Electrode resistance
Single vertical rod resistance (Dwight)
- where
- rod resistance to remote earth (Ω)
- soil resistivity (Ω·m)
- driven rod length (m)
- rod diameter (mm)
Explain this equation
Estimates the resistance to remote earth of one driven rod in uniform soil, for example a pole-mounted transformer earth or one rod of a group.
ρ is the soil resistivity, L the driven length and d the rod diameter, entered in mm and divided by 1000 to give metres. The log term describes how current spreads out from a long thin conductor: most of the resistance sits in the soil close to the rod.
The formula comes from Dwight's analysis of a long thin cylinder with its image above ground. Resistance falls almost in proportion to length because the current spreads into a larger volume of soil, while the diameter only appears inside the logarithm.
A 3 m, 16 mm rod in 100 Ω·m soil is about 33 Ω. Doubling L roughly halves R; doubling d reduces it by only about 10 %.
Watch out: in layered soil the result depends heavily on which layer the rod reaches. A deeper rod into a low-resistivity layer can do far better than this formula suggests.
Resistance to remote earth of one vertical rod driven from the surface into uniform soil.
Enter your values to see the result.
Good to know
This is the Dwight (1936) formula used in BS 7430 and ENA EREC S34 (formula R1). A 3 m × 16 mm rod in 100 Ω·m soil is about 33 Ω. Doubling the length roughly halves R; doubling the diameter changes R by only about 10 %.
Common mistake
Entering the rod length including the part above ground, or the diameter in metres. Diameter is in mm here and only the driven length counts.
Limits
Uniform soil, rod top at ground level, L ≫ d. In layered soil use the resistivity of the layer the rod mostly sits in, or a two-layer method. Ignores contact resistance and backfill; seasonal variation can be ±50 %.
Sources
- ENA EREC S34 Issue 2 (2018) A guide for assessing the rise of earth potential at electrical installations
- BS 7430:2011+A1:2015 Code of practice for protective earthing of electrical installations (withdrawn 2026, replaced by a revised edition)
- V. Pangonilo, Earth rod electrode resistance (worked examples using BS 7430 rod factors)
For competent high-voltage engineers. Results are calculations from the published methods shown and depend entirely on the data you enter. They are not a substitute for a system study, manufacturer data, the applicable standards and Engineering Recommendations, or your organisation’s safety rules. Never use a result to justify working on or near live HV equipment.