Resistance vs Temperature Calculator

How it works

The resistance of a metal rises as it warms, because its atoms vibrate more and scatter the moving electrons more often. Over a moderate range the rise is close to a straight line, described by the temperature coefficient of resistance α: the fractional change in resistance per degree.

Given a resistance R_ref measured at a reference temperature T_ref, the resistance at another temperature T is R_ref × (1 + α × (T − T_ref)). For annealed copper, α ≈ 0.00393 per °C, so a copper winding or wire gains about 0.39 % of its resistance for each degree Celsius it warms.

Temperatures may be entered in °F; the difference is converted to Celsius degrees (× 5/9) because α is per °C. The change is shown in ohms and as a percentage.

Formula

R_T = R_ref × (1 + α × (T − T_ref))
ΔR = R_ref × α × (T − T_ref)
°F difference → °C difference: ΔT(°C) = ΔT(°F) × 5/9

Example

A copper conductor of 10 Ω at 20 °C, warmed to 75 °C, rises to 10 × (1 + 0.00393 × 55) = 12.1615 Ω, an increase of 2.1615 Ω or 21.62 %.

OpenStax College Physics 2e (Example 20.6) heats a tungsten filament of 0.350 Ω at 20 °C to 2850 °C: 0.350 × (1 + 0.0045 × 2830) ≈ 4.807 Ω, quoted there as 4.8 Ω.

Assumptions and limitations

• The change is linear in temperature. Real metals depart from a straight line over wide ranges (tungsten noticeably so between room temperature and incandescence), so results far from the reference temperature are approximate.
• The preset values are typical figures at 20 °C: annealed (standard) copper 0.00393 from NBS Handbook 100, Copper Wire Tables (1966); EC-H19 (1350-H19, 61 % IACS) aluminum 0.00403 from NBS Handbook 109, Aluminum Wire Tables (1972), Table 1, which lists other aluminum grades from 0.00347 (6201-T81) to 0.00408 (EC-O); tungsten 0.0045 and nichrome 0.0004 from OpenStax College Physics 2e (2022), Table 20.2.
• α is treated as the coefficient at the reference temperature, and it varies with that temperature. Handbook 100 gives 1/α_t = 1/α₂₀ + (t − 20) for copper, so at 75 °C copper's α is about 0.00323 per °C, about 18 % below the 20 °C value, so the copper preset used with a 75 °C reference temperature overstates the change by about 22 % (0.00393 ÷ 0.00323). A coefficient for another reference temperature can be entered as Custom α.
• Alloy, purity and temper change α; the presets are typical, not the value for a specific conductor.
• This is an estimate, not an NEC compliance determination or a substitute for the conductor manufacturer's data. Conductor sizing and ampacity are decided under the applicable code by a licensed electrician or the authority having jurisdiction.

Frequently asked questions