What is the Dwight formula?

The Dwight formula gives the earth resistance of a single driven rod: R = (rho / (2 pi L)) times (ln(4L/d) minus 1), where rho is soil resistivity in ohm-metres and L and d are the rod length and diameter in metres. It is the standard textbook model for a vertical electrode.

Why does soil resistivity matter so much?

Resistance scales directly with soil resistivity, so it is the single biggest variable. Wet clay may be 10 ohm-m while dry sand or rock can exceed 1000 ohm-m. The same rod can read under 10 ohms in one soil and over 500 ohms in another.

Why don't parallel rods simply divide the resistance by N?

Each rod has a resistance area in the soil. When rods are close together those areas overlap, so the combined resistance is higher than R divided by N. This tool applies an efficiency factor (about 0.86 for two rods spaced a rod-length apart) to model that overlap.

What is the NEC 25-ohm rule?

NEC 250.53(A)(2) requires that a single made electrode (rod, pipe, or plate) with a resistance over 25 ohms be supplemented by an additional electrode. If a single rod measures 25 ohms or less, no second rod is required, though many installers drive two anyway.

Does this replace a real ground-resistance test?

No. This is an estimate from idealized soil. Always confirm with a fall-of-potential test (3-point method) or a clamp-on ground tester, because real soil is layered and moisture varies with the seasons.

Grounding Electrode System Resistance Calculator

The resistance of a grounding electrode to earth controls how well fault current and lightning are dissipated. This calculator estimates that resistance using the Dwight formula for a driven rod and a parallel-efficiency model for multiple rods, then checks the NEC single-rod 25-ohm rule.

How it works

For one vertical rod, the Dwight formula is:

R = (rho / (2 pi L)) * ( ln(4L / d) - 1 )

where:

rho is soil resistivity in ohm-metres,
L is the buried rod length in metres,
d is the rod diameter in metres.

Resistance falls as the rod gets longer (more contact area with deeper, often moister soil) and as resistivity drops, but it changes only slightly with rod diameter — doubling the diameter barely moves the result, which is why driving a longer rod beats buying a fatter one.

For multiple rods in parallel, the combined resistance is higher than a simple R / N because each rod’s resistance area overlaps its neighbours. The tool applies an efficiency factor (for example about 0.86 for two rods spaced one rod-length apart):

R_combined = R_single / (N * efficiency)

Worked example

An 8 ft × 5/8 in rod in moist loam (rho = 100 ohm-m):

L = 8 ft = 2.44 m, d = 0.625 in = 0.0159 m.
ln(4 × 2.44 / 0.0159) = ln(614) ≈ 6.42.
R = (100 / (2π × 2.44)) × (6.42 − 1) ≈ 6.52 × 5.42 ≈ 35 Ω.

That single rod exceeds 25 Ω, so NEC 250.53(A)(2) calls for a supplemental electrode. Add a second rod at least 6 ft away and the combined resistance drops to roughly 35 / (2 × 0.86) ≈ 20 Ω, which passes.

Notes and tips

Space supplemental rods at least one rod-length apart — closer spacing wastes copper because the resistance areas overlap heavily.
Soil moisture and temperature swing the number seasonally; design for the dry, worst-case season.
The 25-ohm rule is a code minimum, not a performance target. Lightning protection and sensitive electronics often demand 5 ohms or less.

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