Conductor Resistance vs Temperature: Formula and Example

The answer in one minute

For metallic conductors, resistance generally rises as the conductor itself gets hotter. Higher resistance raises the resistive contribution to voltage drop and I²R loss at a given current. The ambient temperature is a thermal condition around the cable; it is not automatically the conductor’s operating temperature. A loaded conductor may run hotter than the surrounding air.

That distinction is the first input decision in a temperature-adjusted voltage-drop estimate. The calculator cannot infer conductor temperature from ambient air alone.

The linear temperature model

Over an ordinary engineering range, resistance is often approximated from a reference value:

Rθ = Rref × [1 + α(θ − θref)]

For copper with a representative coefficient around 0.00393 per °C, a conductor that is 1.00 Ω at 20°C would be approximately:

R80 = 1.00 × [1 + 0.00393 × (80 − 20)] = 1.236 Ω

That is about a 23.6% increase. The same illustrative model gives:

Assumed conductor temperature	Resistance from 1.00 Ω at 20°C
20°C	1.000 Ω
40°C	1.079 Ω
60°C	1.157 Ω
80°C	1.236 Ω

If current and geometry stay the same, the resistive component of voltage drop and I²R loss rise accordingly. The example explains direction and scale; use the coefficient and reference basis supplied with the actual engineering data. Compare temperatures in the simplified voltage-drop calculator.

Conductor temperature is not ambient temperature

Ambient air or soil temperature is one input to conductor heating, not necessarily the conductor temperature itself. Load current, installation method, grouping, thermal insulation, ventilation and heat from neighbouring circuits influence the operating value.

Entering 40°C because the room is 40°C may understate conductor resistance when a loaded cable runs hotter. Conversely, assuming the maximum insulation rating as the normal operating temperature can overstate routine drop. Document whether temperature is measured, calculated, table-based or a conservative assumption.

AC resistance is more than DC resistivity

The simple ρL/A relationship estimates DC resistance from material resistivity and area. Real AC cable resistance can also reflect strand construction, skin effect, proximity effect and metallic components. Manufacturer R/X data is therefore preferable when a cable-specific AC result matters. See how resistance, reactance and power factor enter AC voltage drop before substituting a DC estimate into an AC calculation.

Contact and termination resistance are separate from the uniform conductor estimate. A poor joint can create local heating and voltage drop that the route calculation does not predict.

Use consistent reference data

Check whether resistance is stated per conductor, per kilometre, at 20°C, at a maximum operating temperature, or as a maximum test value. If a source already supplies resistance at 90°C, applying a second temperature correction from 20°C would over-adjust it.

Store the original value, reference temperature, adjusted value and coefficient in the calculation record. That trace lets a reviewer update the result when a better operating-temperature estimate becomes available.

Use the temperature input deliberately

A current calculation does not determine conductor temperature. In simplified resistivity mode, temperature is a user assumption. In custom R/X mode, enter resistance already appropriate to the temperature being assessed; do not apply a second correction to data that was already corrected. The correction changes the resistance term; it does not itself prove that the conductor can carry the load in the intended installation.