Ground Grid Step & Touch Voltage

The IEEE Std 80 simplified method for a uniformly spaced rectangular grid in uniform soil.

1. What this check does

Computes the tolerable touch and step voltages for the body weight and shock duration you choose, the grid resistance and ground potential rise, and the mesh (worst touch) and step voltages of a rectangular grid with equal spacing, then compares them.

2. Inputs used

Soil resistivity; optional surface layer resistivity and thickness.
Grid length and width, conductor spacing, burial depth and conductor diameter; optional ground rods (count, length, on the perimeter or not).
Symmetrical ground fault current 3I0, split factor Sf, fault and shock duration, optional X/R.
Body weight 50 or 70 kg.

3. Formulas and assumptions

Cs = 1 − 0.09 (1 − ρ/ρs) / (2 hs + 0.09) E_touch = (1000 + 1.5 Cs ρs) · k / √ts k = 0.116 (50 kg) or 0.157 (70 kg) E_step = (1000 + 6 Cs ρs) · k / √ts Df = √(1 + Ta/tf · (1 − e^(−2tf/Ta))), Ta = (X/R) / (2πf) IG = Df · Sf · 3I0 Rg = ρ [ 1/LT + 1/√(20A) · (1 + 1/(1 + h√(20/A))) ] GPR = IG · Rg Em = ρ Km Ki IG / LM Es = ρ Ks Ki IG / LS Km = 1/(2π) [ ln( D²/(16hd) + (D+2h)²/(8Dd) − h/(4d) ) + Kii/Kh · ln( 8/(π(2n−1)) ) ] Ks = 1/π [ 1/(2h) + 1/(D+h) + (1 − 0.5^(n−2))/D ] Ki = 0.644 + 0.148 n, n = na·nb·nc·nd, Kh = √(1 + h/h0), h0 = 1 m LM = LC + LR, or LC + [1.55 + 1.22 Lr/√(Lx²+Ly²)] LR with rods on the perimeter LS = 0.75 LC + 0.85 LR

Uniform soil. The simplified equations apply to grids with n up to 25, depth 0.25–2.5 m, spacing above 2.5 m and conductor diameter small compared with depth; outside that range a warning asks for a computer analysis.
The split factor Sf is entered by you — it depends on overhead ground wires, cable sheaths and remote grounds.
Without X/R the decrement factor is 1.0, which understates the current for short fault durations.
Worst-case touch is taken as the mesh voltage at the centre of a corner mesh.

4. What is NOT checked

Two-layer or multilayer soil.
Touch voltage at the fence or outside the grid, and transferred potentials.
Conductor and connection sizing for thermal withstand.
Irregular grids and unequal spacing.

5. Reference standards

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

IEEE Std 80 — guide for safety in AC substation grounding
IEEE Std 81 — measuring earth resistivity and ground impedance
NEC 2023 Article 250 (equipment grounding, context)

6. Validation cases

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

7. Known issues and changes

See the Changelog. Try the tool: Ground Grid Step & Touch Voltage.