Ground resistance, , abbreviated as \(GR\), also called earth resistance, is the resistance encountered by electric current as it flows from a grounding electrode or grounding system into the surrounding earth and ultimately to remote earth, typically a ground electrode such as a rod, plate, or grid, and the surrounding earth. It is specifically the resistance between the grounding electrode under test and a theoretical remote grounding electrode of zero impedance located at an infinite distance, where remote earth is assumed to be at zero potential. This value is determined as the ratio of the voltage rise at the electrode to the current injected into the earth during measurement, reflecting the total opposition to current dissipation provided by the soil path.
Ground Resistance Formula |
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\( R \;=\; \dfrac{ \rho }{ 2 \cdot \pi \cdot L } \cdot \left( ln \dfrac{ 4 \cdot L }{ a } -1 \right) \) (1 Ground Rod) \( R \;=\; \dfrac{ \rho }{ 4 \cdot \pi \cdot L } \cdot \left( ln \dfrac{ 4 \cdot L }{ a } -1 \right) + \dfrac{ \rho }{ 4 \cdot \pi \cdot S } \cdot \left( 1 - \dfrac{ L^2 }{ 3 \cdot S^2 } + \dfrac{ 2 \cdot L^4 }{ 5 \cdot S^2 } ... \right) \) (2 Ground Rods) \( R \;=\; \dfrac{ \rho }{ 4 \cdot \pi \cdot L } \cdot \left( ln \dfrac{ 4 \cdot L }{ a } + ln \dfrac{ 4 \cdot L }{ S } -2 + \dfrac{ S }{ 2 \cdot L } - \dfrac{ S^2 }{ 16 \cdot L^2 } + \dfrac{ S^4 }{ 512 \cdot L^2 } ... \right) \) (Buried Horizontal Wire) Length\(\;L = 2 \cdot L\), Depth\(\;S= \dfrac{S}{2}\) \( R \;=\; \dfrac{ \rho }{ 4 \cdot \pi \cdot L } \cdot \left( ln \dfrac{ 2 \cdot L }{ a } + ln \dfrac{ 2 \cdot L }{ S } - 0.2373 + 0.2146 \cdot \dfrac{ S }{ L } + 0.1035 \cdot \dfrac{ S^2 }{ L^2 } - 0.0424 \cdot \dfrac{ S^4 }{ L^4 } ... \right) \) (Right Angle Turn of Wire) Length of Arm\(\;L = 2 \cdot L\), Depth\(\;S= \dfrac{S}{2}\) \( R \;=\; \dfrac{ \rho }{ 6 \cdot \pi \cdot L } \cdot \left( ln \dfrac{ 2 \cdot L }{ a } + ln \dfrac{ 2 \cdot L }{ S } + 1.071 - 0.209 \cdot \dfrac{ S }{ L } + 0.238 \cdot \dfrac{ S^2 }{ L^2 } - 0.054 \cdot \dfrac{ S^4 }{ L^4 } ... \right) \) (Three Point Star) Length of Arm\(\;L\), Depth\(\;S= \dfrac{S}{2}\) \( R \;=\; \dfrac{ \rho }{ 8 \cdot \pi \cdot L } \cdot \left( ln \dfrac{ 2 \cdot L }{ a } + ln \dfrac{ 2 \cdot L }{ S } + 2.912 - 1.071 \cdot \dfrac{ S }{ L } + 0.645 \cdot \dfrac{ S^2 }{ L^2 } - 0.145 \cdot \dfrac{ S^4 }{ L^4 } ... \right) \) (Four Point Star) Length of Arm\(\;L\), Depth\(\;S= \dfrac{S}{2}\) \( R \;=\; \dfrac{ \rho }{ 126 \cdot \pi \cdot L } \cdot \left( ln \dfrac{ 2 \cdot L }{ a } + ln \dfrac{ 2 \cdot L }{ S } + 6.851 - 3.128 \cdot \dfrac{ S }{ L } + 1.758 \cdot \dfrac{ S^2 }{ L^2 } - 0.490 \cdot \dfrac{ S^4 }{ L^4 } ... \right) \) (Six Point Star) Length of Arm\(\;L\), Depth\(\;S= \dfrac{S}{2}\) \( R \;=\; \dfrac{ \rho }{ 16 \cdot \pi \cdot L } \cdot \left( ln \dfrac{ 2 \cdot L }{ a } + ln \dfrac{ 2 \cdot L }{ S } + 10.98 - 5.51 \cdot \dfrac{ S }{ L } + 3.26 \cdot \dfrac{ S^2 }{ L^2 } - 1.17 \cdot \dfrac{ S^4 }{ L^4 } ... \right) \) (Eight Point Star) Length of Arm\(\;L\), Depth\(\;S= \dfrac{S}{2}\) \( R \;=\; \dfrac{ \rho }{ 16 \cdot \pi^2 \cdot D } \cdot \left( ln \dfrac{ 8 \cdot D }{ d } + ln \dfrac{ 4 \cdot D }{ S } \right) \) (Ring of Wire) Depth\(\;S= \dfrac{S}{2}\) \( R \;=\; \dfrac{ \rho }{ 8 \cdot a } + \dfrac{ \rho }{ 4 \cdot \pi \cdot S } \cdot \left( 1 - \dfrac{ 7 \cdot a^2 }{ 12 \cdot S^2 } + \dfrac{ 33 \cdot a^2 }{ 40 \cdot S^4 } \right) \) (Horizontal Buried Round Plate) Depth\(\;S= \dfrac{S}{2}\) \( R \;=\; \dfrac{ \rho }{ 8 \cdot a } + \dfrac{ \rho }{ 4 \cdot \pi \cdot S } \cdot \left( 1 - \dfrac{ 7 \cdot a^2 }{ 24 \cdot S^2 } + \dfrac{ 99 \cdot a^2 }{ 320 \cdot S^4 } \right) \) (Vertical Buried Round Plate) Depth\(\;S= \dfrac{S}{2}\) |
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| Symbol | English | Metric |
| \( R \) = Ground Resistance | \(\Omega\) | \(\Omega\) |
| \( \rho \) (Greek symbol rho) = Resistivity | \(\Omega-in\) | \(\Omega-m\) |
| \(\large{ \pi }\) = Pi | \(3.141 592 653 ...\) | \(3.141 592 653 ...\) |
| \( L \) = Length | \(in\) | \(mm\) |
| \( a \) = Radius | \(in\) | \(mm\) |
| \( d \) = distance | \(in\) | \(mm\) |
| \( S \) = Space Between Ground Rods | \(in\) | \(mm\) |
| \( D \) = Diameter of Ring | \(in\) | \(mm\) |
Basically, it represents the opposition encountered by fault current, lightning current, or leakage current as it flows from the grounded system into the earth mass. This resistance is not confined to the metal electrode itself, rather it is dominated by the resistivity of the soil in the immediate vicinity of the electrode, especially within a region extending outward from the electrode surface where current density is highest.
Physically, ground resistance arises primarily from the resistivity of the soil volume through which the current spreads radially outward from the electrode surface, along with minor contributions from electrode material resistance and electrode-to-soil contact resistance. Soil resistivity itself, expressed in ohm-meters, varies with factors such as moisture content, temperature, and mineral composition, but the overall ground resistance depends on electrode geometry, burial depth, and the effective area over which current disperses into the earth. Measurement methods, such as the fall-of-potential technique, isolate this value under controlled test conditions to confirm compliance with safety criteria, ensuring the grounding system functions as intended across a range of operating and fault scenarios.
