Ze Calculator
Determine external earth fault loop impedance (Ze) using measured loop impedance values and installation parameters in accordance with BS 7671.
Ze Calculator
How to Use Ze Calculator
Determining the external earth fault loop impedance (Ze) is an essential part of verifying safety during initial installation verification and periodic inspection (EICR) testing. Follow these steps to use the calculator:
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1Select calculation mode. Choose "Measured Ze" if you have measured the value directly at the origin, or "Calculate from Zs and R1+R2" if you are using circuit parameters.
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2Enter measured values. Input the direct Ze value or enter the total measured loop impedance (Zs) and circuit conductor resistances (R1 + R2) in Ohms.
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3Click Calculate. Trigger the calculation engine to process the impedance values.
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4Review calculated Ze. View the final external loop impedance value displayed in Ohms.
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5Compare against typical UK supply characteristics. Check the installation assessment card to see if the value aligns with standard TN-C-S, TN-S, or TT earthing systems.
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6Use results during EICR or installation verification. Record the verified Ze on your electrical installation certificate or condition report.
How to Calculate Ze
External earth fault loop impedance (Ze) represents the impedance of the electrical path from the origin of the installation back to the substation transformer windings. It is a critical component of the total loop impedance, ensuring that protective devices operate within BS 7671 disconnection time limits during a fault.
Ze Calculation Formulas
Depending on your testing method, Ze is determined either by direct measurement or by calculation from total circuit impedance:
Formula 1 — Direct Measurement
Formula 2 — Derivation from Zs
Where:
- Ze = External Earth Fault Loop Impedance (Ω)
- Zs = Total Earth Fault Loop Impedance at the furthest point (Ω)
- R1 + R2 = Sum of line and protective conductor (CPC) resistances (Ω)
Worked Example
Suppose you perform an inspection on a domestic ring main circuit and record the following parameters:
- Measured Total Loop Impedance (Zs) = 0.68 Ω
- Conductor Resistance (R1 + R2) = 0.22 Ω
Apply the subtraction formula to determine the external loop path:
Final Answer: Ze is calculated as 0.46 Ω.
Interpretation: Since this value is higher than 0.35 Ω, it exceeds the standard utility limit for a TN-C-S supply. However, it is within the 0.80 Ω limit allowed for a TN-S supply. The inspector should verify the earthing system type on-site to ensure full safety compliance.
Ze Chart
This table lists typical maximum permitted external loop impedance (Ze) limits for standard UK earthing systems under normal network conditions.
| Supply Type | Typical Maximum Ze (Ω) | Description |
|---|---|---|
| TN-C-S | 0.35 Ω | Protective Multiple Earthing (PME) supply. Combined neutral and earth path. |
| TN-S | 0.80 Ω | Separate line, neutral, and earth conductor path from transformer. |
| TT | 21.00 Ω | Requires RCD protection. Relying on local ground electrode resistance. |
Values should always be verified against the latest BS 7671 requirements and DNO information.
Ze Calculator Frequently Asked Questions
In UK electrical testing, Ze represents the external earth fault loop impedance measured at the origin of an installation, such as the main switch or consumer unit. It is the impedance of the external supply path, including the distributor's cables, substation transformer windings, and the earthing return path. Ze is verified under energized conditions with all bonding conductors disconnected to ensure a true external loop path.
Ze can be calculated by subtracting the protective conductor resistance of the line and CPC (R1 + R2) from the total measured earth fault loop impedance (Zs) at the end of the circuit, using the formula Ze = Zs - (R1 + R2). Alternatively, it can be measured directly at the origin of the installation with parallel paths temporarily isolated, which is the preferred method for initial verification under BS 7671.
A good Ze value is one that falls well within the standard limits set by the Distribution Network Operator (DNO) and BS 7671. For a TN-C-S (PME) supply, the Ze should not exceed 0.35 Ω. For a TN-S supply, the maximum limit is 0.80 Ω. For TT earthing systems, typical values are higher, but a stable earth electrode resistance (Ze) of under 21 Ω (ideally below 100 Ω) is recommended.
Under standard UK utility agreements and BS 7671, the maximum permitted external earth fault loop impedance (Ze) for a TN-C-S (Protective Multiple Earthing) supply is 0.35 Ω. If measurements exceed this value, it indicates a high-resistance fault in the DNO supply neutral/earth conductor, which must be immediately reported to the network provider for investigation and repair.
Ze is the external earth fault loop impedance measured at the origin of the installation (e.g., at the consumer unit) with parallel earth paths isolated. Zs is the total earth fault loop impedance measured at the furthest point of a specific circuit. The difference between them is the resistance of that circuit's line and earth conductors (R1 + R2), mathematically expressed as Zs = Ze + (R1 + R2).
Testing Ze during an Electrical Installation Condition Report (EICR) is vital to verify that the DNO's external earth connection is present and of low enough resistance. If the external earth is compromised or high resistance, the protective devices (MCBs, fuses) will not operate under fault conditions, leading to sustained hazardous touch voltages on exposed conductive parts of the property.
