Estimate earth loop impedance Zs from Ze and R1+R2, or compare measured Zs with a selected Type B, C or D MCB reference. A reference comparison alone does not establish BS 7671 compliance.
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ZS (Earth Loop Impedance) Formula
The ZS value represents the total impedance of the earth fault loop at the point of the circuit. In simple terms, it combines the external supply-side earth loop impedance with the resistance of the circuit conductors involved in the fault path. This calculator estimates Zs from Ze and the combined R1+R2 resistance, or compares a measured Zs with a selected reference for a 230 V TN circuit.
In this relationship:
| Term | Meaning | Typical Unit | Why It Matters |
|---|---|---|---|
| Zs | Total earth fault loop impedance at the circuit | ohms (Ω) | This is the final value used to judge how easily fault current can flow. |
| Ze | External earth loop impedance | ohms (Ω) | Represents the supply-side contribution before the final circuit conductors are added. |
| R1 | Resistance of the line conductor | ohms (Ω) | Increases with conductor length, temperature, and reduced cross-sectional area. |
| R2 | Resistance of the protective conductor | ohms (Ω) | Forms part of the return path during an earth fault. |
Rearranged Forms
For algebraic reference, the same approximate relationship can be rearranged as follows. These individual inverse calculations are not separate modes in this calculator:
The rearrangements require consistent units and compatible impedance/resistance assumptions. This widget accepts the combined conductor resistance R1+R2.
How to Calculate ZS
- Determine the external earth loop impedance, Ze.
- Find the line conductor resistance, R1.
- Find the protective conductor resistance, R2.
- Add the conductor resistances together.
- Add that result to Ze to obtain Zs.
Mathematically, the process is simply:
Example Calculation
Assume the following values are known:
- External earth loop impedance, Ze = 0.35 Ω
- Line conductor resistance, R1 = 0.18 Ω
- Protective conductor resistance, R2 = 0.12 Ω
First add the conductor resistances:
Then add that value to the external impedance:
The calculated earth loop impedance is 0.65 Ω.
Why ZS Is Important
Earth loop impedance affects the magnitude of fault current that can flow during a line-to-earth fault. In general, a lower Zs allows higher fault current, which helps protective devices operate more quickly. A higher Zs limits fault current and can make disconnection slower or inadequate if it exceeds the permitted value for the protective device and circuit arrangement.
A common approximation for fault current is:
Where:
- If = prospective earth fault current
- Uo = nominal line-to-earth voltage
- Zs = earth fault loop impedance
This is why even a modest increase in loop impedance can materially reduce available fault current.
What Affects Earth Loop Impedance
- Circuit length: Longer conductors generally increase resistance.
- Conductor size: Smaller conductors have higher resistance.
- Conductor material: Copper and aluminum have different resistivities.
- Temperature: Resistance rises as conductor temperature increases.
- Connection quality: Loose, corroded, or damaged terminations can raise impedance.
- Supply characteristics: The external impedance seen at the origin can vary between installations.
- Parallel earth paths: Measured values may differ from purely calculated values where additional conductive paths exist.
Using the Calculator Correctly
- Enter all values in ohms.
- Do not mix ohms with milliohms unless you convert first.
- Enter the combined R1+R2 resistance in its single input.
- Choose an operating-temperature reference or the 80% cold/measured allowance. A device-specific maximum overrides the generic calculation; do not reduce an already adjusted maximum again.
- Keep enough decimal places to avoid rounding errors on low-impedance circuits.
Common Mistakes
- Using an estimated value for Ze without checking whether it matches the actual supply arrangement.
- Entering total loop impedance as both Zs and Ze.
- Forgetting that conductor resistance changes with temperature.
- Confusing R1+R2 with either R1 or R2 alone.
- Assuming a calculated value always matches a measured field result exactly.
Practical Interpretation
The calculator gives an approximate resistive estimate of Zs. Reactance, conductor temperature, contact resistance, meter method and parallel return paths can affect actual measurements. The generic reference is 230 × 0.95 divided by 5, 10 or 20 times the Type B, C or D rated current. The 0.95 factor accounts for voltage variation; the separate 0.8 cold/measured allowance accounts for the usual temperature margin. Use current device-specific data and the required disconnection time, particularly for Type D devices. These values are calculated references, not a compliance verdict or a substitute for a published table. TT/RCD protection requires a separate assessment; a supply-only TT impedance excludes the installation electrode.
If you are troubleshooting or verifying a live electrical installation, a proper loop impedance test and qualified review are still important, because safety depends on actual fault performance rather than calculation alone.
