Wire Resistance Calculator
Enter a material's resistivity, the wire length, and its cross-sectional area to get the electrical resistance in ohms — and see how length and thickness pull the result in opposite directions.
Resistance from three inputs
Enter resistivity, length, and cross-sectional area and the wire resistance calculator returns the resistance (R = ρL/A) in ohms instantly.
Use SI units
Resistivity in Ω·m, length in metres, and area in square metres give the resistance in ohms — remember 1 mm² is 0.000001 m².
What is wire resistance?
How a conductor opposes current
This wire resistance calculator turns three measurements — the material's resistivity, the wire's length, and its cross-sectional area — into the electrical resistance in ohms. Resistance is the opposition a conductor offers to the flow of electric current. It depends on what the wire is made of (its resistivity), how long it is, and how thick it is. A long, thin wire of a poorly conducting material resists current strongly; a short, fat wire of copper barely resists it at all. The same number governs how much voltage a cable drops, how warm it runs under load, and how thick a conductor an installation needs.
Enter the resistivity in Ω·m, the length in metres, and the area in square metres to get the wire resistance in ohms instantly.
Wire resistance is the resistivity multiplied by the length and divided by the cross-sectional area.
R = ρ × L / ALength sits in the numerator, so resistance rises in direct proportion to it: double the length and you double the resistance. The cross-sectional area sits in the denominator, so a thicker wire resists less: double the area and you halve the resistance. The resistivity ρ captures the material itself — copper is about 1.68e-8 Ω·m, aluminium about 2.82e-8 Ω·m. Keep length in metres and area in square metres and the answer comes back in ohms.
Suppose you have 10 metres of standard 1 mm² copper wire (ρ = 1.68e-8 Ω·m, A = 0.000001 m²).
Multiply resistivity by length
1.68e-8 × 10 = 1.68e-7 — the resistivity scaled up by the wire length.
Divide by the area
1.68e-7 ÷ 0.000001 = 0.168 — the length term spread over the cross-section.
Read the resistance
R = 0.168 Ω — the resistance of the 10 m copper run. Doubling its length to 20 m would give 0.336 Ω; doubling its thickness instead would give 0.084 Ω.
The formula is exact for a uniform conductor, but a couple of practical points are worth keeping in mind.
Uniform DC conductor and consistent units
This calculator assumes a uniform conductor carrying direct current at a fixed temperature, using a single resistivity value. It does not model the temperature rise of a loaded cable, the skin effect at high AC frequencies, or contact and connector resistance. Keep your units consistent — ohm-metres for resistivity, metres for length, and square metres for area — or the ohms will be wrong: 1 mm² is 0.000001 m², so convert any area in mm² before you enter it.