What the Earthing Conductor Size Calculator does
This calculator sizes a protective earthing or bonding conductor by both of the methods the standards allow, and tells you which one governs. The table method compares the protective conductor with the phase conductor; the adiabatic equation works out the cross-section needed to survive the fault energy without the insulation reaching its limiting temperature. The larger of the two is the answer.
It also shows how the adiabatic result moves as the disconnection time changes, because that single input dominates the calculation and is the one most often taken from the wrong place - the code's maximum permitted disconnection time rather than the time the device actually takes at this fault current.
How to use it
- Enter the phase conductor size. The table method works directly from it.
- Enter the prospective earth fault current at the point of installation. The short-circuit calculator estimates it from the transformer and the cable run.
- Enter the disconnection time the protective device takes at that current, read from its time/current curve. For a current-limiting device, use the published let-through energy instead and work back to an equivalent time.
- Choose the k value that matches the conductor material, the insulation and where the conductor runs. A protective conductor incorporated in a cable starts hot and has a much lower k than a separate one.
- Read both results. The governing method is highlighted, and the standard size shown is the next one up in the series you chose.
Reading the results
The table result is a simple rule: match the phase conductor up to 16 mm², use 16 mm² between 16 and 35 mm², and half the phase conductor above 35 mm². It is quick and usually adequate for final circuits.
The adiabatic result is the thermal truth. It says how much copper is needed to absorb I²t joules without exceeding the insulation's limiting temperature, and on high fault levels with slow devices it can exceed the table figure substantially.
The k value carries the whole thermal story: material, insulation, starting temperature and limiting temperature. Copper with PVC in a separate conductor is 143; the same copper incorporated in a cable, where it starts at 70 °C rather than 30 °C, is 115.
Let-through energy, I²t, is the quantity that actually damages the conductor. Two faults with very different currents and times can be equally dangerous if their I²t is the same.
Worked example: a 70 mm² submain with a 6 kA earth fault cleared in 0.4 s
The table method: 70 mm² is above 35 mm², so the protective conductor is half of it - 35 mm².
The adiabatic method with k = 143 for copper with PVC insulation as a separate conductor: S = sqrt(6000² x 0.4) / 143 = sqrt(14,400,000) / 143 = 3794.7 / 143 = 26.54 mm².
The table figure is larger, so 35 mm² is the answer and the adiabatic requirement is comfortably covered.
Now raise the fault to 20 kA and shorten the clearing time to 0.2 s, which is a plausible board close to a large transformer. S = sqrt(400,000,000 x 0.2) / 143 = 8944.3 / 143 = 62.55 mm². The table would still say 35 mm² - and it would be wrong by a factor of nearly two. The correct answer is the next standard size above 62.55, which is 70 mm².
That is why both methods are worked here. The table rule is a convenience that holds for ordinary final circuits and modest fault levels; near the origin of a large installation, the adiabatic equation is the one that decides.
Formulas and scoring rules
- Adiabatic equation
S = sqrt(I^2 x t) / kIEC 60364-5-54. S in mm², I in amperes, t in seconds. Valid for t up to 5 s.- Table method
S <= 16: S_pe = S ; 16 < S <= 35: S_pe = 16 ; S > 35: S_pe = S / 2IEC 60364-5-54 Table 54.2, for a protective conductor of the same material as the phase conductor.- Let-through energy
I^2 tIn ampere-squared seconds. Take it from the device manufacturer's curve for a current-limiting device.- k, in general
k = sqrt(Qc(B + 20)/rho20 x ln(1 + (theta_f - theta_i)/(B + theta_i)))The standard tabulates k for common combinations; the tabulated figures are what this page uses.- Rounding
The result is rounded up to the next standard conductor size, never down.
Why the disconnection time matters more than anything else
The adiabatic result scales with the square root of the time, so a factor of a hundred in time is a factor of ten in conductor area. Taking 5 s when the device actually clears in 0.05 s overstates the requirement tenfold; taking 0.4 s when the real device takes 3 s understates it by a factor of nearly three.
The figure to use is the time the specific protective device takes at the specific prospective fault current, from its published time/current curve. The maximum disconnection times in the wiring rules - 0.4 s for final circuits, 5 s for distribution circuits in a typical TN system - are limits the design must satisfy, not times to calculate with.
