How do I calculate the resistance of a wire?

R = resistivity × length ÷ cross-section area. With resistivity in ohm-metres, length in metres and area in square metres the answer is in ohms. 60 m of 2.5 mm² copper (1.72 × 10⁻⁸ Ω·m) is 1.72e-8 × 60 ÷ 2.5e-6 = 0.413 Ω.

What is the resistance of 12 AWG copper wire?

The AWG definition makes 12 AWG a 0.0808 in (2.05 mm) wire of 3.31 mm². At copper's 1.72 × 10⁻⁸ Ω·m and 20 °C that is about 1.58 Ω per 1,000 ft, or 5.20 Ω per km. A 100 ft circuit — 200 ft of wire out and back — is about 0.317 Ω.

Do I use one-way length or round trip?

For the resistance a load actually sees on a two-wire circuit, use the round trip: the current goes out on one conductor and back on the other, so 100 ft of cable is 200 ft of wire. Use one-way when you want the resistance of a single conductor, for example to compare with a meter reading end to end.

How much does temperature change wire resistance?

Copper gains about 0.393% of its 20 °C resistance per degree Celsius (aluminium about 0.403%). A copper conductor running at 75 °C (167 °F) is 1 + 0.00393 × 55 = 1.216 times its 20 °C figure — about a fifth higher. Type the conductor temperature and the tool applies it.

Wire resistance calculator

Length of run

Count the length

Conductor size

Metal

Resistivity at 20 °C

Ω·m

Physical constant — copper 1.72e-8, aluminium 2.82e-8. Edit for another alloy.

Conductor temperature

°F

68 °F (20 °C) means no correction.

Temperature coefficient

per °C

Copper 0.00393, aluminium 0.00403.

Current (optional)

The load current, for volts dropped and watts lost.

— Ω

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Show the working — with your numbers

R = ρ × L ÷ A on the size, length and resistivity you type, with a straight-line temperature correction. It is a solid conductor carrying DC — stranding, AC skin effect and reactance all add a little. It says nothing about how much current a conductor may carry; that is your code book's job.

Type the run length, whether to count it out and back, the conductor size as an AWG number or in mm², and the metal. The tool works out the area from the size, the resistance from the resistivity, corrects it for the conductor temperature, and — at the current you give it — the volts dropped and watts lost in the wire.

Worked example

Imperial: a 100 ft run of 12 AWG copper, out and back, so 200 ft (60.96 m) of wire. 12 AWG is 3.31 mm² by the gauge definition. R = 1.72e-8 × 60.96 ÷ 3.309e-6 = 0.317 Ω at 20 °C (68 °F). At 12 A it drops 12 × 0.317 = 3.80 V and turns 12² × 0.317 = 45.6 W into heat in the wire. Running warm at 167 °F (75 °C) the same run is 0.317 × 1.216 = 0.385 Ω.

Metric: a 30 m run of 2.5 mm² copper, out and back, 60 m of wire. R = 1.72e-8 × 60 ÷ 2.5e-6 = 0.413 Ω. At 16 A that is 6.6 V dropped and 106 W lost. At a conductor temperature of 70 °C, × (1 + 0.00393 × 50) = 1.197, so 0.494 Ω.

On the job

Check it against the meter. On a dead, disconnected run, twist the far ends together and read the loop from the near end. That reading is the round trip; subtract your test leads (touch them together first). A reading well above the calculated figure points at a loose termination or a splice, not the wire.

Aluminium needs more metal. Aluminium's resistivity is about 1.64 times copper's, so the same resistance takes about 1.64 times the area — roughly two gauge numbers bigger. That is why aluminium feeders come a size or two up from the copper they replace.

Three gauge numbers doubles the copper. Every 3 AWG numbers smaller doubles the area and halves the resistance: 10 AWG is about half the ohms of 13, 12 AWG about half of 15. It is the quick way to see what going up a size buys.

Quick referencefor conductor resistance

Copper: ρ = 1.72 × 10⁻⁸ Ω·m · α 0.00393 /°C
Aluminium: ρ = 2.82 × 10⁻⁸ Ω·m · α 0.00403 /°C
Copper Ω per km: 17.2 ÷ mm² — 2.5 mm² is 6.88 Ω/km
Per 1,000 ft: Ω/km × 0.3048 — 12 AWG Cu is 5.20 Ω/km, 1.58 Ω/1,000 ft
AWG diameter: 0.005 in × 92^((36 − n) ÷ 39)
Temperature: R × (1 + α × (T − 20 °C)) · °C = (°F − 32) ÷ 1.8

The formula

R = ρ × L ÷ A × (1 + α × (T − 20 °C))

ρ in Ω·m, L in metres (feet × 0.3048, doubled for a round trip), A in m² (mm² ÷ 1,000,000). At a current I, the volts dropped are I × R and the watts lost I² × R.

Questions

How do I calculate the resistance of a wire?: R = resistivity × length ÷ cross-section area. With resistivity in ohm-metres, length in metres and area in square metres the answer is in ohms. 60 m of 2.5 mm² copper (1.72 × 10⁻⁸ Ω·m) is 1.72e-8 × 60 ÷ 2.5e-6 = 0.413 Ω.
What is the resistance of 12 AWG copper wire?: The AWG definition makes 12 AWG a 0.0808 in (2.05 mm) wire of 3.31 mm². At copper's 1.72 × 10⁻⁸ Ω·m and 20 °C that is about 1.58 Ω per 1,000 ft, or 5.20 Ω per km. A 100 ft circuit — 200 ft of wire out and back — is about 0.317 Ω.
Do I use one-way length or round trip?: For the resistance a load actually sees on a two-wire circuit, use the round trip: the current goes out on one conductor and back on the other, so 100 ft of cable is 200 ft of wire. Use one-way when you want the resistance of a single conductor, for example to compare with a meter reading end to end.
How much does temperature change wire resistance?: Copper gains about 0.393% of its 20 °C resistance per degree Celsius (aluminium about 0.403%). A copper conductor running at 75 °C (167 °F) is 1 + 0.00393 × 55 = 1.216 times its 20 °C figure — about a fifth higher. Type the conductor temperature and the tool applies it.

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