Conductor Temperature Rise Calculator

Find how hot a conductor gets when it carries a current for a short time, and the longest time or largest current before it reaches its limit.

Calculated from standard textbook formulas, with every step shown. The formulas are fixed, so the working does not need checking: what matters is the numbers you type in. Use these calculators only if you are competent to choose the inputs (loads, material strength, dimensions, supports) and check your units and assumptions. For learning and checking your own working: design and sign-off are for a qualified engineer. Drafting Central does not store the numbers you type.

How this calculator works

When a current flows for a short time there is no time for the heat to escape, so all of it heats the metal. The temperature rise is the current squared times the resistance times the time, divided by the mass times the specific heat.

For a cable this gives the rise from the material, the cross-section area, the current and the time. It is how a fault current and a breaker trip time are checked against the cable.

Formulas used

  • \theta = \dfrac{I^2 R\, t}{m\, c}
  • \theta = \dfrac{I^2 \rho\, t}{A^2 \rho_d\, c}

Worked example

With the default numbers in the calculator above:

  1. Resistivity at the starting temperature: 2.06 ×10⁻⁸ Ω·m
  2. Temperature rise: 291.30 K
  3. Temperature at the end: 361.30 °C
  4. Longest time at this current before the limit: 0.15 s
  5. Largest current for this time: 2779.20 A

Change the numbers in the calculator to see the full working, every step, for your own case.

Common questions

Why assume no heat leaves?

For a fault that lasts a second or less there is no time to lose heat, so it is the safe case.

What is the temperature limit?

It depends on the insulation. Check the cable maker's data sheet for the short-circuit limit.

Related calculators

Further reading: Standard electrical and heat transfer texts (adiabatic heating of a conductor).

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