 41.4. Each maximum comes from the current Ia that makes the protective device operate in the required time: Zs(max) = (U0 × Cmin) ÷ Ia. This page does not copy the tables. Take the figure for your device from your own copy of BS 7671:2018+A4:2026 or the manufacturer’s data, and use this page to check the sum and apply the 80% rule.
Where the maximum Zs figure comes from
Zs is the impedance of the whole earth fault loop. If it is too high, the fault current is too low for the protective device to operate in time, so every device has a maximum. The circuit’s own figure is Zs = Ze + (R1 + R2), and it must not be more than that maximum.
The maximum is Zs(max) = (U0 × Cmin) ÷ Ia.
- U0 is the nominal voltage to earth, 230 V.
- Cmin is the minimum voltage factor, 0.95 for a low voltage supply provided under the ESQCR (IET Wiring Matters, issue 105, May 2025).
- Ia is the current that makes the device operate within the required time. It comes from the device data.
230 × 0.95 = 218.5, so every maximum is 218.5 divided by Ia.
Maximum Zs for a given Ia: worked sums
These are sums for the Ia values shown, not a list of devices. Look up the Ia for your own device in the device data, then divide. The 0.8 column is the 80% figure for readings taken cold.
| Ia (A) | Sum | Zs(max) (Ω) | × 0.8 (Ω) |
|---|---|---|---|
| 30 | 218.5 ÷ 30 | 7.2833 | 5.8266 |
| 50 | 218.5 ÷ 50 | 4.3700 | 3.4960 |
| 100 | 218.5 ÷ 100 | 2.1850 | 1.7480 |
| 160 | 218.5 ÷ 160 | 1.3656 | 1.0925 |
| 200 | 218.5 ÷ 200 | 1.0925 | 0.8740 |
| 300 | 218.5 ÷ 300 | 0.7283 | 0.5826 |
| 400 | 218.5 ÷ 400 | 0.5462 | 0.4370 |
| 500 | 218.5 ÷ 500 | 0.4370 | 0.3496 |
The 30 A, 160 A and 200 A rows are the same sums as the worked examples in Zs formula and maximum permitted Zs: worked examples. To run any Ia yourself, use the fault loop impedance calculator (max Zs).
The 80% figure for cold readings
Conductor resistance rises as conductors warm up. The IET says the tabulated maximum Zs values apply with conductors at their operating temperature (70 °C assumed), and that the On-Site Guide gives 80% values as a quick check on readings taken cold (IET Inspection and Testing FAQs). The rule: Zs from room-temperature readings should be no more than 0.8 × the maximum Zs.
It errs on the safe side, because the 0.8 factor also scales Ze, which does not warm up with the circuit. A reading over the 80% figure is not automatically a failure. Correct (R1 + R2) to operating temperature, add Ze and compare with the full maximum, as set out in the 80% rule section of the worked-examples post. The 0.8 factor and the 1.20 multiplier are the workbook’s practice figures; the guidance you work to decides the method and the factor.
The largest (R1 + R2) a circuit can have
Rearrange Zs = Ze + (R1 + R2) and the largest (R1 + R2) is Zs(max) − Ze. With Ia = 200 A, Zs(max) = 1.0925 Ω. With Ze = 0.35 Ω, the largest (R1 + R2) at operating temperature is 1.0925 − 0.35 = 0.7425 Ω. The circuit in the worked example has 0.960 Ω once corrected to operating temperature, which is why it does not comply.
Questions
Where do I find the maximum Zs values?
The maximum Zs values for protective devices are published in tables in Chapter 41 of BS 7671. IET Wiring Matters (issue 105, May 2025) names Tables 41.2, 41.3 and 41.4. Take the figure for your device from your own copy of BS 7671:2018+A4:2026, or from the manufacturer’s data. This site does not copy the tables.
How is the maximum Zs worked out?
From the current that makes the device operate in the required time: Zs(max) = (U0 × Cmin) ÷ Ia, with U0 = 230 V and Cmin = 0.95 (IET Wiring Matters, issue 105). The top line is always 218.5, so divide 218.5 by Ia.
What is the 80% rule for Zs?
A rule of thumb for readings taken at room temperature: Zs from cold readings should be no more than 0.8 × the maximum Zs. The IET says the tabulated maxima apply at conductor operating temperature and that the On-Site Guide uses 80% values as a quick check. A reading over the 80% figure still needs the full check before it is called a failure.
How do I work out R1 + R2 from Zs and Ze?
Rearrange Zs = Ze + (R1 + R2) to give (R1 + R2) = Zs − Ze. The largest (R1 + R2) a circuit can have is the maximum Zs minus Ze. That is arithmetic on known values, not a test method. On site, IET Wiring Matters (issue 105, May 2025) says it is not acceptable to measure Zs and subtract Ze to get R1 + R2, because a measured Zs includes parallel paths. Measure R1 + R2 directly.
Practise more
Inspection and Testing Calculations has 200 questions in 14 sections, graded Easy, Core and Challenging, each with a full worked answer, including maximum Zs, the 80% rule and the temperature correction.
Kindle edition free to read with Kindle Unlimited.
Preparing for the 2391-52? See 2391-52 mock exam papers (paperback and Kindle, on Amazon).
Written by a City & Guilds 2391-51 qualified electrician.
Sources
- IET Wiring Matters, issue 105, May 2025: Cmin = 0.95 for a low voltage supply under the ESQCR; maximum earth fault loop impedance values from Tables 41.2, 41.3 and 41.4 of BS 7671; measuring Zs and subtracting Ze is not an acceptable way to find R1 + R2.
- IET Inspection and Testing FAQs: tabulated maximum Zs values assume conductor operating temperature; On-Site Guide 80% values.
- BS 7671:2018+A4:2026, Chapter 41: use your own copy for the values.