Zs Calculator
Calculate the maximum permitted earth fault loop impedance (Zs) according to BS 7671 wiring regulations. Compare measured values to corrected design limits for automatic disconnection compliance.
BS 7671 Zs Calculator
How to Use Zs Calculator
Verifying earth fault loop impedance is a critical inspection and testing requirement for verifying electrical safety in UK installations. Follow these steps to determine compliance with BS 7671:
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1Select protective device type. Choose the installed circuit breaker type (Type B, C, or D MCB) or standard UK fuse (BS 88, BS 1361, or BS 3036 rewirable).
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2Select rated current. Pick the rating of the protective device (In) in Amps.
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3Select disconnection time. For fuses, choose the required automatic disconnection time (0.4s for final circuits under 32A, or 5s for distribution boards and large circuits).
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4Enter nominal voltage and correction factors. Verify Uo is set to the UK nominal voltage (typically 230V) and keep the BS 7671 voltage correction factor (Cmin) at its default of 0.95.
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5Enter measured Zs if available. Input the loop impedance value measured with your multifunction tester at the furthest point of the circuit.
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6Click calculate. The calculator will dynamically look up standard BS 7671 tables to present maximum permitted and temperature-corrected design values.
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7Compare measured and permitted values. Review the compliance card to verify if the measured Zs complies with the corrected design limit.
Practical UK Inspection & Testing Example
During an inspection of a commercial final circuit supplying double socket-outlets, the protective device is identified as a Type B 32A MCB. The nominal supply voltage is 230V and a voltage factor of 0.95 is used. The inspector performs a loop impedance test at the end of the line and records a measured Zs of 1.12 Ω. The maximum permitted Zs tabulated in BS 7671 is 1.44 Ω, which corrected for temperature and safety margins yields a design limit of 1.37 Ω. Since the measured 1.12 Ω is less than or equal to 1.37 Ω, the circuit complies with the disconnection time of 0.4s, resulting in a PASS status.
How to Calculate Zs
Earth fault loop impedance (Zs) calculations ensure that during a fault to earth, the prospective fault current is high enough to trip the circuit protective device before a dangerous touch voltage can cause electric shock. Sizing and verification follows standard mathematical relationships defined by the IET Wiring Regulations.
The Earth Fault Loop Formula
The total loop impedance of a circuit is calculated as the sum of external supply path impedance and conductor resistance:
Where:
- Zs = total loop impedance at the furthest point of the circuit (Ω)
- Ze = external earth loop impedance at the origin of the installation (Ω)
- R1 = resistance of the phase (line) conductor (Ω)
- R2 = resistance of the circuit protective conductor (CPC) (Ω)
Determining Maximum Permitted Zs
To guarantee that the protective device trips automatically, the loop impedance must satisfy the disconnection current requirements:
Where:
- Uo = nominal AC voltage to earth (230V in the UK)
- Cmin = minimum voltage factor (0.95 per BS 7671:2018)
- Ia = current causing automatic disconnection within the required time (e.g., 5s or 0.4s)
Worked Example: Type B 32A MCB
Let's calculate the maximum permitted and corrected design loop impedance for a Type B 32A miniature circuit breaker:
Step 1 — Calculate Disconnection Current (Ia)
For Type B MCBs, instantaneous tripping occurs at 5 times the rated current (In). So:
Step 2 — Calculate Unadjusted Maximum Tabulated Zs
Using the nominal voltage Uo = 230V without correction factor:
Step 3 — Apply Temperature Correction Factor
To verify compliance on site at ambient temperatures, the design limit must account for temperature differences using the correction factor (default 0.95):
Final Answer
The maximum design Zs allowed under standard operating conditions is 1.37 Ω. During cold testing, the measured value must not exceed this corrected limit to guarantee safety under operating temperatures.
Why Correction Factors are Applied in UK Installations
Tabulated Zs values in BS 7671 represent the maximum permissible limits when cables are at their maximum operating temperature (70°C for thermoplastic/PVC insulated cables). However, testing is carried out at ambient temperature (typically 10°C to 20°C) when conductors are cold and have lower resistance. To ensure that the loop impedance will not rise above the safe limit when the cables heat up under load, engineers apply the 80% rule of thumb during on-site tests, or adjust the tabulated limits using correction factors like 0.95 (Cmin) to represent a worst-case voltage scenario.
