Tiza Group

Home / Tools / Grounding resistance

Grounding resistance

Estimate the resistance of a ground rod, a group of rods, a horizontal conductor or a substation grid from the soil resistivity, and get that resistivity from your Wenner readings.

BS 7430:2011+A1:2015rods and horizontal conductorsIEEE 80grid resistance (Sverak) and uniform soilIEEE 81resistivity by the Wenner method

Example cases
Grounding resistance
E1Soil
Ω·m
E2Electrode
m
mm

5/8 in = 15.9 mm.

m
m
m
mm

A 2/0 AWG copper cable is about 10.5 mm.

m
m
m

The grid always includes its perimeter: the resulting actual spacing is used.

m
m
E3Target and current
Ω
A

Both are optional. The target is the design value or the one your local code requires. IG gives the GPR: it is the part of the fault that the electrode discharges to remote earth, after the IEEE 80 split factor Sf, not the total fault.

E4Wenner readings
m
Ω
m
Ω
m
Ω
m
Ω
m
Ω
m
Ω
m

The preloaded readings are an example so the page shows a result. Enter yours: with b less than a/10, ρ = 2πaR is enough. Leave unused rows empty.

Use a decimal point. The calculation runs in your browser and updates as you type.

Estimated resistance

— Ω

Ground potential rise GPR

—

Buried length

— m

Wenner average ρ

— Ω·m

ρ (max + min) / 2

— Ω·m

Max / min variation

—

Resistance by electrode
  • Estimated resistance
  • Target
The curve sweeps the main electrode variable with the other data fixed; the dot is your case.
Wenner apparent resistivity
  • Measured ρa
  • Average
Spacing on a logarithmic scale. A flat curve indicates nearly uniform soil; if it rises or falls with spacing, the soil is layered.

Step-by-step calculation

What it means for your grounding system

    What it is for

    To estimate, before detailed design, how many rods or how much conductor a plant or substation grounding system needs, and to interpret resistivity readings in the field: whether the soil looks uniform or changes with depth. It also helps judge whether a resistance measured with the fall-of-potential test is reasonable for the installed electrode.

    How it is calculated

    BS 7430:2011+A1:2015single rod (Dwight)

    R = ρ / (2πL) · (ln(8L/d) − 1)

    It is the same expression as in the 1998 edition of BS 7430 (10.2).

    BS 7430:2011+A1:2015rods in parallel

    Rn = R · (1 + λα) / n · α = ρ / (2π · R · s)

    R is the resistance of a single rod, s the spacing and n the total number of rods. λ depends on the arrangement:

    Arrangementnλ
    In a line2 to 10 rods1.00 · 1.66 · 2.15 · 2.54 · 2.87 · 3.15 · 3.39 · 3.61 · 3.81
    Hollow square2 to 10, 12, 14, 16, 18, 20 per side2.71 · 4.51 · 5.48 · 6.14 · 6.63 · 7.03 · 7.36 · 7.65 · 7.90 · 8.32 · 8.67 · 8.96 · 9.22 · 9.40

    In the hollow square the total number of rods is 4 · (n − 1). The standard assumes the spacing is at least equal to the rod length, and allows λ = 1.66 for three rods in a triangle or an L. The λ values are those of tables 2 and 3 of the 1998 edition.

    BS 7430:2011+A1:2015straight horizontal conductor

    R = ρ / (PπL) · (ln(2L² / (w · h)) + Q)

    With P = 2 for a single run and Q = −1 for a flat strip or −1.3 for a round conductor (1998 edition, 10.3); w is the width or diameter and h the depth, both in meters. For the round conductor, Q = −1.3 is the ln 2 − 2 of Dwight's formula as given in IEEE Std 142.

    IEEE 80Sverak equation

    Rg = ρ · [1/LT + 1/√(20A) · (1 + 1 / (1 + h · √(20/A)))]

    LT is the total buried length (conductors plus rods), A the grid area and h its depth, valid from 0.25 to 2.5 m. A rectangular grid always has its perimeter conductors: each direction has ⌈side/D⌉ + 1 conductors and the actual spacing is side / ⌈side/D⌉, never larger than requested.

    IEEE 80ground potential rise

    GPR = IG · R

    IG is the grid current: the part of the fault current 3I0 that the electrode discharges to remote earth after the split factor Sf, not the total fault current. Part of it returns through shield wires and cable sheaths.

    IEEE 81Wenner methodIEEE 80uniform soil

    ρa = 4πaR / (1 + 2a/√(a² + 4b²) − a/√(a² + b²))

    It reduces to ρa = 2πaR when b is small compared with a. For a uniform soil model, IEEE 80 suggests taking the average of the apparent resistivities or half the sum of the maximum and minimum. The tool raises an alert when the maximum exceeds 1.5 times the minimum: it is our own criterion to suggest a layered model, not a limit from a standard.

