Earth Fault Loop Impedance Calculator
Check that an earth fault draws enough current to operate the protective device. With the formula, a worked example and typical values.
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Estimate only. Not engineering or safety advice. Check the result against the applicable standard and the equipment data, and have a competent engineer review it before it is relied on. Terms of use.
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About this calculator
This page calculates loop impedance Zs, earth fault current, maximum Zs for this device and 1 more result from nominal voltage to earth, external loop impedance Ze, circuit R1 + R2 and protective device operating current. Change any value or its unit and the result updates. The steps below show the working for the default values, so you can check each line against your own method.
Limits of this calculator
Required disconnection times and the permitted Zs values come from your wiring rules. This only compares the fault current with the device operating current you enter.
Cross-check: 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review.
Verification status: Indicative
Indicative. Estimation only; further engineering checks are required. Basis: Arithmetic addition, bolted fault, device operating current supplied by the user.
What this calculator checks
- Zs = Ze + R1 + R2, the earth-fault current at U0 and the Zs needed for the device operating current you enter.
What remains unverified
- The disconnection time and the permitted Zs from your wiring rules.
- The device trip characteristic, conductor temperature and reactance.
- Ze is yours to obtain from the supply authority or by measurement.
Verification register entry
| Calculation author | Rahul Sharma (author) |
|---|---|
| Technical review | No independent technical review has been carried out |
| Individual professional approval | Not recorded |
| Formula reference | not recorded |
| Standard and edition | IEC 60364-4-41; IEC 60364-5-54, IEC 60364-4-41:2017; IEC 60364-5-54:2011 + A1:2021 Ed 3.1 |
| Standard review state | Public-scope screened; licensed clause review still pending |
| Scope-screening note | Automatic disconnection of supply, earth-fault loop impedance and protective conductors are directly relevant. The calculator uses a simplified TN-loop relation; system type, conductor temperature, measured Ze, protective-device trip characteristic and required disconnection time must be verified. |
| Cross-check test cases | 6 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Indicative |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; licensed clause-by-clause standard review; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Nominal voltage to earth | 230 V |
| External loop impedance Ze | 0.35 Ω |
| Circuit R1 + R2 | 0.55 Ω |
| Protective device operating current | 160 A |
- Zs = Ze + (R1 + R2) = 0.35 + 0.55 = 0.9 Ω
- If = U0 / Zs = 230 / 0.9 = 255.6 A
- Zs(max) = U0 / Ia = 230 / 160 = 1.438 Ω
Assumptions
- Impedances add arithmetically (conservative)
- Conductor resistances are at operating temperature
- Fault is bolted, with no arc impedance
Required disconnection times and the permitted Zs values come from your wiring rules. This only compares the fault current with the device operating current you enter.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Nominal voltage to earth | V | greater than 0 V | |
| External loop impedance Ze | Ω | greater than 0 Ω | |
| Circuit R1 + R2 | Ω | greater than 0 Ω | |
| Protective device operating current | A | greater than 0 A | Current that trips the device within the required time, from its time-current curve |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Loop impedance Zs | Ω | Shown to 3 decimal places | |
| Earth fault current | A | Shown to 1 decimal place | |
| Maximum Zs for this device | Ω | Shown to 3 decimal places | |
| Margin (If / Ia) | (number) | Shown to 2 decimal places |
How it is calculated
Each input is converted to the base unit of its quantity, the formula above is applied in the order shown in the worked example, and each result is shown in the unit you choose. Results are held at full precision and rounded only for display, except where a step selects a standard size, as the worked example shows. A value outside its allowed range is refused with a message instead of giving a result.
How the result changes with nominal voltage to earth
| Nominal voltage to earth (V) | Loop impedance Zs (Ω) | Earth fault current (A) | Maximum Zs for this device (Ω) |
|---|---|---|---|
| 23 | 0.9 | 25.6 | 0.144 |
| 57.5 | 0.9 | 63.9 | 0.359 |
| 115 | 0.9 | 127.8 | 0.719 |
| 230 | 0.9 | 255.6 | 1.438 |
| 460 | 0.9 | 511.1 | 2.875 |
| 920 | 0.9 | 1,022.2 | 5.75 |
| 2,300 | 0.9 | 2,555.6 | 14.375 |
Other inputs are the same as in the worked example above.
Standards and further reading
- IEEE Std 80 (safety in AC substation grounding)
- IEC 60364-5-54 (earthing arrangements and protective conductors)
Soil resistivity varies with season and depth; use measured values and a site-specific design for any installation. These are named as background reading. Elecmetric does not embed clause text or rating tables, and the reviewer record for this calculator is separate from this list.
Frequently asked questions
What do I need to enter?
Enter nominal voltage to earth, external loop impedance Ze, circuit R1 + R2 and protective device operating current. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Impedances add arithmetically (conservative). Conductor resistances are at operating temperature. Fault is bolted, with no arc impedance.
Which calculators should I use next?
Common next steps are Transformer Fault Current and Breaker Rating Selection. The related links at the bottom of this page open them.
How accurate are the results?
Every figure comes from the same tested engine as the Elecmetric calculators and is meant for estimating. 6 reference cases, calculated from textbook formulas coded separately from the engine by the same author, agree with this calculator. This is not an independent review. Check design values against the standard and the equipment data you work to.
Formula guides and reference
Longer explanations with worked examples and tables, written for the same topic.
- Earth Fault Loop and RCD Formulas: Earth fault loop formulas: the loop impedance from the supply and the cable, the fault current
- Earthing Formulas: Earth Rod and Fault Loop: Earthing formulas for the resistance of a vertical earth rod, rods in parallel
More Earthing and Grounding calculatorsAll engineering calculatorsEarth Fault Loop Impedance in Elecmetric