Grounding Resistance Calculator Formula

Understand the math behind the grounding resistance calculator. Each variable explained with a worked example.

Formulas Used

Ground Resistance

resistance = soil_resistivity / (2 * pi * rod_length) * log(4 * rod_length / d_m)

Variables

VariableDescriptionDefault
soil_resistivitySoil Resistivity (rho)(ohm-m)100
rod_lengthRod Length (L)(m)3
rod_diameterRod Diameter (d)(mm)16
d_mDerived value= rod_diameter / 1000calculated

How It Works

Ground Rod Resistance

The resistance of a ground rod depends on soil resistivity and rod geometry.

Formula (simplified for vertical rod)

R = (rho / 2 pi L) ln(4L / d)

where rho is soil resistivity in ohm-metres, L is rod length, d is rod diameter, and ln is the natural logarithm. Lower resistance is better for safety. Most codes require < 5 ohms for power systems and < 25 ohms for lightning protection.

Worked Example

A 3 m x 16 mm ground rod in soil with 100 ohm-m resistivity.

soil_resistivity = 100rod_length = 3rod_diameter = 16
  1. 01d = 0.016 m
  2. 02ln(4 x 3 / 0.016) = ln(750) = 6.62
  3. 03R = 100 / (2 x pi x 3) x 6.62 = 100/18.85 x 6.62 = 35.12 ohm
  4. 04This exceeds 5 ohm. Multiple rods or soil treatment may be needed.

Ready to run the numbers?

Open Grounding Resistance Calculator