Question 1

What is the adiabatic equation and when do I use it?

Accepted Answer

The adiabatic equation S = √(I²t) / k calculates the minimum cross-sectional area of a protective conductor (CPC, earthing, or bonding) that can withstand the thermal energy of a fault current without its insulation exceeding its temperature limit. Use it when the simplified table method (Table 54.7) gives a result you want to verify, when non-standard conductor arrangements are used, or when you need to confirm that a standard T&E CPC is adequate for the prospective fault current.

Question 2

What does the k value represent and where do I find it?

Accepted Answer

The k value is a factor that accounts for the resistivity, temperature coefficient, and heat capacity of the conductor material, combined with the initial and final temperatures of the insulation. It is found in BS 7671 Tables 54.2 to 54.6. For example, copper with PVC insulation at 70°C has k = 115, while copper with XLPE at 90°C has k = 143. A higher k value means the conductor can handle more energy per unit area.

Question 3

How do I find the fault current (I) for the adiabatic equation?

Accepted Answer

The fault current is the prospective earth fault current (PEFC) at the point where the protective conductor is installed. You can measure it using a loop impedance tester and calculating I = Uo/Zs, or use the Fault Current Calculator. On a typical domestic installation, earth fault currents range from 200A to 2,000A depending on the circuit length and Ze value.

Question 4

What disconnection time should I use?

Accepted Answer

Use the maximum disconnection time permitted by BS 7671 for the circuit type: 0.4 seconds for final circuits up to 32A (Reg 411.3.2.2), 5 seconds for distribution circuits and final circuits over 32A (Reg 411.3.2.3). Using the maximum permitted time gives a conservative (larger) conductor size. If the actual device trips faster, the real energy let-through will be lower.

Question 5

When does the adiabatic equation give a larger CPC than Table 54.7?

Accepted Answer

The adiabatic equation typically requires a larger CPC when fault currents are high and disconnection times are long. For example, on a circuit close to the consumer unit with a high PEFC and a 5-second distribution circuit disconnection time, the adiabatic result may exceed the table value. This is common with large distribution boards or sub-main circuits.

Question 6

Can I use the adiabatic equation for main earthing and bonding conductors?

Accepted Answer

Yes. Regulation 543.1.4 applies the same adiabatic equation to earthing conductors, and Regulation 544.1 allows it for bonding conductors. However, the k value used depends on the conductor application — bonding conductors use values from Table 54.6, while earthing conductors typically use Table 54.5 values. For main earthing conductors, you also need to account for the fault current at the origin of the installation.

Application	Insulation	k Value	BS 7671 Table
CPC within multi-core cable	PVC 70°C	115	Table 54.2 / 54.4
CPC within multi-core cable	XLPE 90°C	143	Table 54.2
Separate CPC, not bunched	PVC 70°C	143	Table 54.5
Separate CPC, not bunched	XLPE 90°C	176	Table 54.5
Bare CPC touching cable sheath	Any	159	Table 54.3
Bonding conductor	PVC 70°C	115	Table 54.6

Regulation	Description
543.1.1	General requirements for protective conductors
543.1.3	Adiabatic equation for CPC sizing
543.1.4	Simplified method using Table 54.7
Table 54.2	k values for CPC incorporated in cables
Table 54.3	k values for bare protective conductors
Table 54.4	k values for CPC as a core in cable or bunched
Table 54.5	k values for separate protective conductors not bunched
Table 54.6	k values for bonding conductors
Table 54.7	Minimum CPC sizes from line conductor cross-section

Adiabatic Equation Calculator

How the Adiabatic Equation Works

Adiabatic Equation vs Table Method

k Values from BS 7671

Practical Examples

BS 7671 Regulation References

Frequently Asked Questions