Adiabatic equation — CPC sizing

How the adiabatic equation works

The adiabatic equation checks that a protective conductor can carry the earth-fault current for as long as the protective device takes to clear the fault, without its insulation reaching a damaging temperature. "Adiabatic" means no heat is assumed to escape into the surroundings during that short period — a deliberately pessimistic assumption that keeps the result on the safe side.

Three numbers drive it: the prospective earth-fault current at the point of the fault (I), the actual disconnection time of the device at that current read from its time/current curve (t), and the k factor for the conductor material, insulation and installation method. The answer is a minimum area — the conductor actually installed must be that size or larger, rounded up to a standard size.

Worked example

A 32 A Type B MCB on a radial circuit wired in 70 °C thermoplastic twin and earth. Measured prospective earth-fault current is 800 A, and at 800 A the device curve gives a disconnection time of roughly 0.1 s. The CPC is insulated inside the cable, so k = 115.

S = √(800² × 0.1) ÷ 115 = √64,000 ÷ 115 = 252.98 ÷ 115 = 2.2 mm². The next standard size up is 2.5 mm², so the 1.5 mm² CPC in 2.5 mm² twin and earth would not satisfy the calculation at that fault level and disconnection time, and a larger cable or a different protective device would be needed.

Choosing the right k value

• 115 — Cu, 70 °C thermoplastic, insulated CPC in a cable
• 143 — Cu, 90 °C thermosetting, insulated CPC in a cable
• 143 — Cu, bare, not in contact with cable insulation
• 176 — Cu, bare, touching PVC 70 °C insulation
• 51 — Aluminium, 70 °C thermoplastic
• 46 — Steel wire armour (typical)

Values are taken from BS 7671:2018+A3:2024/A4:2026 Tables 54.2 to 54.6. Using a k value for a bare conductor when the CPC is actually insulated inside a cable will under-size the conductor, so confirm the installation method before selecting.

Common mistakes

• Using the maximum permitted disconnection time (0.4 s or 5 s) instead of the actual time the device takes at the measured fault current.
• Using a design fault current instead of the measured prospective fault current at the far end of the circuit.
• Rounding the answer down to the nearest standard conductor size.
• Applying the equation to disconnection times over 5 s, where the adiabatic assumption no longer holds and a full thermal calculation is required.
• Forgetting that a CPC of 1 mm² or smaller may still need mechanical protection regardless of the calculated result.