The adiabatic equation verifies that a cable's cross-sectional area (CSA) is large enough to survive the heat generated by a fault current before the protective device disconnects. The formula is S² ≥ I²t / k², where S is the conductor CSA in mm², I is the fault current in amps, t is the disconnection time in seconds, and k is a factor from BS 7671 that depends on the conductor material and insulation type.
The k factor represents the thermal capacity of the conductor. Copper has a higher k than aluminium, and XLPE insulation allows a higher operating temperature than PVC, giving a higher k value. A higher k means the cable can tolerate more energy per mm² before damage occurs.
Disconnection time comes from the time-current characteristic of the protective device — the time it takes to disconnect at the prospective fault current. For MCBs this is typically less than 0.1 seconds at high fault currents; for fuses it varies by rating. If you don't have the exact figure, use 0.4 seconds for a 230V circuit or 5 seconds as a conservative worst case.
The adiabatic check is one of three checks required when selecting a cable — the others being current-carrying capacity (CCC) and volt drop. A cable must pass all three.