What the loop is, and why its impedance decides everything

When to use this: designing a circuit and needing to know whether it will disconnect in time before you install it; checking a test result at the end of a job; working out why a long run to an outbuilding will not comply; or deciding whether a Type C breaker is going to cause a problem.

When a line conductor touches earth, the current has to get back to the transformer. It goes out along the line conductor, through the fault, back along the protective conductor, and home through the distributor’s network. That round trip is the earth fault loop, and its impedance is the only thing standing between the supply voltage and an unlimited fault current.

Zs = Ze + (R1 + R2)

Z_e is everything outside your installation — the distributor’s cable and transformer. R₁ is your circuit’s line conductor and R₂ its protective conductor. They add rather than combining any other way because the fault current flows through both of them one after the other: they are in series.

The impedance matters because it sets the fault current, and the fault current is what makes the protective device operate. A high loop impedance means a small fault current, which means a slow disconnection, which means a dangerous touch voltage sitting on exposed metal for longer than a person can safely be in contact with it.

The compliance test, and where the numbers come from

Zs ≤ U0 × Cmin ÷ Ia

• U₀ — nominal line-to-earth voltage. 230 V in the UK.
• C_min — 0.95. The supply is not guaranteed to be at 230 V when the fault happens, and a low supply voltage drives less current through the same impedance, so it takes longer to trip the device. Designing at the nominal voltage is optimistic by exactly that 5%.
• I_a — the current that makes the device operate within the required time.

For a 230 V supply the numerator is always 218.5, so the whole of the breaker table is 218.5 ÷ I_a. And for a circuit breaker, I_a is a fixed multiple of the rating, because it is the magnetic element that operates:

Why a breaker has one figure and a fuse has two

A circuit breaker has two tripping mechanisms. The thermal element handles overloads slowly; the magnetic element handles short circuits in about ten milliseconds. Once the fault current reaches 5 × In on a Type B, the magnetic element operates essentially instantly — so whether the regulation asked for 0.4 s or 5 s makes no difference at all to the impedance you need. One column covers both.

A fuse has no magnetic element. The current needed to clear it in 0.4 s is genuinely larger than the current needed in 5 s, so it gets two columns. That current comes off a measured time/current curve with no closed form, which is why fuse figures are not built into this calculator: there is nothing to derive. Select “fuse or other”, read I_a off the curve for your device, and the rest of the arithmetic is done for you.

The mistake that passes circuits which should fail

This is the single most common error in this subject, and it happens at the end of the job rather than the start.

The tabulated maximum assumes the conductors are at their operating temperature — 70 °C for thermoplastic. That is deliberate: hot copper is more resistive, the loop impedance is higher, and the circuit is at its hardest to disconnect. Compliance has to hold in that condition, not in the easiest one.

You test a circuit cold. Room temperature, nothing loaded, resistance about 20% lower than it will be in service. Compare that reading against the hot limit and you will pass circuits that do not actually comply.

BS 7671 Appendix 14 handles it with a rule of thumb: a cold measurement should be at or below 0.75 × the tabulated maximum. For a 32 A Type B that is not 1.37 Ω but about 1.02 Ω — and a reading of 1.15 Ω, which looks comfortably inside the table, fails.

Where R₁ + R₂ actually comes from

Add the resistance per metre of the two conductors and multiply by the length. A 2.5 mm² conductor is 7.41 Ω/km and a 1.5 mm² is 12.1 Ω/km, so 2.5/1.5 twin and earth is 19.51 mΩ/m at 20 °C. Multiply by 1.20 for 70 °C.

Notice the split. The cpc is 12.1 of that 19.51 — 62% of the total, from the conductor that carries no load current at all. Twin and earth is sold with a reduced cpc, and that reduced cpc is what dominates the loop impedance of most domestic circuits. It is also why increasing the cpc is usually the most effective single change when a circuit fails on Z_s.

Ze, and how much to trust it

Those are declared maxima, not measurements — worst cases the distributor undertakes not to exceed. The real figure is usually a good deal lower. On a marginal design that difference decides the answer, and it is worth measuring rather than assuming.

Why TT needs an RCD, and it is not a matter of preference

A TT earth electrode is commonly tens or hundreds of ohms. A 32 A Type B breaker needs the entire loop under 1.37 Ω. At 100 Ω the fault current is about two amps — the breaker would sit there indefinitely while the fault stayed live.

An RCD is judged on something else entirely: Zs ≤ 50 ÷ IΔn, which comes from the 50 V touch voltage limit rather than from disconnection time. A 30 mA device permits 1,667 Ω. That is three orders of magnitude more headroom, and it is the entire reason TT installations are workable.

The RCD covers fault protection. The circuit still needs an overcurrent device for overload and short circuit, and that device still has its own requirements.

What passing does not prove

A compliant Z_s means the device disconnects within the required time. Two other things have to be true of the same protective conductor and neither is checked here:

• It has to survive the fault — the adiabatic check, S = √(I²t) ÷ k. A conductor can be low-resistance enough to trip the device quickly and still be too small to carry that current for the time it takes.
• Where the Table 54.7 route is used, it has to meet that table’s minimum size regardless of what any calculation says.

How this calculator is checked

Technical reviewer

Salamot Hok

Electrician · 10+ years of installation work in Bangladesh and the wider South Asian region

He reads the result the way an installer would: are the defaults values people actually meet, does the warning fire where you would stop and think, and is the answer something you could buy and fit? The code figures themselves come from the published standards cited below, not from him — that boundary is set out on his profile.

• The maths lives in a pure function with its own test suite, asserted against worked examples from published references and standards. A calculator does not ship until those tests pass.
• 4 sources cited by name and linked, so any figure on the page can be traced back to the document it came from.
• Last reviewed 25 August 2026. Review dates are advanced only when the page is actually re-read, never to look fresh.
• Unusable input returns no answer. Where the inputs do not describe a real design, the calculator says so and withholds the number rather than printing a plausible-looking wrong one.

The full process is written up in the methodology and editorial policy. Results are engineering guidance, not a code sign-off — see the disclaimer. If a result looks wrong, tell us; corrections are answered before anything else.