Wire Resistance Calculator

How conductor resistance works

The resistance of a wire is R = ρ · L / A, where ρ is the material's resistivity (in Ω·m), L the length (m), and A the cross-sectional area (m²). Copper has ρ = 1.68×10⁻⁸ Ω·m, aluminium 2.82×10⁻⁸, gold 2.44×10⁻⁸, and silver 1.59×10⁻⁸ — silver is the best metallic conductor, but copper wins on cost. Resistivity also rises with temperature in metals (positive temperature coefficient), so a hot conductor resists more than a cold one.

Worked example: 30 m of 2.5 mm² copper wire gives R ≈ 0.2 Ω. In Brazil wires are sold by cross-section in mm² (Brazilian standard NBR 5410); the US uses AWG, where a smaller AWG number means a thicker wire (AWG 12 ≈ 3.3 mm², rated near 25 A for residential use). Ampacity per gauge follows NBR 5410, accounting for insulation type and installation method. Joule's law P = R · I² shows why an undersized wire carrying high current heats up: dissipated power scales with the square of current.

Practical applications

Residential electrical installations (NBR 5410 dictates wire gauge per circuit), power-line transmission loss calculations, and selecting the right gauge for long runs to motors, ovens, and shower heaters all rely on this formula. Undersized wiring is a leading cause of residential fires.

FAQ

Why does longer wire mean more resistance? Charge carriers face more collisions with the lattice over a longer path — resistance scales linearly with length. Doubling the run doubles the resistance, all else equal.

Why does thicker wire reduce resistance? A larger cross-section gives current more parallel paths to flow through. Resistance is inversely proportional to area, so doubling A halves R.

Should I use copper or aluminium? Copper is the default for residential branch circuits — lower resistivity, easier to terminate. Aluminium is used in long high-voltage transmission lines because it is lighter and cheaper, despite roughly 60% higher resistivity than copper.