Earthing Conductor Sizing: IEC Adiabatic Equation with Worked Example
Quick answer: an earthing or protective conductor must satisfy both minimum construction rules and thermal short-circuit withstand. The IEC adiabatic equation is S = I√t / k, where S is conductor area, I is earth-fault current, t is disconnection time and k depends on conductor and insulation materials and temperature limits.
What the adiabatic equation checks
During an earth fault, the protective conductor carries high current until the fuse or circuit breaker clears the fault. The adiabatic method assumes the event is short enough that heat remains substantially within the conductor. It checks whether the conductor can absorb the fault energy without exceeding its permitted final temperature.
The equation is:
S = I × √t / k
- S: required cross-sectional area in mm²
- I: prospective fault current through the conductor in amperes
- t: protective-device clearing time in seconds
- k: material and temperature constant from the applicable standard
Worked example
A copper protective conductor with thermosetting insulation must carry 8 kA for 0.20 seconds. Assume the applicable project table gives k = 143.
S = 8,000 × √0.20 / 143 = 25.0 mm²
The calculated minimum is 25 mm², so select at least the next compliant standard size after checking installation rules, mechanical protection, terminals, corrosion, parallel paths and any project minimum. Never select from the equation alone.
How each input changes the result
| Input | If it increases | Design implication |
|---|---|---|
| Fault current I | Required area rises linearly | Use the current actually flowing in the protective path |
| Clearing time t | Required area rises with √t | Obtain time from the device curve at the calculated current |
| Constant k | Required area falls | Use only the correct material, insulation and temperature case |
| Parallel paths | Current may divide | Do not assume sharing without verified impedance and continuity |
Design workflow
- Define the conductor function: PE, bonding conductor, earthing conductor or lightning-protection conductor.
- Calculate the maximum and minimum earth-fault currents at the location.
- Read total clearing time from the protective-device curve, including relay and breaker time where applicable.
- Select the correct k value from the governing standard.
- Apply S = I√t/k and round up to a compliant standard size.
- Verify minimum sizes, mechanical strength, corrosion, routing, joints and terminal capacity.
- Confirm automatic disconnection and touch-voltage performance for the complete earthing system.
Common mistakes
- Using breaker rated current instead of prospective earth-fault current.
- Using an assumed clearing time instead of the time-current curve.
- Selecting k from the wrong insulation or conductor material.
- Ignoring relay, breaker and arc duration in total clearing time.
- Forgetting minimum mechanical sizes and corrosion allowance.
- Assuming steel containment always provides a dependable parallel path.
Earthing Conductor Sizing FAQ
Is the adiabatic result always the final conductor size?
No. It is one thermal check. Standard minimums, mechanical protection, corrosion, voltage drop, bonding requirements and terminal limitations can require a larger conductor.
Which fault current should be used?
Use the prospective current that flows through the conductor for the fault being assessed. The protection study should also check minimum current because it determines whether disconnection is fast enough.
Can the equation be used for long fault durations?
The simplified adiabatic assumption has limits. For long durations, large conductors or unusual thermal conditions, use the method required by the governing standard or a detailed thermal calculation.
Related reading: industrial electrical grounding and earth-fault loop impedance.