Adiabatic CPC Calculator

Check that a circuit protective conductor (CPC) can carry the earth fault current until the device disconnects, using the BS 7671 Reg. 543.1.3 adiabatic equation S = √(I²t) ÷ k, with k from Tables 54.2–54.6.

Guidance only. Results are estimates based on the figures you enter and published tables. All electrical work must be designed, checked and tested by a qualified electrician to the regulations that apply where you are (e.g. BS 7671, NEC).

Fault Current & Disconnection Time

A
Ω
V
s
Read from the device's time/current curve at I.
A

Assumes t = 0.1 s: BS EN 60898 breakers trip in under 0.1 s at or above their instantaneous current (5/10/20 × In). Only valid when I reaches that. The manufacturer's let-through energy gives a smaller, more accurate figure.

A²s

From the manufacturer's energy let-through data at the prospective fault current. Use this for current-limiting devices and very short times (under 0.1 s), where I × t would misstate the energy.

Protective Conductor (k)

k
—

k values are for conductors up to 300 mm². Thermoplastic (PVC) CPCs over 300 mm² have lower k values (see BS 7671).

Minimum CPC Size

Fault energy I²t
—
Minimum CSA (S)
—
√(I²t) ÷ k
Next standard size
—
mm²
Result
—
CPC withstand (k²S²)
—
Max time at this I
—
t = (kS ÷ I)²
Max current for this t
—
I = kS ÷ √t

Get the fault current from the Prospective Fault Current Calculator (use the minimum PEFC) or from Zs in the Max Zs Calculator. Size the line conductors with the Cable Gauge Calculator.

Quick Reference: Selection by Table 54.7

Instead of calculating, Reg. 543.1.1 allows the CPC to be selected from Table 54.7. No calculation is needed if the CPC is at least this size. Row A is for a CPC of the same material as the line conductor. Row B is for a different material, where k1 is the line conductor's k (Table 43.1) and k2 is the CPC's k (Tables 54.2–54.6).

Line conductor S (mm²) S ≤ 16 16 < S ≤ 35 S > 35
A: same materialS16S ÷ 2
B: different materialS × k1/k216 × k1/k2(S ÷ 2) × k1/k2

Where selection gives a non-standard size, use the next larger standard size. T&E cables (e.g. 2.5/1.5 mm²) have a reduced CPC and do not meet Table 54.7, so check them with the adiabatic equation.

Notes & References

  • Equation: BS 7671:2018+A2:2022 Reg. 543.1.3, S = √(I²t) ÷ k. It applies only to disconnection times up to 5 s. I is the fault current through the device, allowing for circuit impedance. t is the device's operating time at that current.
  • k values: Tables 54.2 (separate CPC, initial temperature 30 °C), 54.3 (core in a cable or bunched, initial temperature = conductor operating temperature), 54.4 (sheath/armour), 54.5 (steel conduit, ducting and trunking) and 54.6 (bare conductors, initial 30 °C, final temperature set by the location). Initial and final temperatures are shown under k.
  • Fault current from Zs: I = U0 ÷ Zs. Use the in-service (hot) Zs, not a cold reading. For fuses, a lower current means a longer time and usually a larger I²t, so check the curve at the lowest likely fault current.
  • Minimum sizes (Reg. 543.1.1): a CPC that is not part of a cable or enclosure must be at least 2.5 mm² copper if mechanically protected, or 4 mm² if not.
  • The Table 54.7 selection method needs no calculation. Where the line conductor was sized for short-circuit current and the earth fault current is expected to be lower, calculate instead (Reg. 543.1.1).

This tool is guidance only. It does not replace BS 7671, the IET Guidance Notes, manufacturer's data, or the judgement of a competent person.