Cable Short-Circuit Thermal Withstand: I²t ≤ k²S²

A cable can carry its normal load current and still be thermally damaged by a short circuit before the protective device clears. The short-circuit thermal check compares the fault energy passed through the conductor with the thermal energy the conductor and insulation can withstand for the applicable temperature limits.

1. The adiabatic short-circuit relationship

Equivalent useful forms are:

Where:

• I is the relevant short-circuit current in amperes;
• t is the clearing duration in seconds;
• S is conductor cross-sectional area in mm²;
• k depends on conductor material, insulation and the assumed initial/final temperatures.

The relationship is an adiabatic approximation: during the short event, heat loss from the conductor is neglected. Public IEC-based design guidance applies this form for short durations up to about 5 s, subject to the standard's conditions.

2. Worked example: 10 kA cleared in 0.20 s

Assume:

• prospective short-circuit current I = 10,000 A;
• clearing time t = 0.20 s;
• copper XLPE/EPR conductor;
• example k = 143 A√s/mm² for the stated temperature basis.

The next standard conductor size would therefore be 35 mm² if no larger criterion governs.

Check the selected 35 mm² conductor directly:

Under those assumptions, the 35 mm² conductor passes the adiabatic thermal check.

For comparison, using k = 115 for a copper/PVC example basis would give:

That would move the thermal minimum to the next suitable standard section. The k value is therefore not a generic material constant; its temperature/insulation basis matters.

3. Current-limiting fuses and breakers: use the right I²t

If a protective device is strongly current limiting, the simple prospective-current × clearing-time rectangle can be overly conservative or physically unrepresentative. Where the applicable engineering method permits, compare the conductor limit with the device manufacturer's verified total-clearing let-through I²t for the relevant prospective fault level:

Do not use breaking capacity (Icn, Icu, Ics or a fuse interrupting rating) as if it were an I²t value. Interrupting capability and let-through energy are different characteristics.

Check short-circuit thermal withstand in IEC Cable Sizing

4. Limits of the adiabatic model

• The standard's permitted time range and temperature assumptions must be respected.
• k must match conductor material, insulation and initial/final temperature basis.
• The actual protective-device operating time must correspond to the relevant fault current.
• For non-adiabatic effects, large conductors or cases outside the simplified assumptions, a more detailed method may be required.
• IEC 60949 provides a method that starts from the adiabatic short-circuit current and applies a modifying factor for non-adiabatic heating effects.

5. Practical design workflow

1. Calculate maximum and minimum fault-current conditions at the cable location.
2. Confirm protective-device breaking capacity separately.
3. Obtain the clearing time or verified total-clearing I²t at the relevant prospective fault level.
4. Select k from the adopted standard/data source for the conductor/insulation temperature basis.
5. Check I²t ≤ k²S².
6. Verify that the same cable also passes continuous ampacity and voltage-drop criteria.
7. For current-limiting coordination, retain the manufacturer curve/table reference used for I²t.

Adjacent checks

Read I²t Let-Through Energy Explained for the protection-side concept, then use FaultChain when you need to review upstream fault current and protection as a chain rather than as an isolated cable calculation.

Engineering references

IEC 60364-4-43:2023 is the current IEC overcurrent-protection publication. IEC 60949 covers thermally permissible short-circuit currents including non-adiabatic heating effects. A public IEC-based worked-method reference is the Electrical Installation Guide — cable short-circuit withstand.