What wire resistance is and why it matters
Every conductor resists the flow of current, and the resistance of a wire depends on what it is made of, how long it is and how thick it is. Long, thin wires resist more than short, thick ones, and copper resists less than aluminum or iron. Resistance turns some of the electrical energy into heat and causes a voltage drop along the wire, which is why undersized extension cords get warm and low-voltage lighting runs dim at the far end.
Use this calculator to estimate the resistance of a straight run of round wire when you know the material, the length and the conductor diameter. It is useful when planning low-voltage runs such as speakers, LED strips or automotive circuits, when checking a coil of wire with a multimeter, or when comparing copper against aluminum. Enter an optional current to see the voltage drop and power lost in the wire itself.
Formula and variables
R = ρ × L / A, with A = π × (d / 2)²
- ρ (rho) is the resistivity of the material in ohm-metres at 20 °C. The calculator uses 1.68 × 10⁻⁸ for copper, 2.65 × 10⁻⁸ for aluminum, 1.59 × 10⁻⁸ for silver, 2.44 × 10⁻⁸ for gold and 9.71 × 10⁻⁸ for iron.
- L is the length in metres. For a two-wire circuit use the total out-and-back length.
- d is the conductor diameter, entered in millimetres and converted to metres.
- A is the cross-sectional area. The result panel shows it in mm².
- Voltage drop is I × R, and power lost as heat is I² × R.
Worked example
Take 50 m of copper wire with a 2 mm diameter. The radius is 1 mm, so A = π × (0.001 m)² = 3.1416 × 10⁻⁶ m², or 3.142 mm². Then R = 1.68 × 10⁻⁸ × 50 / 3.1416 × 10⁻⁶ = 0.2674 Ω. Per metre that is 5.348 mΩ. If 10 A flows, the voltage drop is 10 × 0.2674 = 2.674 V and the wire dissipates 10² × 0.2674 = 26.74 W. On a 12 V supply that is a large loss, showing why thicker wire is needed for long low-voltage runs.
Common mistakes and how to interpret the result
- Confusing diameter and radius. The area depends on the square of the radius, so entering a radius as the diameter makes the result four times too large.
- Forgetting the return path. Current travels out and back, so a circuit that is 25 m from source to load has 50 m of conductor.
- Ignoring temperature. Resistivity values apply at 20 °C. Copper resistance rises roughly 0.4% per degree Celsius, so hot wire resists more.
- Using solid-wire numbers for stranded cable. Stranded wire has slightly higher resistance for a given overall diameter because of gaps between strands. Use the rated copper area when known.