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)
Spreading resistance of a hemispherical earth electrode
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 Spreading resistance of a hemispherical earth electrode
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.