Earth Rods in Parallel Calculator
Combined earth resistance of several rods allowing for mutual interference. 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 combined resistance from single rod resistance, number of rods and utilisation factor. 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
Doubling the rods does not halve the resistance. Deeper rods or lower-resistivity backfill often work better than more rods.
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: Simplified parallel-rod model.
What this calculator checks
- Combined resistance Rn = R1 / (n × u) for the number of rods and the utilisation factor you enter.
What remains unverified
- The utilisation factor is yours: it depends on rod spacing and soil, and is not calculated here.
- Measured soil resistivity and seasonal variation.
- Step and touch voltage.
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 | IEEE 81; IEC 60364-5-54, IEEE 81-2025; IEC 60364-5-54:2011 + A1:2021 Ed 3.1 |
| Standard review state | Public-scope screened; licensed clause review still pending |
| Scope-screening note | Ground-electrode measurement and earthing arrangements are relevant. R/n with a utilisation factor is an approximation; mutual resistance, spacing, soil layering and seasonal variation are not modelled. |
| 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 |
|---|---|
| Single rod resistance | 30 Ω |
| Number of rods | 4 |
| Utilisation factor | 0.85 |
- Rn = 30 / (4 × 0.85) = 8.8235 Ω
Assumptions
- Rods driven in the same soil
- Utilisation factor is user-supplied
Doubling the rods does not halve the resistance. Deeper rods or lower-resistivity backfill often work better than more rods.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Single rod resistance | Ω | greater than 0 Ω | |
| Number of rods | (number) | 1 or more, up to 100 | |
| Utilisation factor | (number) | 0.3 or more, up to 1 | Falls as rods are spaced closer; about 0.8 to 0.9 at spacing of twice the rod length |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Combined resistance | Ω | Shown to 3 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 single rod resistance
| Single rod resistance (Ω) | Combined resistance (Ω) |
|---|---|
| 3 | 0.882 |
| 7.5 | 2.206 |
| 15 | 4.412 |
| 30 | 8.824 |
| 60 | 17.647 |
| 120 | 35.294 |
| 300 | 88.235 |
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 single rod resistance, number of rods and utilisation factor. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
Rods driven in the same soil. Utilisation factor is user-supplied.
Which calculators should I use next?
Common next steps are Earth Rod Resistance and Earth Grid Resistance. 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.
- Earthing Formulas: Earth Rod and Fault Loop: Earthing formulas for the resistance of a vertical earth rod, rods in parallel
- Earth Electrode Spacing Formulas: Earth electrode spacing formulas: two rods in parallel, the interaction factor
More Earthing and Grounding calculatorsAll engineering calculatorsEarth Rods in Parallel in Elecmetric