Current-limiting devices change the question
An HRC fuse or a current-limiting circuit-breaker interrupts a heavy fault before the current reaches its prospective peak, so the energy that actually reaches the conductor is far less than I²t calculated from the prospective current and the nominal clearing time. Manufacturers publish let-through energy curves for exactly this reason.
When you have that figure, put it straight into S = sqrt(I²t) / k as the numerator. It routinely allows a smaller protective conductor than the prospective-current calculation, and it is the correct approach rather than a shortcut.
Bonding conductors are a different question
Main protective bonding conductors - to incoming water, gas and structural steel - are sized in relation to the supply neutral rather than by the adiabatic equation, with national rules and practical minimums that vary by country. Supplementary bonding in a bathroom or a special location has its own rules again.
This page sizes circuit protective conductors. For main bonding, read the requirement in the wiring rules that apply where the work is being done; they are prescriptive, and they are not arithmetic.
Limitations: what the result does not prove
- The adiabatic equation applies for disconnection times up to 5 seconds. Beyond that the conductor loses heat to its surroundings and a thermal calculation is needed instead.
- It sizes for thermal withstand only. The protective conductor must also give an earth-fault loop impedance low enough for the device to operate at all, which is a separate calculation.
- Main and supplementary bonding conductors are sized by prescriptive national rules, not by this equation.
- Mechanical minimums apply on top: a bare buried copper earthing conductor is commonly required to be at least 16 mm², and a conductor not protected against mechanical damage has its own floor.
- Nothing here is a compliance statement. A qualified engineer must verify the design against the applicable standard and the local regulations.
Privacy: where your data goes
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Standards and sources
- IEC 60364-5-54 - Earthing arrangements and protective conductors - checked 19 Sep 2026
- NFPA 70 - National Electrical Code - checked 19 Sep 2026
- IEC 60364-4-41 - Protection against electric shock (disconnection times)
Frequently asked questions
What is the adiabatic equation for earth conductors?
S = sqrt(I²t) / k, where S is the minimum cross-section in mm², I is the fault current in amperes, t is the disconnection time in seconds and k is a constant for the conductor material, its insulation and the temperatures involved. It assumes none of the heat escapes during the fault, which is why it is limited to 5 seconds.
What k value should I use?
It depends on three things: the conductor material, the insulation, and whether the conductor is separate or incorporated in a cable. Copper with PVC as a separate conductor is 143; incorporated in a cable, where it starts at 70 °C, it is 115. Aluminium is roughly two thirds of copper: 95 and 76. Bare copper in a restricted area can be 159.
Why are there two methods, and which one wins?
The table method is a simple proportional rule that suits ordinary final circuits. The adiabatic equation is the thermal calculation. The standard permits either, but the conductor must satisfy both, so the correct answer is the larger of the two - which this page always shows.
Is half the phase conductor always enough above 35 mm²?
No, and that is the important limitation of the table method. At high fault levels with a slow protective device it can be substantially undersized, as the 20 kA example on this page shows. Near the origin of a large installation, work the adiabatic equation rather than trusting the halving rule.
Do I use the maximum permitted disconnection time?
No. Use the time the device actually takes at the prospective fault current, from its time/current curve. The 0.4 s and 5 s figures in the wiring rules are maximum permitted times that the design must not exceed; using them as calculation inputs can oversize the conductor by a factor of ten or, if the real device is slower, undersize it.
Does the earth conductor have to be the same material as the phase?
No, but the table method assumes it is. If the protective conductor is a different material - an aluminium armour used as a protective conductor with copper phases, say - the table rule has to be adjusted by the ratio of the two k values, and the adiabatic calculation with the correct k is the cleaner route.
Can a cable's steel wire armour be the protective conductor?
Frequently yes, and it is common practice for SWA cable. The check is exactly the one on this page: work out the armour's cross-sectional area from the cable data sheet, use the k value for steel with that insulation - typically around 52 for steel with PVC - and confirm it meets the adiabatic requirement, then confirm the loop impedance separately.
What about a TT system with an RCD?
The thermal calculation is the same, but the fault current is very different. In a TT system the earth fault current is limited by the earth electrode resistance and may be only a few amperes, so the adiabatic requirement is tiny and the table method governs. The real design problem there is the loop impedance and the RCD, not the conductor size.
Last reviewed by the A2Z.Tools team against the sources listed above.
