Resistance of vertical earth rods
Resistance to earth of a single vertical electrode — rod, pipe or angle — in uniform soil, of n rods in a row or in a ring with their mutual influence, and the number of rods for a required resistance.
R_1 = ρ / (2π · L) · (ln(8 · L / d) − 1)R_n = R_1 · (1 + λ · α) / n, α = ρ / (2π · R_1 · s)λ_row = 2 · (1/2 + 1/3 + … + 1/n)λ_ring = Σ sin(π / n) / sin(π · k / n), k = 1 … n − 1η = 1 / (1 + λ · α)A single rod follows Dwight's formula (IEEE Std 142, BS 7430) for a rod whose top is at ground level; burying the top 0.5–0.8 m deep lowers the resistance by about 5 %, so the result is on the safe side. The mutual influence follows BS 7430, treating the neighbouring rods as point sources. A horizontal strip connecting the rods lowers the resistance further and is not included. The soil is uniform; for two-layer soil use the methods of IEEE Std 80.
Source: IEEE Std 142 (Green Book) and BS 7430 — resistance of a vertical rod and of a group of rods; PUE, ch. 1.7 — resistance limits
Inputs
You can change a field's unit: the value is converted to the formula's units automatically.
The measured value corrected for frozen or dry soil. As a guide: clay and loam 20–100 Ω·m, sandy loam 150–400, sand 400–1 000 and more.
Usually 2.5–5 m.
Round bar 16–20 mm; for an angle with a leg b the equivalent diameter is ≈ 0.95 · b (50 × 50 angle: 47.5 mm).
1 for a single rod.
Usually one or two rod lengths; the mutual influence formula is accurate for s ≥ L.
PUE (ch. 1.7): not above 4 Ω for the earthing of a transformer neutral in a 380/220 V network; for ρ > 100 Ω·m the limit may be multiplied by 0.01 · ρ, but not more than tenfold.
Unit converter for this formulaResistivity · Length · Resistance
- Ω·m1
- Ω·mm²/m1,000,000
- Ω·cm100
Copper 0.0175 Ω·mm²/m, aluminium 0.028 Ω·mm²/m at 20 °C. Soils: 10 to 1 000 Ω·m and more.
- R_1 — Resistance of one rod–
- η — Utilisation factor of the rods–
- n_req — Rods needed for R_norm–pcs
Results are engineering estimates from standard formulas; for design decisions check them against the codes, project documents and specialists' calculations. The formulas carried over from the original set are unchanged, and their errors are described in the notes.