How do you calculate the resistance of a wire?
Multiply the resistivity by the length and divide by the cross-section: R = ρL / A. Then correct for temperature, which for copper means multiplying by 1 + 0.00393 × (T − 20 °C).
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Wire resistance calculator
From a material, a length and an AWG size or diameter, this wire resistance calculator finds the DC resistance, corrected for temperature. It also solves for the length that gives a target resistance and the thinnest gauge that stays under one.
Solve for
Examples
Wire size given as
One-way conductor length. Double it for a go-and-return run.
Length unit
°C
A
Optional: voltage drop and power in the wire.
Resistance at 20 °C
842.1 mΩ
- Resistance at 20 °C
- 842.1 mΩ
- Temperature factor R(T) / R(20 °C)
- 1
- Resistivity at 20 °C
- 17.24 nΩ·m
- Resistance per meter
- 84.21 mΩ/m
- Resistance per 1000 ft
- 25.67 Ω
- Diameter
- 0.5106 mm
- Cross-section
- 0.2047 mm²
DC resistance of a solid round wire. A stranded conductor measures about 2 % higher for the same cross-section (NBS Handbook 100, for sizes up to 2,000,000 circular mils, about 1000 mm²), and at high frequency skin effect raises the resistance further.
Same wire in other materials
| Material | R at 20 °C | R at 20 °C |
|---|---|---|
| Copper, annealed (100 % IACS) | 842.1 mΩ | 842.1 mΩ |
| Aluminum, hard-drawn (61 % IACS) | 1.381 Ω | 1.381 Ω |
| Silver, pure annealed | 775.6 mΩ | 775.6 mΩ |
| Gold, pure annealed | 1.082 Ω | 1.082 Ω |
| Tungsten | 2.593 Ω | 2.593 Ω |
| Nichrome 80/20 (Nikrothal 80) | 53.24 Ω | 53.24 Ω |
| Constantan (CuNi44, ISOTAN) | 23.93 Ω | 23.93 Ω |
How do you calculate wire resistance?
Use R = ρL ÷ A, then correct for temperature. 10 m of 24 AWG copper (ρ = 1.7241 × 10⁻⁸ Ω·m, A = 0.2047 mm²) is 842.1 mΩ at 20 °C. Copper gains 0.393 % per °C, so the same wire is 1.057 Ω at 85 °C.
Wire resistance formula
Resistance grows with length and shrinks with cross-section. The material sets the resistivity, and temperature moves it.
R = ρ(T) × L ÷ A
- R
- resistance in Ω
- ρ(T)
- resistivity of the material at temperature T, in Ω·m
- L
- conductor length in m (double it for a go-and-return run)
- A
- cross-section in m²; for a round wire A = π d² ÷ 4
Copper and aluminum add a straight-line temperature correction to the wire resistance equation, taken from their standards:
ρ(T) = ρ20 × (1 + α20 × (T − 20 °C))
- ρ20
- resistivity at 20 °C
- α20
- 0.00393 per °C for annealed copper, 0.00403 per °C for hard-drawn aluminum
Silver and gold are interpolated from the Matula recommended tables, tungsten uses the White and Minges polynomial, and nichrome uses the Kanthal temperature factor, because none of those is a single straight line over its working range. The AWG diameter follows the definition of the gauge:
d = 0.127 mm × 92^((36 − n) ÷ 39)
- n
- gauge number; 00, 000 and 0000 are −1, −2 and −3
How to calculate wire resistance: worked examples
Example 1: 10 m of 24 AWG hookup wire
d = 0.5106 mm, so A = 0.2047 mm². R = 1.7241 × 10⁻⁸ × 10 ÷ (0.2047 × 10⁻⁶) = 842.1 mΩ at 20 °C. At 85 °C the factor is 1 + 0.00393 × 65 = 1.255, giving 1.057 Ω.
Example 2: copper versus aluminum, 25 mm², 50 m, at 40 °C
Copper: 37.19 mΩ. Hard-drawn aluminum: 61.08 mΩ, 1.64 times as much. Aluminum also has the slightly larger coefficient, 0.00403 per °C.
Example 3: a 20 Ω nichrome heater from 0.5 mm wire, running at 400 °C
A = 0.1963 mm² and Ct at 400 °C is 1.04, so ρ = 1.134 µΩ·m. L = R × A ÷ ρ = 3.464 m. Cold, the same element measures 19.23 Ω.
