Wire Resistance Calculator
Wire resistance is R = ρ L / A: 100 m of 2.5 mm² annealed copper (ρ = 0.017241 Ω·mm²/m at 20 °C) has R = 0.017241 × 100 ÷ 2.5 = 0.6897 Ω.
0.689655172413793 Ω
Full answer, then cut to fewer decimals (not rounded):
- 0.689655172413793 Ω
- 0.68965517241379 Ω
- 0.6896551724137 Ω
- 0.689655172413 Ω
- 0.68965517241 Ω
- 0.6896551724 Ω
- 0.689655172 Ω
- 0.68965517 Ω
- 0.6896551 Ω
- 0.689655 Ω
- 0.68965 Ω
- 0.6896 Ω
- 0.689 Ω
- 0.68 Ω
- 0.6 Ω
- ρ = 1.7241 µΩ·cm = 1.7241 × 10⁻⁸ Ω·m (100 %IACS)
- A = 2.5 mm²
- R = 1.7241 × 10⁻⁸ Ω·m × 100 m ÷ 0.0000025 m² = 0.689655 Ω
- Resistivity is at 20 °C; copper resistance rises by about 0.39 % per °C.
Resistance Formula and %IACS
R = ρ L / A ρ = 1 / σ σ = %IACS / 100 × 58 MS/m
R resistance (Ω), ρ resistivity (Ω·m), L length (m), A cross-section (m²), σ conductivity (S/m)
| Conductor | µΩ·cm | Ω·mm²/m | %IACS |
|---|---|---|---|
| Annealed copper | 1.724 | 0.01724 | 100 |
| Hard-drawn copper | 1.777 | 0.01777 | 97 |
| Aluminium 1350 (EC) | 2.826 | 0.02826 | 61 |
| Silver | 1.59 | 0.0159 | 108 |
| Gold | 2.44 | 0.0244 | 70.7 |
| Brass C26000 | 6.2 | 0.062 | 27.8 |
| Stainless steel 304 | 72 | 0.72 | 2.39 |
| Nichrome 80/20 | 108 | 1.08 | 1.6 |
Annealed copper is exact by the IACS definition (NBS Handbook 100). Other values are typical for the grade and vary with purity, temper and alloy.
Worked Examples
- 100 m of 2.5 mm² copper: R = 0.017241 × 100 ÷ 2.5 = 0.6897 Ω; the loop of a 100 m two-wire run is twice that.
- 50 m of 16 mm² aluminium (61 %IACS, ρ = 0.02826 Ω·mm²/m): R = 88.33 mΩ.
- 1000 ft of solid copper wire, 0.0808 in diameter (12 AWG): R = 1.589 Ω.
- 2 m copper busbar, 50 × 5 mm: R = 0.1379 mΩ.
Frequently asked questions
What is the formula for wire resistance?
R = ρ L / A: resistivity times length divided by cross-sectional area. With ρ in Ω·mm²/m, L in m and A in mm², R comes out directly in ohms (copper: ρ = 0.017241 Ω·mm²/m).
What is %IACS?
Conductivity as a percentage of the International Annealed Copper Standard, a reference copper of exactly 58 MS/m (1.7241 µΩ·cm) at 20 °C. Resistivity is ρ = 1 / (%IACS/100 × 58 × 10⁶) Ω·m.
Do I use one-way or round-trip length?
Use the total conductor length that carries current. For a two-wire circuit (out and back), the loop resistance uses twice the cable run.
How does temperature change the resistance?
Metal resistance rises with temperature: R(T) ≈ R₂₀ (1 + α (T − 20 °C)), with α ≈ 0.00393 /°C for annealed copper and about 0.0040 /°C for aluminium. This calculator gives the 20 °C value.
Why is aluminium cable larger than copper for the same current?
EC-grade aluminium has about 61 %IACS, so its resistivity is 1/0.61 ≈ 1.64 times that of copper. It needs about 64 % more cross-section for the same resistance, but it is much lighter.
What is specific resistance?
Specific resistance is another name for resistivity ρ: the resistance of a conductor 1 m long with a 1 m² cross-section (Ω·m). In cable work it is usually given in Ω·mm²/m, which is 0.017241 for annealed copper.
What happens to resistance when a wire is stretched?
Stretching keeps the volume constant, so if the length becomes n times longer the area becomes n times smaller and the resistance becomes n² times larger. Doubling the length of a wire by stretching makes its resistance four times higher.
How do I calculate cable resistance from mm²?
Divide resistivity × length by the cross-section: for copper, R = 0.017241 × L[m] ÷ A[mm²] Ω at 20 °C. A 50 m run of 4 mm² copper is 0.017241 × 50 ÷ 4 = 0.2155 Ω per conductor.
Sources
- Copper Wire Tables, NBS Handbook 100 (International Annealed Copper Standard), National Bureau of Standards (now NIST) .
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Wire Resistance Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/wire-resistance/
IEEE
Scientific Converters, "Wire Resistance Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/wire-resistance/