    Limits of the calculation

    • These are uniform-soil estimates, not a design. Real soil is almost never uniform: moisture, layers and season change the result.
    • A substation grid is designed with a two or more layer model and with the IEEE 80 step and touch voltages, which this tool does not calculate.
    • The formulas do not account for the conductor joining the rods or the interaction between the grid and other nearby electrodes.
    • They do not check compliance with the local code.
    • The actual resistance is verified with a ground resistance test after construction.

    Frequently asked questions

    How is the ground resistance of a rod calculated?

    With Dwight's formula, as given in BS 7430: R = ρ / (2πL) · (ln(8L/d) − 1), where ρ is the soil resistivity, L the buried length and d the rod diameter. A 2.4 m, 5/8 inch rod in 100 Ω·m soil gives about 40 Ω. Length matters far more than diameter.

    How many ground rods do I need?

    It depends on the resistivity and on the resistance the design requires. Several rods in parallel lower the resistance, but not in proportion to their number, because they interact; BS 7430 corrects that effect with a factor for each arrangement, provided the spacing is at least equal to the rod length. In high-resistivity soil a long horizontal conductor or a grid is usually the better option.

    How is soil resistivity calculated with the Wenner method?

    Four electrodes are driven in line with equal spacing a, current is injected through the outer pair and the voltage is measured between the inner pair. If the electrodes are shallow compared with the spacing, the apparent resistivity is ρ = 2π · a · R (IEEE 81). Measuring at several spacings shows how it changes with depth; if it changes a lot, the soil is not uniform and a layered model is needed.

    We design and measure your grounding system

    We design your substation grid or plant grounding system with a soil model and step and touch voltages. Soil resistivity and installed-system resistance measurements are done in Colombia, or elsewhere on request.

    See design and studiesContact us

    Other tools

    COMTRADE generatorCreate a COMTRADE fault record (.cfg/.dat or .cff) for your test set: fault, DC offset and breaker opening.ANSI / IEEE C37.2 device numbersDevice function numbers 1 to 94, common suffixes and their IEC 61850 logical node, with search.Relay coordinationUp to six relays, reclosers and fuses on a log-log plot, with the IEEE C57.109 damage curve, inrush and the coordination margin of each pair.Inverse-time curvesCalculator and log-log plot of the IEC 60255-151 and IEEE C37.112 curves, with the coordination margin.CT burdenLead resistance, relay burden and comparison with the rated burden of the current transformer.Short-circuit currentQuick estimate of the three-phase fault at the secondary of a transformer.COMTRADE viewerOpen .cfg/.dat or .cff fault records in your browser: waveforms, digital channels, cursor and RMS. The file is not uploaded.IEC 61850 SCL viewerOpen .scd, .cid or .icd files in your browser: IEDs, GOOSE and SV addresses, datasets, subscribers and checks. The file is not uploaded.GOOSE and SV addressesCheck IEC 61850 multicast MAC, APPID, VLAN and priority, find duplicates and export the table as CSV.Process bus networkSV and GOOSE bandwidth, worst-case latency, PRP, HSR or RSTP redundancy and PTP time error of an IEC 61850 network.Interlocking table and CILO equationsInterlocking matrix per device, IEC 61850 EnaOpn and EnaCls equations, GOOSE signals between bays and FAT/SAT test cases per configuration.Per-unit base conversionBase current and impedance, conversion between %, pu and ohms, and change of base for transformers, generators and lines.Harmonic distortion THD and TDDVoltage THD and current TDD against the IEEE 519-2022 limits, with the spectrum as a bar chart.Symmetrical componentsPhase quantities to zero, positive and negative sequence and back (Fortescue), with phasor diagrams and what they mean for 46, 67Q and 51N.Vector group compensation (87T)TAP of each winding, phase compensation matrix, zero-sequence removal and the HV-to-LV clock diagram.Primary and secondary impedance (21)Primary to secondary ohms with the CT and VT ratios, line Z1, Z0 and k0, and zone reaches on the R-X plane.CT saturationRequired versus available voltage (5P/10P, PX or C class), time to saturation and the saturated waveform.DGA interpretationIEEE C57.104-2019 DGA status, Duval triangles 1, 4 and 5, IEC 60599 ratios and CO₂/CO of your transformer.Insulation temperature correctionInsulation resistance at 40 °C (IEEE 43) or 20 °C, PI, DAR and power factor of transformers and bushings, with the trend.Capacitor bankkvar to correct the power factor, steps of the automatic bank, capacitance and resonance with the transformer.Cable voltage dropΔV and % with R and X per km, copper or aluminium, mm² or AWG/kcmil, and the short-circuit check of the cable size.Battery sizingAh, number of cells and charger of a DC battery bank from its duty cycle, per IEEE 485 and IEEE 1115.Technical glossarySubstation, protection and communications terms, explained in one or two sentences.
    WhatsApp