Wire resistance calculator
Enter the wire and length, get its resistance.
How do you calculate wire resistance?
R = ρ × L ÷ A: resistivity times length divided by the cross-sectional area. At 20 °C copper has ρ = 1.68 × 10⁻⁸ Ω·m and aluminum 2.65 × 10⁻⁸ Ω·m (OpenStax University Physics).
Example
OpenStax: 5 m of 12-gauge copper wire (2.053 mm across, 3.31 mm²) has a resistance of about 0.025 Ω. 100 feet of it is about 0.155 Ω.
How are AWG sizes defined?
No. 0000 is 0.4600 inch and No. 36 is 0.0050 inch, with 38 sizes between in a geometric series: d = 0.005 in × 92^((36 − n)/39). 12 AWG is 0.0808 inch and 14 AWG 0.0641 inch.
Does temperature matter?
Yes — resistance rises about 0.39% per °C for copper and aluminum: ρ = ρ₂₀ (1 + 0.0039 × (T − 20)). 12 AWG copper at 75 °C is about 21% more resistive than at 20 °C.
Is this the voltage drop on my circuit?
Multiply the resistance of the whole path (out and back) by the current. The voltage drop calculator does this for you.
How does the resistance change with the AWG number?
Smaller AWG numbers are thicker wires, and each step changes the diameter by the same factor, 92^(1/39) = 1.1229. Three steps change the cross-sectional area by a factor of about 2.01: 12 AWG has twice the area, and so half the resistance, of 15 AWG. Ten steps change the area by about 10.2. For 100 feet of copper at 20 °C, 14 AWG is 0.246 Ω, 12 AWG 0.155 Ω and 10 AWG 0.097 Ω.
How much worse is aluminum than copper?
For the same size, aluminum's resistivity of 2.65 × 10⁻⁸ Ω·m is about 1.58 times that of copper at 1.68 × 10⁻⁸ Ω·m. So 100 feet of 12 AWG aluminum is 0.244 Ω, against 0.155 Ω for copper. To match the resistance of copper, aluminum has to have about 1.6 times the cross-sectional area, which is why aluminum feeders are one or two sizes larger.
The formula and its inputs
The resistance of a uniform wire is R = ρ L ÷ A, where ρ is the resistivity of the metal, L is the length and A is the cross-sectional area. The area comes from the AWG diameter: the American Wire Gauge defines the diameter of No. 36 as 0.005 inch and No. 0000 as 0.460 inch, with 39 geometric steps between them (ASTM B258), and the area is π d² ÷ 4. Resistivity depends on the temperature: ρ(T) = ρ₂₀ [1 + α (T − 20 °C)], with α = 0.0039 per °C for both copper and aluminum. The values at 20 °C are those of OpenStax University Physics, Volume 2, Table 9.1. The calculator reports the diameter, the area and the resistance per 1,000 feet as well.
Worked example: 100 feet of 12 AWG copper
The diameter is 2.053 mm, so the area is 3.309 mm². The length is 100 ft = 30.48 m. R = 1.68 × 10⁻⁸ × 30.48 ÷ 3.309 × 10⁻⁶ = 0.1548 Ω at 20 °C. At 75 °C the resistivity is higher by 0.0039 × 55 = 21.5%, so the same wire measures 0.1880 Ω. A circuit has a conductor out and a conductor back, so a load 100 feet from the source has a loop resistance of 0.3095 Ω (200 ft of wire). At 15 A, the voltage lost in that loop is 4.64 V. For 1,000 feet of 12 AWG copper the resistance is 1.548 Ω.
Where this applies
The formula describes the DC resistance of a solid round conductor. Stranded wire is slightly higher than the solid value for the same gauge, because of the gaps between strands and the lay of the strands. For alternating current at power frequencies in household-sized wire, the AC resistance is nearly the same as the DC value; in large conductors and at higher frequencies the current crowds toward the surface (skin effect) and the resistance rises. The calculator ignores contact resistance at terminals and joints, which can matter more than the wire itself in poor connections.
Common mistakes
Using the one-way length for a circuit loop, so the resistance is half the true value, is the most common. Mixing feet and meters is another: the form has a unit selector. Assuming copper resistance at 20 °C applies to a hot conductor in a conduit or attic undercounts the loss. Using the AWG number as a size in millimeters, or forgetting that larger numbers mean thinner wire, leads to the wrong gauge. And a resistance is not a voltage drop: multiply by the current, and use the voltage drop calculator for the percentage and the code limits.
Sources: OpenStax University Physics, Volume 2, chapter 9 (resistivity, Table 9.1, and the temperature dependence of resistivity); ASTM B258 for American Wire Gauge diameters. Related: voltage drop calculator, wire size calculator and Ohm's law calculator.