Earth resistance calculation is used to estimate how effectively an earth electrode or electrode arrangement can dissipate electrical current into the surrounding soil.
The calculated value depends on soil resistivity, electrode dimensions, the number of electrodes and their spacing.
This guide explains the calculation used for a vertical earth rod and how multiple rods affect the final earth resistance.
What Is Earth Resistance?
Earth resistance is the calculated resistance associated with the path from an earth electrode into the surrounding soil.
It is normally expressed in ohms (Ω).
The value is influenced by both the physical electrode and the electrical properties of the soil around it.
For this reason, an earth rod that performs well in one location may produce a very different calculated resistance in another location.
Soil Resistivity
Soil resistivity is normally expressed in Ω·m.
It describes how strongly the soil resists the flow of electrical current.
For an earthing calculation, a measured soil resistivity value is generally more useful than simply describing the soil as clay, sand or rock.
If the soil resistivity is higher, the calculated electrode resistance will generally also be higher.
Single Earth Rod Calculation
For a vertical rod, the calculator uses:
Where:
- R = single rod resistance in Ω
- ρ = soil resistivity in Ω·m
- L = rod length in m
- d = rod diameter in m
The equation shows why both soil properties and electrode geometry matter.
Effect of Rod Length
Rod length is a strong geometric input.
Increasing length allows the electrode to interact with a larger depth of surrounding soil.
Effect of Rod Diameter
Rod diameter also appears in the equation, but inside a logarithmic term.
Therefore, increasing diameter generally produces a smaller resistance improvement than the same kind of change in soil resistivity or electrode length.
Example
Consider a vertical rod with:
- Soil resistivity = 100 Ω·m
- Rod length = 3 m
- Rod diameter = 17.2 mm
Using the calculator's single-rod equation gives a calculated resistance of approximately 33.1 Ω.
This is the resistance of the individual rod before considering the effect of multiple electrodes.
Multiple Earth Rods
If one rod does not provide the required resistance, additional rods may be considered.
However, multiple rods cannot simply be treated as independent resistors connected in parallel.
The surrounding soil is shared.
Each electrode influences the current distribution around the other electrodes.
This is called electrode interference.
Rod Spacing
Rod spacing is therefore an important input.
The calculator evaluates the ratio:
s / L
Where:
- s = centre-to-centre rod spacing
- L = rod length
When spacing is small relative to rod length, electrode interaction becomes more significant.
Increasing spacing can reduce the mutual influence between electrodes.
Array Resistance
The calculator uses the single rod resistance, number of rods and an interference factor to estimate the resistance of the electrode array.
For example, with:
- 100 Ω·m soil resistivity
- 3 m rods
- 17.2 mm rod diameter
- 3 rods
- 3 m spacing
the calculator screenshot example gives:
Single rod resistance ≈ 33.11 Ω
Array resistance ≈ 15.45 Ω
The result is therefore not simply:
33.11 ÷ 3
because electrode interference is included.
Why the Number of Rods Matters
Adding rods can reduce the calculated resistance.
However, every additional rod does not necessarily provide the same reduction as the previous rod.
The improvement depends on electrode spacing and the surrounding soil.
This is why a useful earth resistance calculator should display both the number of rods and the interference factor.
Target Earth Resistance
The calculator allows the user to enter a target resistance.
For example, if the target is 1 Ω and the calculated array resistance is 15.45 Ω, the arrangement is above the selected numerical target.
The calculator can then estimate the number of rods required to approach the target under its calculation assumptions.
The target itself must come from the actual installation requirements. It should not be treated as a universal value for every electrical system.
Calculated Resistance vs Measured Resistance
A calculated earth resistance is a design estimate.
A measured earth resistance is obtained from an installed earthing system using an appropriate field-testing method.
The measured result can differ from the calculated result because real soil conditions are not perfectly uniform.
Possible causes include:
- soil layers
- moisture variation
- electrode installation
- connections
- seasonal changes
- actual electrode geometry
Common Mistakes
Dividing Single Rod Resistance by Rod Count
This ignores electrode interaction.
Ignoring Soil Resistivity
Without a realistic soil resistivity value, the calculation may not represent the actual site.
Assuming Bigger Diameter Solves Everything
Rod diameter affects the equation, but increasing diameter does not necessarily provide a dramatic reduction in resistance.
Using a Universal Resistance Target
Different installations may have different design criteria.
Practical Calculation Workflow
A practical calculation sequence is:
1. Obtain soil resistivity.
2. Select electrode dimensions.
3. Calculate single rod resistance.
4. Define number of rods.
5. Define rod spacing.
6. Apply electrode interference.
7. Calculate array resistance.
8. Compare with the design target.
9. Evaluate whether additional electrodes or a different arrangement are required.
10. Verify the installed system where field testing is required.
Frequently Asked Questions
How do I calculate earth resistance?
For a vertical rod, the calculator uses soil resistivity, rod length and rod diameter in the single-electrode equation, then evaluates multiple electrodes using their number and spacing.
Does soil resistivity affect earth resistance?
Yes. Soil resistivity is a major factor in the calculated resistance of an earth electrode.
Does a longer earth rod reduce resistance?
Generally, increasing electrode length can reduce the calculated resistance, subject to the assumptions and actual soil profile.
Does increasing rod diameter reduce earth resistance?
It can, but the effect is limited by the logarithmic relationship in the electrode equation.
Why do multiple rods need spacing?
Because nearby electrodes interact through the surrounding soil. Adequate spacing can reduce mutual interference.
Final Takeaway
Earth resistance calculation is not simply a matter of choosing a rod and assigning a resistance value.
The result comes from the relationship between soil resistivity, electrode geometry, number of electrodes and their spacing.
A calculator is useful for understanding these relationships and evaluating preliminary earthing arrangements before final site verification.