Wenner Four-Pin Soil Resistivity (IEEE 81) & Dwight Ground-Rod Resistance

IEEE 81 Wenner 4-pin geometry and when probe depth b matters

In Frank Wenner’s (1915) four-terminal earth survey (IEEE Std 81), four equally spaced probes at interval a (meters) are driven to depth b, current I is injected through the outer pair, and voltage V (resistance R = V / I in ohms) is measured across the inner pair. The exact apparent soil resistivity is rho = 4 * PI() * a * R / (1 + 2*a / SQRT(a^2 + 4*b^2) - a / SQRT(a^2 + b^2)).

When spacing a >= 20 * b (shallow pins), the denominator converges to 2 and simplifies to rho_shallow = 2 * PI() * a * R. Once soil resistivity rho is known, H. B. Dwight’s IEEE-80 equation gives the resistance to remote earth of a vertical ground rod of length L and radius r_rod: R_rod = (rho / (2 * PI() * L)) * (LN(4 * L / r_rod) - 1).

Exact IEEE-81 Wenner Soil Resistivity Formula

Include probe burial depth b explicitly so tight indoor/substation pin spacings (where b / a > 0.05) never underestimate soil resistivity.

=LET(sp_a, B2, dep_b, B3, res_r, B4, denom, 1 + (2 * sp_a) / SQRT(sp_a ^ 2 + 4 * (dep_b ^ 2)) - sp_a / SQRT(sp_a ^ 2 + dep_b ^ 2), ROUND((4 * PI() * sp_a * res_r) / denom, 2))

Dwight Single Vertical Ground-Rod Resistance Formula

Evaluate R_rod in ohms from apparent resistivity E3, driven length B5, and rod radius B6, checking compliance against the NEC 250.53 25-ohm target.

=ROUND((E3 / (2 * PI() * B5)) * (LN((4 * B5) / B6) - 1), 2)

Further reading

• IEEE Std 81 — Guide for Measuring Earth Resistivity, Ground Impedance, and Earth Surface Potentials