Earth Electrode Resistance Calculator

All logarithms are natural; dimensions inside each formula are in metres. Results estimate low-frequency spreading resistance in a uniform conductive half-space.

Wenner: $\rho_a=2\pi aR$ for shallow contacts. For small contacts at a common depth $b$, use $\rho_a=4\pi aR/f$, where $f=1+2/\sqrt{1+4(b/a)^2}-1/\sqrt{1+(b/a)^2}$. Source: Wenner (1916), printed p.470, attached s2 p.2. The corrected equation assumes tip-only contacts.

Rod: $R_1=\rho[\,\ln(8L/d)-1\,]/(2\pi L)$, Dwight (1936). A straight row uses $R_n=[R_1+\rho\lambda/(2\pi s)]/n$, with $\lambda=2[H_{n-1}-(n-1)/n]$ and $\lambda=0$ for one rod. This finite-row factor is derived here: average all pair potentials $\rho/(2\pi ks)$ with equal rod currents. It is the far-field mutual-screening approximation, not a copied factor table or a full equipotential solution. Use $s\ge2L$. Sunde’s field treatment motivates the mutual-potential method; end-rod current differences are neglected.

Plate: $A=2B^2$ and $R_p=(\rho/4)\sqrt{\pi/A}$. This explicitly uses both faces, following the IS 3043:2018 convention explained by Indian Railways CAMTECH (2021), printed pp.5 and 39. Use a conventional square plate with adequate cover; cover checks applicability rather than changing this formula.

Strip: $d_e=2\sqrt{wt/\pi}$ and $R_s=\rho\ln[L^2/(1.85hd_e)]/(2\pi L)$. Historical BS 7430:2011+A1:2015 long-conductor approximation, reproduced in Al-Shawesh et al. (2021), attached s13 p.5, equation (23). Equal-area conversion is an approximation to the flat cross-section.

Ring: $R_r=\rho\ln[4D/\sqrt{dh}]/(\pi^2D)$, Sunde’s shallow thin-wire ring expression, equation (33) in Al-Shawesh et al., attached s13 p.5. $D$ is centreline ring diameter and $d$ conductor diameter; replacing outer radius by centreline radius is a thin-wire approximation. A ring is not treated as a straight strip of equal length.

Season and TT: $\rho_d=k_s\rho$ and $R_e=k_sR_{\mathrm{base}}$. Then $R_A=R_e+R_{\mathrm{PE}}$; the screening inequality is $R_AI_{\Delta n}\le U_L$. The displayed allowable $R_A$ is $U_L/I_{\Delta n}$. It is not a complete fault-loop or trip-time calculation.

The soil is homogeneous, isotropic, linear and in intimate contact with bare electrodes. Resistivity is a site measurement or an explicit user assumption, not a soil-type table. A Wenner result is interpreted as an equivalent uniform value only after checking its representativeness.

Rods are identical, vertical, top approximately flush with the surface, with negligible metal and bonding impedance. The straight-row correction assumes equal currents and well-separated rods. Buried leads contribute no earth conductance in this model. There is no simple parallel combination of a ring, rods and a plate.

The plate is square, 0.6–1.2 m per side, with both faces exposed to soil and at least 1.5 m top cover for the stated 2018 baseline. Strip equivalent diameter is based on cross-sectional area. Ring and strip burial are uniform. Thin-wire formulas omit end, local contact and corrosion effects.

The seasonal multiplier is user supplied. The illustrative default 1.2 has no normative status; use 1 if resistivity already represents the design worst season. Protective-conductor resistance is added separately and is not multiplied by the soil factor. The entered TT voltage limit is selected by a qualified designer for the actual installation.

Preliminary design only. Installation work, verification and commissioning measurements belong to a qualified person. Confirm electrode resistance in the field, protective-conductor continuity, equipotential bonding and the protective device’s operation.

Model guards: rod length at least 20 diameters; rod-row spacing at least 2L; strip length at least 10 burial depths and burial at least 5 equivalent diameters; ring diameter at least 10 burial depths and burial at least 5 conductor diameters. These are stated approximation limits, not a replacement for normative electrode dimensions. Layered or frozen soil, conductive backfill, concrete reinforcement, nearby metalwork and combined electrodes need a more detailed model. Low resistance alone does not establish electrical safety.

Rules and editions reviewed 2026-10-27: PUE (Rules for Electrical Installations), seventh edition, Chapter 1.7 (Ministry of Energy Order 204 of 2002), particularly 1.7.59, restricts TT use and requires RCD-based automatic disconnection; verify the application and protective operating current required by the adopted rules. DIN VDE 0100-540:2024-06 covers earthing arrangements, protective conductors and bonding, including mechanical and corrosion requirements; disconnection requirements also involve the applicable shock-protection rules. IS 3043:2018 is the explicitly identified plate-formula baseline; BIS now lists IS 3043:2026. The new edition and its transition/adoption must be checked. BSI lists BS 7430:2026 as replacing BS 7430:2011+A1:2015; the strip calculation is a historical analytical approximation, not a claim of 2026 conformity.

IEEE 80-2013 including the 2015 corrigendum addresses AC substation grounding, with fault duration, current division, conductor duty and permissible step/touch potentials. IEEE lists it as inactive-reserved. Those safety studies are outside this calculator. No tables or figures of these standards are reproduced. Check against the standard in force and the network operator’s installation requirements.

The TT card checks only the rated-current resistance inequality, commonly associated with IEC 60364-4-41:2005+A1:2017 TT fault protection. It does not select an RCD or verify required operating time, waveform compatibility, additional protection, selectivity or failure of a protective conductor. RA × IΔn is not prospective fault touch voltage. A smaller local voltage limit or a separate electrode-resistance requirement can govern.