Wire Resistance Calculator

What does this quantity describe?

The DC resistance of a homogeneous conductor is proportional to its length and the material's resistivity, and inversely proportional to its cross-section: R = ρ·L/A. ρ is a temperature-dependent material constant, about 0.0175 Ω·mm²/m for copper at 20°C.

Much like a water pipe, greater length raises resistance and a larger cross-section lowers it. A long, thin extension cord behaves electrically like a long, narrow hose: at high current, a noticeable voltage drop develops along the cable length, just as a noticeable pressure loss develops along a hose at high flow.

Formula and variables

R = ρ · L / A

• R = ρ · L / A
• L = R · A / ρ
• A = ρ · L / R

Choose the inputs correctly

Enter three of the four quantities to find the fourth. Use a ρ value matching the actual operating temperature, since many metals' resistivity changes with temperature. For voltage-drop calculations, L counts as the sum of the outgoing and return conductor.

How to use the calculator

Select the target quantity and enter the three known values with units. For a voltage-drop estimate, first calculate R and multiply by the expected operating current (V_drop = R·I).

Worked example

Given ρ = 0.0175 Ω·mm²/m (copper), L = 10 m and A = 10 mm², substitution gives R = 0.0175 · 10/10 = 0.0175 Ω.

Understand the result and units

A conductor resistance of 0.0175 Ω produces a voltage drop of about 0.28 V at, say, a 16 A operating current over this 10 m run. Doubling length or halving cross-section would quadruple or double that voltage drop respectively.

Resistivity is given in Ω·mm²/m (convenient for cross-sections in mm²) or Ω·m (SI-coherent). Conductor resistance is given in Ω, or mΩ for very thin or long conductors.

How much does conductor resistance change with temperature?

Copper's resistivity rises with a temperature coefficient of about 3.9×10⁻³ per °C, roughly 0.39% per kelvin. A copper conductor heated from 20°C to 70°C therefore has about 20% higher resistance than at 20°C. For cables that run noticeably hot in service — from heavy continuous load or unfavourable installation conditions — resistivity should be corrected to the actual operating temperature rather than using the uncorrected 20°C table value.

Typical applications

Conductor resistance calculations are used to size cable cross-sections for long cable runs, estimate voltage drop in extension cords and solar installations, and design windings for motors and transformers.

Assumptions, limits and common mistakes

The formula applies to DC at constant temperature with a homogeneous cross-section. At high-frequency AC, the skin effect reduces the effectively used conductor cross-section and raises AC resistance above the DC value calculated here.

Common mistake: For voltage-drop calculations, don't forget that current flows through both the outgoing and return conductor — the relevant length is therefore double the one-way cable length if both are to be captured in the same formula. Also, don't take resistivity from a 20°C table uncorrected if the conductor runs noticeably hotter in operation.