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Wire Resistance Calculator

Find the resistance of a wire.

How it is calculated

The tool uses R = ρ × L / A. Length L is in metres and the cross-section area A in mm², which the tool converts to m² (× 10⁻⁶). The resistivity ρ at room temperature comes from the material you pick, in Ω·m: copper 1.68 × 10⁻⁸, aluminium 2.65 × 10⁻⁸, gold 2.44 × 10⁻⁸, silver 1.59 × 10⁻⁸. An unknown material is treated as copper. The result is in ohms with 4 significant digits; a result of 10,000 Ω or more, or below 0.0001 Ω, is written as a power of ten, for example 1.68 × 10⁷ Ω. Area must be above zero, and length cannot be negative. Resistance rises with temperature and the tool does not correct for it. For a two-wire circuit, enter the full out-and-back length.

Worked example

50 m of copper wire with a 2.5 mm² cross-section. Area in m²: 2.5 × 10⁻⁶. Resistivity of copper: 1.68 × 10⁻⁸ Ω·m. R = 1.68 × 10⁻⁸ × 50 / (2.5 × 10⁻⁶) = 8.4 × 10⁻⁷ / (2.5 × 10⁻⁶) = 0.336 Ω. At 10 A the wire alone would drop 3.36 V.

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Common mistakes

  • Entering the area in m² or as the wire diameter. The field is the cross-section area in mm², so a 2.5 mm² cable is 2.5 and a diameter must be turned into area with π × d² / 4 first.
  • Entering one-way length for a circuit that has go and return wires. Resistance is of the entire length, so double the distance.
  • Choosing copper for an aluminium cable. Aluminium resists about 58% more for the same size.
  • Ignoring heat. Warm wires have higher resistance than the room-temperature value.

About this calculator

This calculator finds a wire's electrical resistance using R = ρL/A — the material's resistivity (ρ) times length (L), divided by cross-sectional area (A) — accounting for the fact that longer, thinner wires resist current more than shorter, thicker ones, and that copper and aluminum have very different resistivity values.

Electricians and DIY builders use it to check whether a wire gauge is appropriate for a run length before voltage drop becomes a problem, and electronics hobbyists use it to predict resistance in custom wiring or heating-element designs where the wire itself is part of the circuit's behavior, not just a connector.

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Comments (1)

  • Editorial team

    If your wire is specified by diameter rather than cross-section, convert it first: area equals pi times the diameter squared divided by four. A 1.8 mm solid conductor is about 2.54 mm², close to a 2.5 mm² cable. Stranded wire has small gaps, so its effective copper area can be a little lower than the nominal figure. Which wire sizes do you usually work with, mm² or AWG?

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