Calculate a single ground rod’s resistance, soil resistivity, length, or diameter from any one known value and selected units with one missing input.
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Ground Resistance Formula
This calculator uses the common single vertical ground rod approximation in uniform soil. Leave exactly one field blank, then enter the other three values. The calculator converts the inputs to base units, solves the missing value, and converts the result back to the unit you selected.
- R = ground resistance, in ohms (Ω)
- rho = soil resistivity, in ohm-meters (Ω·m)
- L = length of the ground rod, in meters (m)
- D = diameter of the ground rod, in meters (m)
- ln = natural logarithm
- pi = 3.14159…
When ground resistance is the missing value, the calculator applies the formula directly:
When soil resistivity is the missing value, the formula is rearranged as:
When rod diameter is the missing value, the calculator uses:
When rod length is the missing value, the length cannot be isolated cleanly with simple algebra because L appears both inside the logarithm and in the denominator. The calculator solves this equation numerically:
- Ground resistance mode: uses soil resistivity, rod length, and rod diameter to estimate the resistance of one vertical rod.
- Soil resistivity mode: uses a measured or target resistance with known rod dimensions to estimate the equivalent soil resistivity.
- Rod length mode: solves for the practical rod length needed to reach a target resistance with the given soil resistivity and diameter.
- Rod diameter mode: calculates the diameter that would satisfy the target resistance for the given soil resistivity and rod length.
Typical Soil Resistivity Ranges
Soil resistivity changes with moisture, temperature, minerals, compaction, and seasonal conditions. These values are approximate starting points, not substitutes for field testing.
| Soil or material condition | Typical resistivity range | Effect on ground resistance |
|---|---|---|
| Wet clay or marshy soil | 10 to 50 Ω·m | Usually lower resistance |
| Clay or moist loam | 20 to 100 Ω·m | Often favorable for grounding |
| Loam or garden soil | 50 to 200 Ω·m | Moderate resistance |
| Sand or gravel | 200 to 1,000 Ω·m | Higher resistance |
| Dry rock or very dry soil | 1,000+ Ω·m | Often difficult to ground effectively |
Ground Resistance Result Context
| Estimated resistance | General interpretation |
|---|---|
| Less than 5 Ω | Very low resistance for a grounding electrode system. |
| 5 to 25 Ω | Common target range for many grounding designs. |
| 25 to 100 Ω | May be acceptable in some cases, but often improved with additional electrodes or longer rods. |
| More than 100 Ω | High resistance. Soil conditions, rod depth, and electrode layout should be reviewed. |
Example Calculations
Example 1: Calculate ground resistance
You have soil resistivity of 100 Ω·m, a rod length of 3 m, and a rod diameter of 0.016 m.
The estimated ground resistance is about 30.09 Ω.
Example 2: Calculate soil resistivity
You measured a ground resistance of 25 Ω using a 3 m rod with a diameter of 0.016 m.
The estimated soil resistivity is about 83.09 Ω·m.
FAQs
What does ground resistance mean?
Ground resistance is the electrical resistance between a grounding electrode, such as a ground rod, and the surrounding earth. Lower resistance usually means fault current, lightning current, or static charge has an easier path into the ground. The result depends strongly on soil resistivity and electrode geometry.
Why does increasing rod length usually reduce ground resistance?
A longer rod contacts more soil and reaches deeper layers that may contain more moisture. In the formula, increasing L generally lowers the resistance because the current spreads through a larger volume of earth. The reduction is not perfectly linear, so doubling the rod length does not always cut the resistance in half.
Why does rod diameter have a smaller effect than rod length?
Rod diameter appears inside the natural logarithm term, so diameter changes affect the result more slowly than length or soil resistivity. A larger diameter can reduce resistance, but increasing rod length, adding rods, or improving electrode spacing usually has a larger effect.