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# The Mathematical Formula for Calculating Earth Resistance

What is the mathematical formula for calculating the resistance-to-ground of parallel electrodes?

The simplified calculation for predicting the resistance-to-ground (earth) of a given length grounding rod is:

R=(p/(2*pi*L))*(ln*(4L/a)-1)) + (p/(2*pi*s))*(1-(L squared/3s(10X8)) + (2L(10×4)/5s(10×4)…)

Where:

• R= Resistance
• p= soil resistivity
• L = Length of the rod
• a= radius of the rod
• ln= natural log
• s = rod spacing

The above is the hand formula, however it does not take into account multi-layered soils.  We highly recommend using a computer program such as CDEGS.

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