Resistivity of common wire materials
Values at 20 °C from the sources listed below. The coefficient is the mean between 20 °C and 100 °C, for comparison.
| Material | ρ at 20 °C | µΩ·cm | Mean α (per °C) | Basis |
|---|---|---|---|---|
| Copper, annealed (100 % IACS) | 17.24 nΩ·m | 1.724 | 0.00393 | International Annealed Copper Standard |
| Aluminum, hard-drawn (61 % IACS) | 28.26 nΩ·m | 2.826 | 0.00403 | IS 398 Part 1 (maximum resistivity) |
| Silver, pure annealed | 15.88 nΩ·m | 1.588 | 0.00383 | Matula 1979, 99.999 % metal |
| Gold, pure annealed | 22.15 nΩ·m | 2.215 | 0.00375 | Matula 1979, 99.999 % metal |
| Tungsten | 53.1 nΩ·m | 5.31 | 0.0045 | White and Minges fit, 100 to 3600 K |
| Nichrome 80/20 (Nikrothal 80) | 1.09 µΩ·m | 109 | 0.000125 | Kanthal Nikrothal 80 datasheet |
| Constantan (CuNi44, ISOTAN) | 490 nΩ·m | 49 | about 0 | Isabellenhütte ISOTAN datasheet |
AWG resistance chart: copper wire at 20 °C
This copper wire resistance chart is computed from the exact geometric diameter and the annealed copper standard. Printed tables round small diameters to 0.1 mil, so for gauges thinner than about 30 AWG they can differ from these values by up to about 3 %: NBS Handbook 100 lists 1080 Ω per 1000 ft for 40 AWG.
| AWG | Diameter | Area | mΩ per m | Ω per 1000 ft |
|---|---|---|---|---|
| 0000 | 11.68 mm | 107.2 mm² | 0.1608 | 0.04901 |
| 00 | 9.266 mm | 67.43 mm² | 0.2557 | 0.07793 |
| 0 | 8.251 mm | 53.48 mm² | 0.3224 | 0.09827 |
| 2 | 6.544 mm | 33.63 mm² | 0.5127 | 0.1563 |
| 4 | 5.189 mm | 21.15 mm² | 0.8152 | 0.2485 |
| 6 | 4.115 mm | 13.3 mm² | 1.296 | 0.3951 |
| 8 | 3.264 mm | 8.366 mm² | 2.061 | 0.6282 |
| 10 | 2.588 mm | 5.261 mm² | 3.277 | 0.9988 |
| 12 | 2.053 mm | 3.309 mm² | 5.211 | 1.588 |
| 14 | 1.628 mm | 2.081 mm² | 8.285 | 2.525 |
| 16 | 1.291 mm | 1.309 mm² | 13.17 | 4.015 |
| 18 | 1.024 mm | 0.823 mm² | 20.95 | 6.385 |
| 20 | 0.8118 mm | 0.5176 mm² | 33.31 | 10.15 |
| 22 | 0.6438 mm | 0.3255 mm² | 52.96 | 16.14 |
| 24 | 0.5106 mm | 0.2047 mm² | 84.21 | 25.67 |
| 26 | 0.4049 mm | 0.1288 mm² | 133.9 | 40.81 |
| 28 | 0.3211 mm | 0.08098 mm² | 212.9 | 64.9 |
| 30 | 0.2546 mm | 0.05093 mm² | 338.5 | 103.2 |
| 32 | 0.2019 mm | 0.03203 mm² | 538.3 | 164.1 |
| 36 | 0.127 mm | 0.01267 mm² | 1361 | 414.8 |
| 40 | 0.07987 mm | 0.00501 mm² | 3441 | 1049 |
Wire resistance vs temperature: factor by material
Multiply the 20 °C resistance by these factors. Blank cells are outside the published data for that material.
