Earth Cable Size Calculation: The Adiabatic Equation Explained
The earth conductor has to survive the fault current for as long as the protection takes to clear it. The adiabatic equation gives the minimum area, and the answer depends heavily on clearing time.
The equation
S = I × √t ÷ k
- S: minimum cross-section area in mm²
- I: earth fault current in amperes
- t: time for the protection to clear the fault in seconds
- k: factor for the conductor material and temperature limits, taken from the standard
Worked example
Illustrative example, not a project. Earth fault current 10 kA, protection clearing time 0.5 s, copper conductor with k assumed as 143 (take the real value for your insulation and temperatures from the standard).
- √t = √0.5 = 0.707
- S = 10,000 × 0.707 ÷ 143 = 49.5 mm²
- Next standard size: 50 mm²
If the clearing time were 1 s instead, S = 10,000 × 1 ÷ 143 = 70 mm². This is why protection settings and earthing conductor sizes must be designed together. See protection coordination.
Other checks
- Impedance: the earth fault loop must be low enough for the protection to operate.
- Touch and step voltage: depends on the earth electrode system and soil. See earthing design.
- Mechanical and corrosion: minimum sizes and materials for the environment.
Calculate it
The earth conductor sizing calculator includes this check. For the national code context, see the IS 3043 summary and IEC 60364.
Written by the Vision Matrix Institute editorial team. Worked examples use stated, illustrative assumptions; check them against your project data, the applicable standards and manufacturer datasheets before use.
Frequently Asked Questions
How do you calculate earth cable size?
Use S = I × √t ÷ k, where I is the earth fault current in amperes, t the protection clearing time in seconds, and k a factor for the conductor material, insulation and temperature limits. Round up to the next standard size.
Where does k come from?
From the applicable standard, which gives values for combinations of conductor material, insulation and initial and final temperatures. Use the value for your conductor, not a generic figure.
Does a larger fault current or longer clearing time need a bigger conductor?
Yes. Required area rises with the fault current and with the square root of the clearing time, so slow protection forces bigger earthing conductors.
Is thermal withstand the only check?
No. Earthing also needs a low-impedance path so protection operates, safe touch and step voltages, mechanical strength and corrosion resistance. Those checks are separate.
Want to learn this properly?
This topic is covered in depth in our Electrical Design – Data Center Specialist program.
Ask us on WhatsAppLearn to do this on a full project in the Electrical Design – Data Center Specialist program, or read the data center design guide.