Electrode resistance
Horizontal buried conductor or strip (Dwight / Sunde)
- where
- conductor radius (m)
- conductor diameter, or half the tape width (mm)
- twice the burial depth (m)
- burial depth (m)
- conductor resistance to remote earth (Ω)
- soil resistivity (Ω·m)
- total conductor length (m)
Explain this equation
Gives the resistance of a straight buried horizontal conductor, such as bare copper laid with a cable, a tape tail from a substation or a single run of a ring.
a is the conductor radius (d in mm divided by 2000) and s is twice the burial depth, which places the image of the conductor above the ground surface. L is the total length. The two log terms describe the conductor's own field and the effect of its image, and the small s/L terms are end corrections.
The shape follows from Dwight's method of averaging the potential along a line source and its mirror image in the ground surface. Length dominates: resistance falls roughly as 1/L, with only a weak dependence on diameter and depth.
20 m of 10 mm conductor at 0.6 m in 100 Ω·m soil is about 8.4 Ω. The rough rule 2ρ/L gives 10 Ω, which is deliberately conservative.
Watch out: beyond about 60√ρ metres the conductor's own impedance stops the far end contributing, so very long runs give less benefit than the formula predicts.
Resistance of a straight horizontal wire, stranded conductor or tape buried at shallow depth, such as a cable-route earth or a ring tail.
Enter your values to see the result.
Good to know
Dwight’s formula for a buried horizontal wire (IEEE 142 Table 4-5), written here with the total length L and depth h. For L ≫ h it reduces to Sunde’s ρ/(πL)·[ln(2L/√(2ah)) − 1]. For flat tape use an equivalent diameter equal to half the tape width (equivalent radius = width/4), as in EREC S34 formula R7. The second output is the rough BS EN 50522 rule of thumb R ≈ 2ρ/L.
Common mistake
Assuming a very long buried conductor keeps reducing resistance. Beyond roughly 60√ρ metres its own series impedance limits the useful length at 50 Hz.
Limits
Uniform soil, straight conductor, L ≫ h and L ≫ d, resistive (low-frequency) behaviour only. BS 7430 gives an equivalent coefficient form (P, Q) for strips and other shapes; that table is not reproduced here. Bends, rings and stars need the shape-specific formulas.
Sources
- H.B. Dwight, Calculation of resistances to ground, AIEE Transactions 55 (1936) 1319–1328; reproduced in IEEE Std 142-2007 Table 4-5
- E.D. Sunde, Earth Conduction Effects in Transmission Systems, Dover (1968)
- 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)
- BS EN 50522 Earthing of power installations exceeding 1 kV a.c. (2010; superseded by EN 50522:2022)
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.