Wire Resistance Calculator
Compute conductor resistance R = ρL/A.
R = — Ω
Cobre: 1,68×10⁻⁸ Ω·m · Alumínio: 2,82×10⁻⁸ Ω·m
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.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.