Circuits and conductors
Resistance and temperature
- where
- resistance at final temperature (Ω)
- resistance at reference temperature (Ω)
- temperature coefficient at reference temperature (1/°C)
- final temperature (°C)
- reference temperature (°C)
Explain this equation
Works out a conductor’s resistance at a new temperature from its value at a reference temperature. Used to correct test readings and to estimate hot conductor resistance.
R₂ is the resistance at the final temperature T₂. R₁ is the known resistance at the reference temperature T₁. α is the material’s temperature coefficient: the fractional change in resistance per °C, about 0.00393 for copper at 20 °C.
Over normal working ranges, metal resistance rises roughly in a straight line with temperature. α(T₂ − T₁) is the fractional increase, and adding 1 gives the factor to scale R₁ by.
Sense check: copper heated from 20 °C to 70 °C rises by about 20%, so 10 Ω becomes about 11.97 Ω. Copper at 70 °C is about 1.2 times its 20 °C value.
Watch out: use the temperature change, not the temperature itself, and use an α quoted at your reference temperature.
Within an appropriate range a metal conductor’s resistance rises approximately linearly with temperature. Calculate the temperature change, multiply by the supplied coefficient and add one.
Multiply this dimensionless factor by reference resistance. The coefficient must correspond to the reference temperature used.
Enter your values to see the result.
Common mistake
Multiplying by temperature instead of temperature change.
Limits
Linear approximation; supplied material coefficient, not a universal constant.
Sources
The tools calculate the displayed equation. They do not automatically choose cable sizes, approve installations, supply current regulatory tables, certify equipment or replace inspection and testing.