Electrode resistance
Rods in parallel (BS 7430 λ factor)
- where
- spacing factor
- soil resistivity (Ω·m)
- resistance of one rod alone (Ω)
- spacing between adjacent rods (m)
- combined resistance of the group (Ω)
- BS 7430 group factor for the arrangement and number of rods
- total number of rods
Explain this equation
Finds the combined resistance of several identical rods connected together, in a straight line or around a hollow square, allowing for the fact that they share the same soil.
R1 is the resistance of one rod on its own and N the total number of rods. α measures how strongly neighbouring rods influence each other: it compares the potential a rod produces at distance s with its own resistance. λ is the BS 7430 factor that sums those mutual effects for the chosen arrangement.
Without coupling the group would be R1/N. Each rod raises the soil potential around its neighbours, so the bracket (1 + λα) increases the result. The rods are modelled as hemispheres of the same resistance, which is reasonable when spacing is at least the rod length.
Ten rods of 89.6 Ω at 1.5 m spacing in 180 Ω·m soil give about 16 Ω in line, not 9 Ω. Doubling the spacing halves α and brings the result closer to R1/N.
Watch out: λ is tabulated only for 2–10 rods in line and up to 20 rods per side for a square; wider spacing gives better use of each rod.
Combined resistance of a group of identical vertical rods, allowing for the mutual resistance between them.
Enter your values to see the result.
Good to know
BS 7430 treats each rod as a hemisphere with the same resistance. λ for rods in a line: 2 → 1.00, 3 → 1.66, 4 → 2.15, 10 → 3.81. For a hollow square with n rods per side (total N = 4(n − 1)), λ ranges from 2.71 (4 rods) to 9.44 (76 rods). EREC S34 formula R5 uses the same form with a factor k from its Figure B.1 for rods around a grid periphery (k ≈ 2.6 for 4 rods). Keep spacing at least equal to the rod length; closer spacing wastes copper.
Common mistake
Dividing the single-rod resistance by the number of rods. Mutual coupling means 10 rods in a 15 m line give about one-sixth of the single rod, not one-tenth.
Limits
Uniform soil, identical rods, spacing not less than about the rod length (the hemisphere model becomes poor at close spacing). λ values are from BS 7430:2011+A1:2015 Tables (now superseded by the 2026 revision, which was not checked). Hollow-square λ for 11, 13, 15, 17, 19 rods per side is linearly interpolated.
Sources
- 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)
- ENA EREC S34 Issue 2 (2018) A guide for assessing the rise of earth potential at electrical installations
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.