Every circuit has a protective conductor, the earth wire, that carries fault current back to the source when a line conductor touches metalwork. It has to survive that current without overheating until the circuit breaker trips. SS 638 (Regulation 543.1.1L) gives two ways to make sure it does: calculate the size with the adiabatic equation (543.1.3), or select it from a table (543.1.4L).
The adiabatic equation
S = √(I²t) / k
| S | Minimum cross-sectional area of the protective conductor, in mm² |
| I | Fault current (r.m.s.) for a fault of negligible impedance, in amperes, allowing for the circuit's impedance and the current-limiting effect of the breaker |
| t | Time the breaker takes to disconnect at that fault current, in seconds, read from its tripping curve |
| k | A factor for the conductor material and its starting and maximum allowed temperatures |
I²t is a measure of the heat energy the fault puts into the conductor. The equation is called adiabatic because it assumes none of that heat escapes during the fault: the conductor has no time to cool, so all the energy raises its temperature. That assumption holds for short faults, so the equation applies only to disconnection times up to 5 seconds.
If the result is not a standard size, use the next standard size up.
Choosing k
k depends on the conductor material, its insulation, and whether it runs cool on its own or warm inside a cable. A conductor that starts hotter can absorb less fault energy before reaching its limit, so its k is lower. Values for copper from SS 638:
| Protective conductor (copper) | 70°C PVC | 90°C thermosetting |
|---|---|---|
| Separate insulated conductor, not in a cable or bunched with cables Table 54.2, starts at 30°C |
143 | 176 |
| Core of a cable, or bunched with cables Table 54.3, starts at the cable's operating temperature |
115 | 143 |
Values for thermoplastic conductors above 300 mm² are lower. SS 638 Tables 54.4 to 54.6 cover cable sheaths and armour, steel conduit and trunking, and bare conductors.
When the calculation is needed
SS 638 requires the calculation where the line conductors were sized for short-circuit current and the earth fault current is expected to be lower than the short-circuit current. A lower fault current can take the breaker longer to clear, which lets more energy into the protective conductor.
Selecting from the table instead
If you do not calculate, Table 54.7 (Regulation 543.1.4L) sets the minimum size of the protective conductor from the size of the line conductor, S:
| Line conductor S (mm²) | Same material as the line conductor (mm²) | Different material (mm²) |
|---|---|---|
| S ≤ 16 | S | (k1 / k2) × S |
| 16 < S ≤ 35 | 16 | (k1 / k2) × 16 |
| S > 35 | S / 2 | (k1 / k2) × S / 2 |
k1 is the k value for the line conductor and k2 the k value for the protective conductor, each for its own material and insulation. The ratio scales the size up when the protective conductor is made of a material that can absorb less fault energy, such as steel conduit protecting copper conductors.
If the table gives a size that is not standard, use the nearest larger standard size.
In Goldberg multicore cables the green/yellow earth core is the same size as the line cores, as in 3G 2.5, so the cable meets this table on its own.
Other rules
- Separate protective conductors: one that is not part of a cable and not inside conduit, trunking or another enclosure must be at least 2.5 mm² copper where it is protected against mechanical damage, and 4 mm² where it is not.
- Shared protective conductors: one serving several circuits is calculated for the most onerous fault current and disconnection time among them, or sized to match the largest line conductor.
This is a summary of SS 638:2018, Regulations 543.1.1L to 543.1.4L. Always use the standard itself for design, and have it checked by a Licensed Electrical Worker. Need help choosing a cable? Ask our team.
