Sizing an earth electrode — the calculation formulas for rod and plate electrodes

The guides on measuring earthing resistance and the Wenner four-point method for soil resistivity cover how the earthing resistance of an existing electrode, or the soil resistivity on site, is measured. This article covers the reverse, preceding step: how the dimensions of an electrode still to be installed are approximately calculated, starting from a known or estimated soil resistivity.

Why this is an approximation, not a normative formula

IEC 60364-5-54 (on which NEN 1010 §542 is based) describes the requirements for earth electrodes qualitatively (type, minimum dimensions, corrosion and mechanical protection) and refers to on-site measurement for the actual resistance value, not to one prescribed calculation formula. In technical practice and literature (based among other things on classical electrode theory, as also applied in related standards such as BS 7430), commonly used approximation formulas are nevertheless applied to make a first-order estimate of the required electrode dimensions in advance.

Rod electrode

For a vertical rod driven into the ground, the approximation is:

R ≈ ρ / (2πL) × ln(4L / d)

ρ is the soil resistivity (Ω·m), determined via a measurement such as the Wenner four-point method.
L is the length of the rod in the ground (m).
d is the diameter of the rod (m).
R is the resulting earthing resistance (Ω).

Because the length L appears both inside the logarithm and in the denominator, the resistance drops sharply at first as the rod is driven deeper, but that reduction gradually flattens out at greater lengths — a second rod placed in parallel at a sufficient distance from the first often gives a more effective resistance reduction than driving one rod much deeper.

Plate electrode

For a horizontally buried plate electrode, the approximation is:

R ≈ ρ / (4√A)

A is the area of the plate (m²), measured on one side.
The other quantities are as above.

Why the soil resistivity (ρ) is the dominant uncertainty

In both formulas, the earthing resistance is directly proportional to the soil resistivity ρ, which can vary considerably — not only between different soil types (clay, sand, peat, rock), but also seasonally at the same location (moisture content, frost). A calculation based on an assumed or one-off measured ρ value therefore gives a first-order estimate, not a guaranteed final value; the actually measured earthing resistance of the installed electrode (see the guide on earthing resistance measurement and the clamp-on method) therefore always remains decisive, regardless of what the pre-calculated value suggested.

Note: this article covers the calculation formulas as a first-order design indication based on classical electrode theory. For the normative requirements on the type, minimum dimensions and mechanical/corrosion protection of an earth electrode, the full text of NEN 1010 §542 and IEC 60364-5-54 is decisive.

Practical relevance

When designing a new earthing arrangement — for example for a TT system where the earth electrode directly co-determines the required RCD disconnection time (see the guide on the TT system) — a calculation made in advance with an estimated or previously measured ρ value gives an indication of the required number and length of rod electrodes. This estimate must always be confirmed after installation with an actual measurement, and supplemented with additional electrodes if it deviates (for example due to local soil heterogeneity).

Common mistakes

Treating the calculated resistance as the final value without carrying out an actual measurement after installation — local soil variation can make the real value deviate considerably from the calculation.
Using a single ρ measurement taken at one point in time for the final design, without accounting for seasonal variation (a dry summer soil typically gives a higher ρ than the same soil in a wet winter).
Only increasing the rod length when the calculated resistance is too high, while several parallel rods placed at a sufficient distance from each other often give a more effective and practical solution than one very long rod.
Applying the formulas as if they were a normative requirement from IEC 60364-5-54, when they are classical, widely used approximation formulas in engineering practice — the standard itself does not mandate a calculation formula and refers to measurement instead.