Earthing Calculator
Earth electrode resistance, earthing conductor size and the number of rods required, following IS 3043 and IEC 60364-5-54.
Inputs
Clay 5–50, loam 50–200, sand 200–1000, rock >1000
Formula
- Single rod: R = ρ / (2πL) × (ln(8L/d) − 1)
- n rods: R_n = R / n × (1 + λ), λ accounts for mutual interference
- Conductor size: A = I × √t / k (IEC 60364-5-54 adiabatic equation)
The resistance of a driven rod is dominated by the soil immediately around it, so length helps far more than diameter — doubling the length nearly halves the resistance while doubling the diameter changes it by only a few percent. Multiple rods must be spaced at least their own length apart, otherwise their resistance shells overlap and the group performs worse than n parallel rods.
Step-by-step calculation
Single rod
ρ/(2πL) × (ln(8L/d) − 1)
33.109 Ω
Spacing ratio
s / L
1
Group resistance
R/n × (1 + λ)
15.451 Ω
Conductor area
I √t / k
69.93 mm²
Worked example
- 3 m rod, 17.2 mm diameter, soil 100 Ω·m: R = 100 / (2π × 3) × (ln(8 × 3 / 0.0172) − 1) = 33.5 Ω.
- Three rods at 3 m spacing with a 1.2 interference factor: R ≈ 33.5 / 3 × 1.2 = 13.4 Ω.
- Earth conductor for 10 kA cleared in 1 s in copper: A = 10 000 × √1 / 143 = 70 mm².
Assumptions
- Uniform soil resistivity; real sites are layered and require a Wenner four-probe survey.
- Rods are vertically driven and connected by a buried conductor.
Tips
- Space rods at least one rod-length apart; closer spacing wastes copper.
- Chemical earthing or bentonite backfill can cut resistance by 30–60% in rocky soil.
Warnings
- IS 3043 requires ≤ 1 Ω for generating stations and substations, ≤ 5 Ω for large installations and ≤ 8 Ω for domestic.
- Soil resistivity rises sharply in dry seasons — design against the driest condition.
Standards & references
- IS 3043:2018
- IEC 60364-5-54
- IEEE 80
Frequently asked questions
What earth resistance value is acceptable?
IS 3043 asks for 1 Ω at power stations and substations, 5 Ω for large industrial installations and up to 8 Ω for small domestic installations.
How do I lower earth resistance?
Drive longer rods, add rods spaced at least one rod-length apart, or improve the soil around the electrode with bentonite or a chemical earthing compound.
How is the earthing conductor sized?
With the adiabatic equation A = I√t/k, where I is the prospective fault current, t the disconnection time and k a material constant — 143 for copper, 95 for aluminium and 78 for steel.
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