Conductor Resistance Temperature Correction

Also known as temperature coefficient of resistance

R_{2} = R_{1} \left[ 1 + \alpha (T_{2} - T_{1}) \right]

Worked example: 10 Ω copper, 20 °C → 75 °C gives 12.1615 Ω — press Try an example to run it live, then adjust anything.

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Conductor Resistance Temperature Correction explained

Metals conduct worse when hot: heat jostles the lattice and scatters the electrons. Copper's coefficient is about 0.00393 per kelvin referenced to 20 °C, aluminium's about 0.00403, so a 10 Ω copper winding at 20 °C measures 10 × (1 + 0.00393 × 55) = 12.16 Ω at 75 °C — a 22% rise. Because a kelvin and a Celsius degree are the same size, only the temperature difference matters; if your α is quoted per °F, choose that unit and the solver handles it.

This relation is quietly one of the most useful in the trade. It turns a winding's cold and hot resistance into a motor's average winding temperature, the basis of the standard heat-run test — no thermocouple can reach the middle of a coil, but its resistance always can. It is also why cable ampacity tables assume a conductor temperature, why voltage-drop constants differ between 20 °C and 75 °C, and why platinum's clean, repeatable version of this curve makes the RTD the workhorse of industrial temperature measurement.

Conductor Resistance Temperature Correction formula

R_{2} = R_{1} \left[ 1 + \alpha (T_{2} - T_{1}) \right]

Where

$R_{2}$ = Resistance at T₂ (Ω)
$R_{1}$ = Resistance at T₁ (Ω)
$\alpha$ = Temperature coefficient (1/K)
$T_{2}$ = New temperature (°C)
$T_{1}$ = Reference temperature (°C)

Missing one of these? Work it out first, then come back

Resistance at T₂ — Series RLC Impedance, Series RL or RC Impedance
Resistance at T₁ — Series RLC Impedance, Series RL or RC Impedance
Temperature coefficient — PV Temperature Derate, Thermal Linear Expansion
New temperature — Ideal Gas Law, Antoine Equation (Vapour Pressure)
Reference temperature — F-Value (Equivalent Time at Reference Temperature), Nurse-Saul Equivalent Age

Part of this formula set

Voltage drop

4 formulasSingle-phase and three-phase voltage drop, percent drop and conductor resistance at temperature — sizing a conductor for a long run.