Ground Rod and Wire Resistance

Estimating the resistance of driven rods, a buried horizontal ground wire, and both together in uniform soil.

1. What this check does

Estimates the resistance to remote earth of one driven rod with the Dwight formula, of several rods by the average-potential method with a line-source mutual resistance, of a buried horizontal wire with Dwight's horizontal-wire formula, and of rods and wire together as parallel resistances.

2. Inputs used

Electrode type: rods, a buried horizontal wire, or both.
Soil resistivity (Ω·m).
Rods: length, diameter, number, spacing and arrangement (line or ring).
Wire: total length, burial depth and conductor size (AWG, kcmil or mm²; the radius of a solid conductor of the same area is used).

3. Formulas and assumptions

Rods

Single rod

R_1 = \dfrac{\rho}{2\pi L}\left(\ln\dfrac{4L}{a} - 1\right)

Dwight. a = rod radius.

Mutual

R_{ij} = \dfrac{\rho}{4\pi L}\,\ln\dfrac{\sqrt{L^2 + d^2} + L}{\sqrt{L^2 + d^2} - L} \;\xrightarrow{\,d \gg L\,}\; \dfrac{\rho}{2\pi d}

n rods

R = \dfrac{1}{n^2}\sum_i \sum_j R_{ij}, \qquad R_{ii} = R_1

Average-potential method.

Horizontal wire and combination

Horizontal wire

R = \dfrac{\rho}{4\pi L}\left[\ln\dfrac{4L}{a} + \ln\dfrac{4L}{s} - 2 + \dfrac{s}{2L} - \dfrac{s^2}{16L^2} + \dfrac{s^4}{512L^4}\right]

Total length 2L, radius a, burial depth s/2 (Dwight, as given in IEEE 142).

Rods and wire

R = \dfrac{R_{\text{rods}}\, R_{\text{wire}}}{R_{\text{rods}} + R_{\text{wire}}}

Parallel, neglecting mutual interaction.

Uniform soil of the resistivity entered.
The mutual term is the potential of a line current source with its image; it is less accurate when rods are closer than about twice their length.
The wire formula assumes the wire is long compared with twice its burial depth; a short wire is flagged.
Rods and wire are combined in parallel, the usual practice. Because both use the same soil the real value is somewhat higher, between the parallel value and the lower of the two alone; the tool reports that range.
For a meshed grid with rods, the IEEE 80 Ground Grid tool (Sverak and Schwarz equations) is the better model.

4. What is NOT checked

Layered soil, seasonal moisture and frost.
Step and touch voltage (see Ground Grid).
Conductor sizing for fault current.
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 (Dwight formulas)
H. B. Dwight, Calculation of Resistances to Ground (1936)
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 and Wire Resistance.