Copper vs Aluminium Conductor Calculator
Resistance of a copper and an aluminium conductor, and the aluminium size that matches copper. 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 copper resistance, aluminium resistance, same size, aluminium size for equal resistance and 1 more result from copper cross-section and length. 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
Aluminium needs about 1.64 times the area but weighs about half as much. Terminations, ampacity tables and bending radius are separate checks.
Cross-check: 15 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: Engineering reference
Engineering reference. Formula and method documented and tested against separately coded reference calculations. Not yet Verified: the evidence listed on this page is still needed.
What this calculator checks
- The arithmetic of the published formula for the values you entered, in the units shown.
What remains unverified
- That the inputs suit your application. Take ratings, resistances and constants from the manufacturer data sheet or project specification.
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 | Not applicable: The calculator compares conductor resistivity using a textbook relationship. Material specifications and conductor resistance are standardized separately; no single standard governs this comparison equation. |
| Standard review state | Not applicable |
| Scope-screening note | not recorded |
| Cross-check test cases | 15 reference vectors (tests/reference_vectors.json) |
| Review date | not recorded |
| Next review date | not recorded |
| Status | Engineering reference |
Needed before this calculator can be marked Verified: reviewer name, qualification and review date; exact formula reference; formula source (textbook or standard); next review date.
Formula
Worked example
| Input | Value |
|---|---|
| Copper cross-section | 95 mm² |
| Length | 100 m |
- Rcu = ρ L / A = 0.018148 Ω
- Ral = 0.029752 Ω
- ρAl / ρCu = 1.6393, so aluminium needs 155.7 mm²
- Mass ratio = 1.6393 × 2700 / 8960 = 0.494
Assumptions
- ρ at 20 °C: copper 1.7241e-8, aluminium 2.8264e-8 Ω·m
- Density: copper 8960, aluminium 2700 kg/m³
Aluminium needs about 1.64 times the area but weighs about half as much. Terminations, ampacity tables and bending radius are separate checks.
Inputs and results
| Input | Unit | Allowed or shown | Note |
|---|---|---|---|
| Copper cross-section | mm² | greater than 0 mm² | |
| Length | m | greater than 0 m |
| Result | Unit | Allowed or shown | Note |
|---|---|---|---|
| Copper resistance (20 °C) | Ω | Shown to 5 decimal places | |
| Aluminium resistance, same size | Ω | Shown to 5 decimal places | |
| Aluminium size for equal resistance | mm² | Shown to 1 decimal place | |
| Aluminium mass vs copper (equal resistance) | (number) | 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 copper cross-section
| Copper cross-section (mm²) | Copper resistance (Ω) | Aluminium resistance, same size (Ω) | Aluminium size for equal resistance (mm²) |
|---|---|---|---|
| 9.5 | 0.18148 | 0.29752 | 15.6 |
| 23.8 | 0.07244 | 0.11876 | 39 |
| 47.5 | 0.0363 | 0.0595 | 77.9 |
| 95 | 0.01815 | 0.02975 | 155.7 |
| 190 | 0.00907 | 0.01488 | 311.5 |
| 380 | 0.00454 | 0.00744 | 623 |
| 950 | 0.00181 | 0.00298 | 1,557.4 |
Other inputs are the same as in the worked example above.
Standards and further reading
- IEC 60364-5-52 (selection and erection of wiring systems, current-carrying capacity)
- IEC 60364-4-43 (protection against overcurrent, short-circuit withstand k factors)
- IEC 60228 (conductor sizes)
- IEC 60287 (calculation of cable current rating)
Ampacity and grouping factors come from your cable data sheet or your licensed copy of the standard; see STANDARDS.md for the method constants Elecmetric does use. 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 copper cross-section and length. Change the unit of a value with its selector and the result stays the same.
What does this calculator assume?
ρ at 20 °C: copper 1.7241e-8, aluminium 2.8264e-8 Ω·m. Density: copper 8960, aluminium 2700 kg/m³.
Which calculators should I use next?
Common next steps are Voltage Drop from Conductor Size and Cable Size for Voltage Drop. 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. 15 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.
- Conductor Resistance Formulas and Temperature: Conductor resistance formulas: resistance from length, area and resistivity, correction for temperature
- Cable Size Formulas: Current and Short-Circuit: Cable sizing formulas for current capacity with correction factors, conductor resistance and temperature
More Cable Engineering calculatorsAll engineering calculatorsCopper vs Aluminium Conductor in Elecmetric