Maximum Zs table
The highest earth fault loop impedance each protective device will still disconnect through in time — derived from Zs ≤ U0 × Cmin ÷ Ia, and printed beside the published BS 7671 values so the derivation can be checked.
The rule
Zs ≤ U0 × Cmin ÷ Ia
U0 is the nominal line-to-earth voltage (230 V in the UK), Cmin is 0.95 — allowing for the supply sitting at the bottom of its tolerance — and Ia is the current that makes the device operate within the required disconnection time. At 230 V the numerator is always 218.5, so every figure below is 218.5 ÷ Ia.
For a circuit breaker Ia is a fixed multiple of the rating, because it is the magnetic element that operates: 5 × In for Type B, 10 × for Type C and 20 × for Type D. That is why a breaker has one Zs figure rather than separate ones for 0.4 s and 5 s — the magnetic trip operates in about ten milliseconds either way.
Of the 27 published values checked, 27 land on the same figure to two decimal places; the largest disagreement anywhere is 0.005 Ω. The derived value is in bold below and the published one in brackets.
Circuit breakers — BS EN 60898
| Rating | Type B | Type C | Type D | Ia, Type B | Ia, Type C | Ia, Type D |
|---|---|---|---|---|---|---|
| 6 A | 7.28 Ω (7.28) | 3.64 Ω (3.64) | 1.82 Ω (1.82) | 30 A | 60 A | 120 A |
| 10 A | 4.37 Ω (4.37) | 2.19 Ω (2.19) | 1.09 Ω (1.09) | 50 A | 100 A | 200 A |
| 16 A | 2.73 Ω (2.73) | 1.37 Ω (1.37) | 0.68 Ω (0.68) | 80 A | 160 A | 320 A |
| 20 A | 2.19 Ω (2.19) | 1.09 Ω (1.09) | 0.55 Ω (0.55) | 100 A | 200 A | 400 A |
| 25 A | 1.75 Ω (1.75) | 0.87 Ω (0.87) | 0.44 Ω (0.44) | 125 A | 250 A | 500 A |
| 32 A | 1.37 Ω (1.37) | 0.68 Ω (0.68) | 0.34 Ω (0.34) | 160 A | 320 A | 640 A |
| 40 A | 1.09 Ω (1.09) | 0.55 Ω (0.55) | 0.27 Ω (0.27) | 200 A | 400 A | 800 A |
| 45 A | 0.97 Ω | 0.49 Ω | 0.24 Ω | 225 A | 450 A | 900 A |
| 50 A | 0.87 Ω (0.87) | 0.44 Ω (0.44) | 0.22 Ω (0.22) | 250 A | 500 A | 1000 A |
| 63 A | 0.69 Ω (0.69) | 0.35 Ω (0.35) | 0.17 Ω (0.17) | 315 A | 630 A | 1260 A |
45 A has no published figure because it is not a rating BS EN 60898 lists, but it is sold and the arithmetic is identical, so it is derived here rather than left out.
What a cold measurement has to beat
The table above assumes the conductors are at their operating temperature, because that is when resistance is highest and the circuit is hardest to disconnect. You test a circuit cold. BS 7671 Appendix 14 gives a rule of thumb: a cold measurement should be at or below 0.75 × the tabulated maximum.
| Rating | Type B, cold | Type C, cold | Type D, cold |
|---|---|---|---|
| 6 A | 5.46 Ω | 2.73 Ω | 1.37 Ω |
| 10 A | 3.28 Ω | 1.64 Ω | 0.82 Ω |
| 16 A | 2.05 Ω | 1.02 Ω | 0.51 Ω |
| 20 A | 1.64 Ω | 0.82 Ω | 0.41 Ω |
| 25 A | 1.31 Ω | 0.66 Ω | 0.33 Ω |
| 32 A | 1.02 Ω | 0.51 Ω | 0.26 Ω |
| 40 A | 0.82 Ω | 0.41 Ω | 0.20 Ω |
| 45 A | 0.73 Ω | 0.36 Ω | 0.18 Ω |
| 50 A | 0.66 Ω | 0.33 Ω | 0.16 Ω |
| 63 A | 0.52 Ω | 0.26 Ω | 0.13 Ω |
This is where circuits get passed that should not be. A 32 A Type B reading 1.15 Ω looks comfortably inside the 1.37 Ω table figure, and fails against the 1.02 Ω one.
