Wire Length from Resistance Calculator
Enter the target resistance, wire diameter and material to find the required length.
Result
How it is calculated
Resistance of a round wire is R = ρ × L / A, so the length for a target resistance is L = R × A / ρ. R is the target resistance in ohms and must be above zero. The diameter is entered in millimetres (also above zero) and turned into a cross-section A = π × (d / 2)² in m². ρ is a fixed resistivity in Ω·m taken from a built-in list: copper 1.68×10-8, aluminum 2.65×10-8, gold 2.44×10-8, silver 1.59×10-8, iron 9.71×10-8, tungsten 5.60×10-8, nichrome 1.10×10-6. The length comes out in metres with three decimals, and the area and resistivity used are shown too. An unknown or empty material falls back to copper. There is no temperature correction, and the wire is assumed solid and round.
Worked example
You want a heating element with a resistance of 24 Ω made from 0.5 mm nichrome wire. Radius: 0.25 mm = 0.00025 m. Area: π × 0.00025² = 1.9635×10-7 m². Length: 24 × 1.9635×10-7 / 1.10×10-6 = 4.284 m. Nichrome has a high resistivity, so just over 4 metres is enough. Copper wire of the same thickness would need about 280.5 m to reach the same 24 Ω, and aluminum about 177.8 m, because their resistivity is far lower.
Common mistakes
- Entering the diameter in metres or centimetres. The field is in millimetres: a 0.5 mm wire is typed as 0.5, and typing 5 for 0.5 mm makes the length a hundred times too long.
- Entering the radius as the diameter. Since area scales with the square, this makes the length four times too short.
- Leaving the material at copper for heating wire or resistor wire. If no material is chosen the tool silently uses copper, while nichrome needs far less length for the same ohms, so check the material is set.
- Expecting the length to hold at operating temperature. Resistance rises as the wire heats, and the tool uses fixed values with no temperature correction.
- Entering the resistance of a whole circuit or a wire pair. The result is one conductor's length; for a go-and-return cable, the cable run is half of it.
About this calculator
A wire's resistance depends on its material, length, and cross-sectional area through R = ρL/A, where ρ is the material's resistivity, L is length, and A is cross-sectional area. Solving for length gives L = R·A/ρ — the length of wire needed to hit a target resistance for a chosen diameter and material. Copper (ρ ≈ 1.68×10⁻⁸ Ω·m) and aluminum (ρ ≈ 2.65×10⁻⁸ Ω·m) are the most common conductors and differ noticeably in how much wire it takes to reach the same resistance.
Electricians and electrical engineers use this to size wire runs and check voltage drop over distance, while hobbyists use it for projects like winding transformer or inductor coils, building heating elements, or choosing speaker wire gauge for long cable runs.
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