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
| Variable | Description | Default |
|---|---|---|
soil_resistivity | Soil Resistivity (rho)(ohm-m) | 100 |
rod_length | Rod Length (L)(m) | 3 |
rod_diameter | Rod Diameter (d)(mm) | 16 |
d_m | Derived value= rod_diameter / 1000 | calculated |
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
- 01d = 0.016 m
- 02ln(4 x 3 / 0.016) = ln(750) = 6.62
- 03R = 100 / (2 x pi x 3) x 6.62 = 100/18.85 x 6.62 = 35.12 ohm
- 04This exceeds 5 ohm. Multiple rods or soil treatment may be needed.
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