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.

Frequently Asked Questions

What is typical soil resistivity?

Wet clay: 10-100 ohm-m. Sandy loam: 50-300 ohm-m. Dry sand: 500-5000 ohm-m. Gravel: 1000-5000 ohm-m. Rock: 2000-100,000 ohm-m. Moisture and mineral content have the strongest effect.

How do I reduce ground resistance?

Use longer rods (doubling length reduces R by about 40%), multiple rods spaced apart (parallel combination), chemical soil treatment (bentonite, conductive cement), or ground enhancement materials.

How is soil resistivity measured?

The Wenner four-pin method (ASTM G57) is standard. Four equally spaced pins are driven into the soil and resistance is measured between the inner pair while current flows through the outer pair.

Ready to run the numbers?

Open Grounding Resistance Calculator