Zs Chart
This table lists the maximum permitted earth loop impedance (Zs) and temperature-corrected limits for standard Type B, Type C, and Type D MCBs at UK nominal supply voltage (230V) with a correction factor of 0.95.
| Device Type | Rating (In) | Maximum Zs (Uncorrected) | Corrected 95% Zs |
|---|---|---|---|
| Type B MCB (BS EN 60898) | 6A | 7.67 Ω | 7.28 Ω |
| Type B MCB (BS EN 60898) | 10A | 4.60 Ω | 4.37 Ω |
| Type B MCB (BS EN 60898) | 16A | 2.88 Ω | 2.73 Ω |
| Type B MCB (BS EN 60898) | 20A | 2.30 Ω | 2.19 Ω |
| Type B MCB (BS EN 60898) | 32A | 1.44 Ω | 1.37 Ω |
| Type B MCB (BS EN 60898) | 40A | 1.15 Ω | 1.09 Ω |
| Type B MCB (BS EN 60898) | 63A | 0.73 Ω | 0.69 Ω |
| Type C MCB (BS EN 60898) | 6A | 3.83 Ω | 3.64 Ω |
| Type C MCB (BS EN 60898) | 10A | 2.30 Ω | 2.19 Ω |
| Type C MCB (BS EN 60898) | 16A | 1.44 Ω | 1.37 Ω |
| Type C MCB (BS EN 60898) | 20A | 1.15 Ω | 1.09 Ω |
| Type C MCB (BS EN 60898) | 32A | 0.72 Ω | 0.68 Ω |
| Type C MCB (BS EN 60898) | 40A | 0.58 Ω | 0.55 Ω |
| Type C MCB (BS EN 60898) | 63A | 0.37 Ω | 0.35 Ω |
| Type D MCB (BS EN 60898) | 6A | 1.92 Ω | 1.82 Ω |
| Type D MCB (BS EN 60898) | 10A | 1.15 Ω | 1.09 Ω |
| Type D MCB (BS EN 60898) | 16A | 0.72 Ω | 0.68 Ω |
| Type D MCB (BS EN 60898) | 20A | 0.58 Ω | 0.55 Ω |
| Type D MCB (BS EN 60898) | 32A | 0.36 Ω | 0.34 Ω |
| Type D MCB (BS EN 60898) | 40A | 0.29 Ω | 0.27 Ω |
| Type D MCB (BS EN 60898) | 63A | 0.18 Ω | 0.17 Ω |
Always verify values against the latest edition of BS 7671 and device manufacturer documentation to ensure full safety compliance.
Zs Calculator Frequently Asked Questions
In electrical installations, Zs is the total earth fault loop impedance of a circuit. It is the sum of the external path impedance (Ze) and the resistance of the circuit line and protective conductors (R1 + R2) from the origin to the furthest point of the circuit. A low Zs is crucial to ensure that enough fault current flows to trip the protective device quickly during a fault.
Maximum Zs is the highest allowable earth fault loop impedance for a specific protective device to ensure automatic disconnection of the electrical supply within the time limits specified by BS 7671 (e.g., 0.4 seconds for final circuits or 5 seconds for distribution circuits). If the actual circuit loop impedance exceeds this maximum value, the protective device may not operate in time, creating a shock risk.
Zs is measured using an earth loop impedance tester (often part of a multifunction tester). The test is performed at the furthest point of the circuit with the supply energized. The tester connects to the line, neutral, and earth terminals and draws a brief current to measure the loop resistance. It can be measured directly or calculated as the sum of Ze and the measured (R1 + R2).
Ze is the external earth fault loop impedance. It represents the impedance of the supply network up to the origin of the installation (usually the consumer unit or distribution board). Ze includes the resistance of the substation transformer windings, the line conductor of the distributor network, and the earth return path (which varies depending on the earthing system: TN-C-S, TN-S, or TT).
BS 7671 incorporates a voltage factor, Cmin, which is typically 0.95 for UK 230V/400V installations. This factor accounts for fluctuations in the mains supply voltage. By multiplying the nominal voltage (Uo) by Cmin, we calculate a lower minimum fault current, which translates to a safer, lower maximum permitted Zs value. This ensures the circuit remains safe even when the supply voltage drops slightly.
If Zs is too high, the prospective earth fault current will be too low. Consequently, during a line-to-earth fault, the protective device (fuse or circuit breaker) will take too long to disconnect the supply, or might not trip at all. This leaves metallic parts of the installation energized at a dangerous touch voltage, creating a severe risk of electric shock and potential electrical fires.
Ze is the external loop impedance measured at the origin of the installation (supplied by the network provider), whereas Zs is the total loop impedance of a specific circuit measured at its furthest point. The difference between them is the resistance of the circuit's own line and protective conductors, mathematically expressed as Zs = Ze + (R1 + R2).
Yes, BS 7671 requires Zs testing (or verification by calculation) during both initial verification of new installations and periodic inspection and testing (EICRs) of existing systems. It is one of the most critical safety tests to prove that the automatic disconnection of supply (ADS) works as designed, guaranteeing protection against electric shock under fault conditions.