Earth fault loop impedance
How to calculate Zs from R1+R2
Zs = Ze + (R1+R2). Enter the conductor sizes and run length to get R1+R2 and the expected Zs, cold and at operating temperature, checked against the device's maximum Zs, with the longest run before it fails.
Resistance per metre at 20°C from the IET On-Site Guide (Table I1). Expected hot Zs uses the GN3 1.20 multiplier for 70°C thermoplastic; the maximum is BS 7671 Table 41.3 (0.4 s, Cmin 0.95). Guide only.
How to calculate Zs from R1+R2
Zs is the earth fault loop impedance, and it is the sum of two parts: Zs = Ze + (R1+R2). Ze is the external loop impedance at the origin, and R1+R2 is the resistance of the circuit's own line conductor (R1) and protective conductor (R2), end to end. Knowing the value before you test means you can spot a wrong reading on site instead of after the assessor reads the certificate.
Typical R1+R2 values
R1+R2 comes from the conductor sizes and the run length. Using the resistance per metre in the IET On-Site Guide, 2.5/1.5 mm² twin and earth is about 19.5 mΩ/m, so a 20 m run is roughly 0.39 Ω. A 1.5/1.0 mm² lighting circuit is about 30.2 mΩ/m. Multiply the per-metre figure by the length and divide by 1000 for R1+R2 at 20°C.
Why the 1.20 multiplier
The resistance-per-metre figures are quoted at 20°C. Conductors run hotter under load, which raises their resistance, so Guidance Note 3 applies a 1.20 multiplier for 70°C thermoplastic to estimate the Zs the device actually sees when the circuit is working. That hot figure is the one to compare with the BS 7671 Table 41.3 maximum, which is what this tool does.
The longest run before it fails
Rearranging the same sum gives the maximum length this cable and device combination can reach before the hot Zs hits the limit. It is the quick check for a long radial, a garden office or a sub-main. If a run is too long the fixes are a larger conductor to cut R2, a more sensitive device, or RCD additional protection. Pair this with the max Zs checker and the cable size calculator.
FAQs
How do you calculate Zs?
Zs is the earth fault loop impedance: Zs = Ze + (R1+R2). Ze is the external loop impedance at the origin and R1+R2 is the resistance of the circuit's line and protective conductors. For the disconnection check, correct R1+R2 to operating temperature with the 1.20 multiplier, so expected Zs = Ze + 1.20 times the cold R1+R2.
What are typical R1+R2 values?
R1+R2 depends on the conductor sizes and the run length. Using the IET On-Site Guide resistance per metre, 2.5/1.5 mm2 twin and earth is about 19.5 milliohms per metre, so a 20 m run is roughly 0.39 ohms; 1.5/1.0 mm2 lighting is about 30.2 milliohms per metre. Multiply the per-metre figure by the length and divide by 1000.
What is R1+R2?
R1+R2 is the combined resistance of a circuit's line conductor (R1) and its protective conductor (R2), measured end to end. Added to Ze it gives Zs, the earth fault loop impedance the protective device has to see to disconnect in time.