Calculation
RA = ρ / (2π·r)
Spreading resistance falls with larger electrode radius and rises with the soil's specific resistivity.
Halbkugelerder-Modell RA = ρ/(2π·r); Erdungstechnik-Literatur (Wikipedia Erdungswiderstand, Elektropraktiker)
Earth Electrode Resistance Calculator (Hemisphere)
Spreading resistance falls with larger electrode radius and rises with the soil's specific resistivity.
MINTSI
02
Result
Select a target and calculate.
Understand the inputs
- Spreading resistance RA — Resistance between the electrode and the so-called reference earth far away.
- Soil resistivity ρ — Soil property; depends on soil type and moisture, commonly 50 to 500 Ω·m.
- Hemisphere radius r — Radius of the earth electrode idealised as a hemisphere.
Example
ρ=100 Ω·m and r=0.5 m give RA≈31.83 Ω.
Assumptions and limits
Ideal hemispherical electrode in homogeneous, isotropic soil with no layering; real electrodes (rod, ring earth), soil stratification and seasonal moisture variation are excluded.
Understand Earth Electrode Resistance Calculator (Hemisphere)
This calculator estimates the spreading resistance of an earth electrode simplified as a hemisphere in homogeneous soil, a classic basic model of earthing engineering.
What does this quantity describe?
For a hemispherical electrode of radius r in soil with resistivity ρ, RA=ρ/(2π·r). The resistance arises from current spreading out from the electrode surface into the surrounding soil.
Formula and variables
RA = ρ / (2π·r)
RA = ρ / (2π·r)
| Symbol / input | Meaning |
|---|---|
| Spreading resistance RA | Resistance between the electrode and the so-called reference earth far away. |
| Soil resistivity ρ | Soil property; depends on soil type and moisture, commonly 50 to 500 Ω·m. |
| Hemisphere radius r | Radius of the earth electrode idealised as a hemisphere. |
Choose the inputs correctly
ρ is the soil's specific resistivity at the site, r the radius of the electrode idealised as a hemisphere.
How to use the calculator
Take ρ from a soil measurement or from experience values for the soil type present; derive r from the actual or a comparable equivalent electrode.
Worked example
ρ=100 Ω·m and r=0.5 m give RA≈31.83 Ω.
Understand the result and units
A larger electrode radius or lower soil moisture (higher ρ when dry) change spreading resistance in opposite directions.
ρ is a resistivity (Ω·m), r a length. RA is output as a resistance.
Typical applications
Rough first estimation of earthing resistance in electrical installation work, and as a teaching basic model before considering rod, ring or foundation earth electrodes.
Assumptions, limits and common mistakes
Ideal hemispherical electrode in homogeneous, isotropic soil with no layering; real electrode shapes, soil stratification, frost and seasonal moisture variation are excluded.
Common mistake: Do not confuse ρ with the specific resistance of metallic conductors; soil values are many orders of magnitude higher.
Frequently asked questions
What is “Spreading resistance of a hemispherical earth electrode” used for?
Rough first estimation of earthing resistance in electrical installation work, and as a teaching basic model before considering rod, ring or foundation earth electrodes.
Where do the input values come from?
ρ is the soil's specific resistivity at the site, r the radius of the electrode idealised as a hemisphere.
What does the result not cover?
Ideal hemispherical electrode in homogeneous, isotropic soil with no layering; real electrode shapes, soil stratification, frost and seasonal moisture variation are excluded.