Earth Fault Loop Impedance Calculator — BS 7671

Zs is the total impedance of the earth fault loop path. It consists of Ze (the external earth fault loop impedance from the supply transformer to your installation) plus R1+R2 (the circuit conductor impedances — R1 being the line conductor and R2 the circuit protective conductor). Zs must be low enough to allow sufficient fault current to flow to operate the protective device within the required disconnection time.

Maximum Zs values are specified in BS 7671 Tables 41.2, 41.3 and 41.4. They depend on the protective device type and rating. For example, a 32A Type B MCB has a maximum Zs of 1.37 ohms for 0.4 second disconnection. This 1.37 ohm figure reflects the Cmin = 0.95 voltage factor, which was introduced by the 17th Edition Amendment 3 (effective 1 July 2015) and reduced the previous value of 1.44 ohms; the maximum Zs tables have been unchanged from the 17th Edition through the 18th Edition and its amendments A2:2022 and A4:2026. Final circuits up to 63A supplying socket outlets require 0.4 second disconnection; distribution circuits may use 5 second values.

When you measure R1+R2 with a low-resistance ohmmeter, the conductors are at ambient temperature (typically 20 degrees Celsius). Under fault conditions, the conductors heat up to their maximum operating temperature (typically 70 degrees Celsius for thermoplastic insulation). Conductor resistance rises with temperature, so the measured value must be corrected upwards. This calculator uses the BS 7671 On-Site Guide convention: multiply R1+R2 by (230 + operating temp) / (230 + ambient temp). For a 70 degrees Celsius thermoplastic conductor measured at 20 degrees Celsius this gives a factor of 1.20 (90 degrees Celsius thermosetting/XLPE gives 1.28). The factor is applied to the circuit conductors only, so Corrected Zs = Ze + (R1+R2) x factor, and Ze is added back uncorrected. That is deliberate: the factor's published home is conductor resistance, because On-Site Guide Table I1 and Guidance Note 3 Table B1 list R1+R2 per metre at 20 degrees Celsius and On-Site Guide Table I3 / Guidance Note 3 Table B3 correct those figures to operating temperature. Ze is the external loop back to the transformer. It does not carry your circuit's design current, it does not reach 70 degrees Celsius, and a distributor's declared Ze is already a worst-case figure. Correcting the measured R1+R2 this way lets the resulting Zs be compared directly against the BS 7671 Tables 41.2 and 41.3 limits. This is a different correction from the on-site 0.8 rule in Appendix 3 of BS 7671 (older books cite Appendix 14, which is where it lived before the 18th Edition moved it): there, instead of correcting the measurement, you leave the whole measured loop cold and compare it against 80 percent of the tabulated limit. That screening rule is blunter and stricter than the method used here, because de-rating the limit scales the external part of the loop as well, at an effective 1.25 against this 1.20 on the conductors alone. Anything that passes the 0.8 check passes here too, but not the other way round, so a circuit can pass on this page and still fail the 0.8 check. Guidance Note 3 Appendix A and On-Site Guide Appendix B publish maximum measured Zs values on that 0.8 basis, tabulated for a 10 degrees Celsius ambient, with a further table of factors for other ambient temperatures. The two methods are alternatives for verification and their factors are not interchangeable.

Ze is the external earth fault loop impedance measured at the origin of the installation (before any of your circuits). It depends on your supply type: TN-S typically gives Ze around 0.35 to 0.8 ohms, TN-C-S (PME) around 0.2 to 0.35 ohms, and TT systems may be much higher. Zs is the total loop impedance at any point in the circuit and equals Ze plus the impedances of the line and earth conductors of the circuit (R1+R2).

If Zs exceeds the maximum permitted value, the protective device may not operate quickly enough to disconnect the supply during an earth fault. This creates a risk of electric shock. Options to remedy this include: using a larger cable cross-section to reduce R1+R2, shortening the circuit length, installing an RCD (which can protect circuits with higher Zs values), or changing to a protective device with a higher maximum permitted Zs. Use our Cable Sizing Calculator to select a larger cable, or see our RCD Selection Guide for RCD options.