If you learned 0.8, that was the older figure. The change to 0.75 arrived alongside the Cmin factor of 0.95 entering the maximum-Zs calculation, which brought the tabulated maxima down 5% at the same time. Check which basis a set of figures is on before mixing it with a modern table.
RCDs — Zs ≤ 50 ÷ IΔn
An RCD is judged on touch voltage rather than disconnection time, so its limits come from a different rule entirely and are orders of magnitude larger.
| IΔn | Maximum Zs |
|---|---|
| 10 mA | 5000 Ω |
| 30 mA | 1667 Ω |
| 100 mA | 500 Ω |
| 300 mA | 167 Ω |
| 500 mA | 100 Ω |
A 30 mA device permitting 1667 Ω against a 32 A Type B breaker’s 1.37 Ω is the entire reason a TT installation is workable: no overcurrent device would ever operate through an earth electrode’s impedance. The RCD covers fault protection only — the circuit still needs an overcurrent device for overload and short circuit.
Fuses are not here, and that is deliberate
A fuse has no magnetic element. The current that clears it in 0.4 s is genuinely larger than the current that clears it in 5 s, which is why the fuse tables have two columns and the breaker table has one. That current comes off a measured time/current characteristic with no closed form — there is nothing to derive, and reproducing BSI’s figures is not something this site does.
Read Ia off the curve for your device at the disconnection time you need and put it into the loop impedance calculator, or take the maximum Zs straight from BS 7671 Tables 41.2 and 41.4.
R1 + R2 for standard twin and earth
The half of Zs you control. Both conductors carry the fault current in series, so their resistances add. Derived from the IEC 60228 conductor resistances the cable resistance table uses, so the two cannot disagree.
| Line / cpc | 20 °C | 70 °C | 90 °C | cpc share |
|---|---|---|---|---|
| 1 / 1 mm² | 36.20 (36.2) | 43.31 | 46.16 | 50% |
| 1.5 / 1 mm² | 30.20 (30.2) | 36.13 | 38.51 | 60% |
| 2.5 / 1.5 mm² | 19.51 (19.51) | 23.34 | 24.88 | 62% |
| 4 / 1.5 mm² | 16.71 (16.71) | 19.99 | 21.31 | 72% |
| 6 / 2.5 mm² | 10.49 (10.49) | 12.55 | 13.38 | 71% |
| 10 / 4 mm² | 6.44 (6.44) | 7.71 | 8.21 | 72% |
| 16 / 6 mm² | 4.23 (4.23) | 5.06 | 5.39 | 73% |
All figures in mΩ/m. The temperature columns are the 20 °C figure multiplied by 1.196 and 1.275.
Look at the last column. In 2.5/1.5 twin and earth the reduced cpc — a conductor that carries no load current at all — contributes 62% of R1 + R2. That is why increasing the cpc is usually the most effective single change when a circuit fails on Zs, and why the adiabatic check bites on the cpc rather than the line conductor.
Ze — the part that is not yours
| System | Declared maximum Ze |
|---|---|
| TN-S | 0.8 Ω |
| TN-C-S | 0.35 Ω |
| TT | none — must be measured |
These are worst cases the distributor undertakes not to exceed, not measurements, and the real figure is usually lower. On a marginal design that difference decides the answer.
Using this table
It is free to quote and reproduce with attribution to this page. To have the arithmetic done — including R1 + R2 from your cable and length, the pass/fail, and the cold-test comparison — use the earth fault loop impedance calculator.
Satisfying Zs proves the device disconnects in time. The protective conductor must also survive the fault — see the adiabatic calculator and the k values reference — and meet the Table 54.7 minimum where that route is used. Neither is evaluated here.
The derivation, the sources and the review process behind these figures are set out in the methodology. This page is reviewed by Salamot Hok, electrician with 10+ years of installation experience. Results are engineering guidance, not a code sign-off — see the disclaimer.
Sources
- BS 7671 — Requirements for Electrical Installations (IET Wiring Regulations) — electrical.theiet.org
- IEC 60364-4-41 — Protection against electric shock — webstore.iec.ch
- IEC 60228 — Conductors of insulated cables — webstore.iec.ch
ElectroCalculators is not affiliated with BSI, the IET or the IEC. Standard titles, table references and regulation numbers are cited for identification.