Resistivity & Wire Resistance Calculator

Resistance of a conductor from material, length, cross-section and temperature.

What it does

The resistance of a wire or bar depends on its material, length and cross-section, and rises with temperature: R = ρ·L / A.

Where it's used

Cable voltage drop, nichrome heater elements, home-made current shunts and busbars.

How to use it

Choose the material (or Custom with your own ρ and α).
Enter the conductor length.
Describe the cross-section by diameter, AWG gauge, area or as a rectangular bar.
Add the operating temperature and the current to see voltage drop and heat.

The formula explained

ρ: resistivity of the material at 20 °C, in Ω·m
L: length of conductor
A: cross-sectional area
α: temperature coefficient — how fast resistance rises per °C
T: conductor temperature

Worked example

20 m of 2.5 mm² copper at 40 °C carrying 10 A.

Inputs:

Material: Copper
Length: 20 m
Cross-section: Area (mm²)
Area: 2.5 mm²
Conductor temperature: 40 °C
Current: 10 A

The calculator gives:

Resistance: 145 mΩ
ρ at 40 °C: 18.12 nΩ·m
Cross-section area: 2.5 mm²

Tips and common mistakes

For a supply cable the current goes out and back: use twice the cable length.
Copper resistance rises by about 0.4 % for every °C.
A higher AWG number means a thinner wire.

Questions people ask

What is the resistivity of common conductors?

At 20 °C, roughly: silver 1.59, copper 1.68, gold 2.44 and aluminium 2.65 × 10⁻⁸ Ω·m. Steel and nichrome are far higher, which is why nichrome is used for heating wire.

Why are aluminium cables thicker than copper ones?

Aluminium’s resistivity is about 1.6 times copper’s, so it needs about 1.6 times the cross-section for the same resistance. It is still lighter and cheaper, which is why overhead power lines use it.

How do AWG sizes compare with mm²?

Some common ones: 18 AWG ≈ 0.82 mm², 14 AWG ≈ 2.08 mm², 12 AWG ≈ 3.31 mm², 10 AWG ≈ 5.26 mm². Every 3 AWG steps roughly halves or doubles the area.

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