Earthing calculator: soil resistivity, rods and grid

What this calculator does

Three steps of the same job: turning earth tester readings into soil resistivity, estimating the resistance of a rod or a set of them, and calculating that of a buried grid.

Resistivity by the Wenner method

Four probes in line, equally spaced, current through the outer two and voltage between the inner two. Apparent resistivity follows from

ρ = 2 π a R

with spacing a in metres and reading R in ohms. Each measurement averages the soil down to a depth of the order of that spacing, so sweeping several spacings is what reveals the structure: if resistivity grows with a, there is a more resistive layer underneath; if it falls, there is water or a more conductive layer.

That detail is not minor. Designing a grid with the resistivity measured at 2 metres, when the grid will work against the first 10 metres of soil, is the classic mistake that ends in an earthing system that does not comply.

Vertical rod

For a cylindrical rod driven vertically, Dwight’s formula:

R = ρ / (2 π L) × (ln(4L/r) − 1)

with L the buried length and r the radius. Length dominates the result; diameter sits inside a logarithm and hardly matters. Doubling the diameter of a 3-metre rod lowers its resistance by about 10%; doubling the length, by nearly 45%.

For several rods the calculator applies an efficiency factor that you control, 0.8 by default: two rods close together do not halve the resistance, because their zones of influence overlap. The further apart — at least one rod length — the higher the efficiency.

Earthing grid

For a buried grid, Sverak’s equation as given in IEEE 80:

R = ρ [ 1/L_T + 1/√(20A) × (1 + 1/(1 + h√(20/A))) ]

where A is the enclosed area, L_T the total length of buried conductor and rods, and h the depth. It gives the resistance of the whole and, with the fault current, the ground potential rise (GPR), which is the figure that drives the insulation of the telecoms and control circuits entering the substation.

Worked example

Soil of 100 Ω·m measured with Wenner at 4 m (reading 3.98 Ω → ρ = 100 Ω·m).

• One 3 m rod, 16 mm diameter: 33.5 Ω
• Four rods at 0.8 efficiency: 10.5 Ω
• A 1,000 m² grid with 500 m of conductor at 0.5 m depth: 1.57 Ω
• With a 5 kA fault, the grid lifts the installation 7,850 V above remote earth

What this calculator does not do

It does not calculate step and touch voltages, which decide personnel safety and require the full grid geometry, the surface gravel layer and the clearing time. It does not model two-layer soils, which is what most real sites have. And it does not replace measurement: resistivity varies with moisture and temperature, so the design value must be taken in the worst season.

What measures it

Resistivity and earth resistance are measured with a four-terminal earth tester, which is what makes the Wenner method possible. For low-voltage installation testing, multifunction testers include earth and loop measurement.