Single Ground Rod Resistance to Earth
Single Ground Rod Resistance to Earth
A grounding electrode’s job is to provide a low-resistance path into the earth for fault current and lightning energy, and that resistance depends mainly on the soil’s resistivity and the rod’s length and diameter. A simplified rod formula lets engineers estimate this resistance before driving and testing the electrode in the field.Grounding systems that test above code-required resistance thresholds put both equipment and personnel at risk during a fault, since the ground path is what limits touch and step voltages — so this calculation is typically a first estimate, refined with additional rods or a ground grid if the soil resistivity turns out to be high.
The rod resistance is R = ρ/(2πL)·(ln(4L/d) − 1), a simplified form of the classical driven-rod grounding equation. where ρ is the soil resistivity, L is the rod’s driven length, and d is the rod diameter.
Inputs
rho_soil := 100 Ohm·m=100 kg·m^3/A^2/s^3
L_rod := 3 m=3 m
d_rod := 0.016 m=16 mm
The logarithmic term captures how the rod’s length-to-diameter ratio shapes the current flow into the surrounding soil, and scaling by resistivity and length gives the rod’s resistance to earth.
R_gnd := rho_soil/(2·pi·L_rod)·(ln(4·L_rod/d_rod) - 1)=29.82 Ω
Results
A resistance near 30 Ω for a single rod in moderately resistive soil is a common result, and many codes require 25 Ω or less for a single electrode. If the calculated (or field-measured) resistance exceeds that threshold, the standard fix is to drive an additional rod in parallel or use a longer rod, since resistance falls off only logarithmically with length, not linearly.
Assumptions & limitations
- Single vertical rod in uniform, homogeneous soil.
- Soil resistivity assumed constant with depth and season.
- Formula is an approximation; field testing (fall-of-potential method) is required for verification.