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14 — Calculators

Calculate thermal short-circuit withstand

During a short circuit a multiple of the operating current flows for fractions of a second. The cable has to take it until disconnection — not permanently, but without damage to the insulation. The proof is short, yet it is often skipped entirely.

Input

The time the protective device needs at this current. From the characteristic; markedly shorter for current-limiting devices.

Depends on conductor material and insulation and is given in the standard you apply. For copper with PVC it is around 115, higher for copper with cross-linked polyethylene.

Result

Minimum cross-section required
—mm²
Assessment
—
Longest permissible disconnection timeFor the cross-section present, at this current.
—s
Next standard cross-section
—mm²

A guide, not a design to standard. We give no warranty for the correctness of the results, the applicable standards and case-by-case verification govern.

Worked example

The default case the calculator starts with, worked through once. Change the values above and it recalculates immediately.

Inputs

Short-circuit current
6 kA
Disconnection time
0.1 s
Material factor k
115
Cross-section present
16 mm²

Result

Minimum cross-section required
16.5 mm²
Assessment
The cross-section is not sufficient: the cable is thermally overloaded before disconnection.
Longest permissible disconnection time
0.094 s
Next standard cross-section
25 mm²

Formula

  • A_min = I_k · √t / k
  • rearranged: t_max = (k · A / I_k)²
  • equivalently: I²·t ≤ k²·A²

Assumptions and standards

  • The material factor k depends on conductor material and insulation and is entered here. It is given in the standard you apply.
  • The formula holds for disconnection times up to about five seconds. Below that it is assumed no heat escapes — all the loss stays in the conductor.
  • With current-limiting protective devices the actual stress is lower than the calculation suggests. The let-through value from the data sheet then governs, not I²·t from this formula.

Frequently asked

Which disconnection time should I use?

The time the protective device needs at exactly this short-circuit current — read from its characteristic. Not the required disconnection time from the protection condition: that is an upper limit for personal safety, not the actual behaviour of the device.

Does this apply to the protective conductor too?

Yes, and there it matters especially. Under fault the protective conductor carries the same current as the line conductor but is often made smaller. Do the proof for it separately.

Why show the longest permissible disconnection time?

Because that is the practical counter-question. With the cross-section fixed, it says how quickly disconnection has to happen — and whether the chosen device delivers that.

Calculating is the easy part.

A formula gives you a number. Designing a plant also demands installation method, grouping, discrimination, the standards in force and a look at the installed base. That is what we take on.

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