Ground Rod Resistance

Estimating driven rod resistance in uniform soil.

1. What this check does

Estimates the resistance to remote earth of one driven rod with the Dwight formula, and of several rods by the average-potential method with a hemispherical approximation of mutual resistance.

2. Inputs used

Soil resistivity (Ω·m).
Rod length and diameter.
Number of rods, spacing and arrangement (line or ring).

3. Formulas and assumptions

Single rod R₁ = ρ / (2πL) · (ln(4L / a) − 1), a = rod radius Mutual Rᵢⱼ ≈ ρ / (2π dᵢⱼ) n rods R = (1 / n²) · Σᵢ Σⱼ Rᵢⱼ, Rᵢᵢ = R₁

Uniform soil of the resistivity entered.
The mutual term treats each distant rod as a hemisphere; it is less accurate when spacing is under about twice the rod length, where it tends to understate resistance.
Connecting conductors are not counted as electrodes.

4. What is NOT checked

Layered soil, seasonal moisture and frost.
Ground grid design, step and touch voltage.
Lightning and high-frequency impedance.

5. Reference standards

Pointers only; consult the edition adopted by your authority having jurisdiction.

NEC 2023 250.53(A)(2), 250.53(A)(3) — supplemental electrode and rod spacing
IEEE Std 142 — grounding of industrial and commercial power systems
IEEE Std 81 — measuring earth resistivity and ground impedance

6. Validation cases

Hand-calculated cases run on every change. See Validation.

7. Known issues and changes

See the Changelog. Try the tool: Ground Rod Resistance.