| Material | −40 °C | 0 °C | 25 °C | 50 °C | 75 °C | 100 °C | 150 °C | 200 °C |
|---|---|---|---|---|---|---|---|---|
| Copper, annealed (100 % IACS) | 0.764 | 0.921 | 1.020 | 1.118 | 1.216 | 1.314 | 1.511 | 1.707 |
| Aluminum, hard-drawn (61 % IACS) | 0.758 | 0.919 | 1.020 | 1.121 | 1.222 | 1.322 | 1.524 | 1.725 |
| Silver, pure annealed | 0.773 | 0.924 | 1.019 | 1.114 | 1.210 | 1.307 | 1.504 | 1.703 |
| Gold, pure annealed | 0.780 | 0.926 | 1.018 | 1.112 | 1.205 | 1.300 | 1.493 | 1.689 |
| Tungsten | 0.740 | 0.912 | 1.022 | 1.133 | 1.246 | 1.360 | 1.592 | 1.830 |
| Nichrome 80/20 (Nikrothal 80) | 1.001 | 1.004 | 1.007 | 1.010 | 1.015 | 1.020 | ||
| Constantan (CuNi44, ISOTAN) | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 |
Where the model stops
This is the DC resistance of one solid round conductor. Use the conductor temperature, not the room temperature: a loaded cable runs hotter than its surroundings, and that raises its resistance and its losses together. Stranded conductors read about 2 % high, and enameled, tinned or plated wire can differ from the base metal. Alloy resistance wire is sold to a tolerance (ISOTAN is ±10 % on resistivity), so measure a sample if the value matters. Terminations often add more resistance than a short length of wire, so use a four-wire measurement on anything below about 1 Ω.
Glossary
- Resistivity (ρ)
- The resistance of a unit cube of a material, in Ω·m. It depends on the material and the temperature, not on the shape.
- Temperature coefficient (α)
- The fractional change in resistance per °C, quoted at a reference temperature, here 20 °C.
- IACS
- International Annealed Copper Standard: the 1913 reference that defines 100 % conductivity as 1/58 Ω·mm²/m at 20 °C.
- AWG
- American Wire Gauge. A geometric series of 39 steps between 0.0050 in (36 AWG) and 0.4600 in (0000 AWG).
- Temperature factor (Ct)
- Ratio of resistance at temperature T to resistance at 20 °C, as heating-alloy datasheets publish it.
Related guides
- AWG wire gauge calculator: diameter, area and typical current for any gauge.
- Wire voltage drop calculator: the same resistance applied to a load.
- Ohm's law calculator: turn the resistance into a drop or a current.
Frequently asked questions
What is the resistance of 24 AWG copper wire?
84.21 mΩ per meter at 20 °C, or 25.67 Ω per 1000 ft. Ten meters is 842.1 mΩ.
What is copper wire resistance per foot?
It depends on the gauge. 24 AWG at 20 °C is 0.02567 Ω per foot, or 84.21 mΩ per meter. The AWG resistance chart on this page lists other gauges.
Can I use this as a cable resistance calculator?
Yes. Treat each conductor as one wire and double the length for a go-and-return run. Stranded conductors read about 2 % higher than a solid wire of the same total cross-section.
How much does copper resistance increase with temperature?
About 0.39 % per °C around room temperature. Going from 20 °C to 100 °C raises it by 31.4 %. NBS Handbook 100 treats the curve as linear up to 200 °C.
How much higher is aluminum resistance than copper?
1.64 times the copper value for the same cross-section, because hard-drawn aluminum is 61 % of the conductivity of annealed copper. An aluminum conductor needs about 1.64 times the area to match.
Why do resistivity tables list different values for copper?
Wire tables use the International Annealed Copper Standard, 1.7241 × 10⁻⁸ Ω·m at 20 °C, which is a defined reference for commercial wire. Physics handbooks list pure annealed copper, 1.678 × 10⁻⁸ Ω·m at 293 K, which is 2.7 % lower. This calculator uses the wire standard.
Does stranded wire have higher resistance than solid wire?
Slightly. NBS Handbook 100 uses 2 % more resistance than a solid rod of the same total cross-section for sizes up to 2,000,000 circular mils (about 1000 mm²), rising to 5 % for the largest conductors, because each strand follows a longer helical path.
What is the resistivity of nichrome wire?
1.09 µΩ·m at 20 °C for Kanthal Nikrothal 80, about 63 times copper. It rises only 4 % by 400 °C, so a heater holds nearly the same resistance hot as cold.
Does AC change the resistance of a wire?
Yes, at high enough frequency. Skin effect pushes the current toward the surface and reduces the effective cross-section. This calculator gives the DC value, which is also the mains-frequency value for small conductors.
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Sources
- NBS Handbook 100, Copper Wire Tables (standard annealed copper, AWG definition)
- IS 398 Part 1:1996, aluminum conductors (resistivity and temperature coefficient, clauses 4.1 and 4.3)
- Matula, Electrical Resistivity of Copper, Gold, Palladium and Silver, J. Phys. Chem. Ref. Data 8(4), 1979
- Tolias, Analytical expressions for thermophysical properties of tungsten (White and Minges fit), arXiv:1703.06302
- Kanthal, Nikrothal 80 material datasheet (resistivity and temperature factor)
- Isabellenhütte, ISOTAN (CuNi44) datasheet
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