Soil Resistivity — Wenner Apparent Resistivity

What this calculation gives you

Convert the measured resistance and equal electrode spacing from a valid four-pin Wenner test into apparent soil resistivity. The field resistance reading is an input; it is not itself soil resistivity.

Governing equation(s)

For four collinear, equally spaced pins with outer current electrodes and inner potential electrodes:

ρa = 2πaR

If potential and current are measured separately: R = V/I, so ρa = 2πa(V/I).

For spacing in feet and output in Ω·cm: ρa(Ω·cm) = 191.5 × aft × RΩ.

Variables

Units

• If a is in centimetres and R is in ohms, ρa is in Ω·cm.
• If a is in metres and R is in ohms, ρa is in Ω·m.
• If spacing is in feet and output is Ω·cm, use the controlled 191.5 form.
• 1 Ω·m = 100 Ω·cm.

The formula constant never removes the need to identify the input length unit and output resistivity unit.

Conditions and assumptions

• Four collinear, equally spaced electrodes are used, with outer current and inner potential electrodes.
• The basic 2πaR relationship uses the authorized equal-spacing Wenner geometry and standard shallow-electrode approximation.
• The input resistance comes from a valid field measurement; this calculation does not validate the field test.
• Nearby parallel metallic structures, poor connections/contact, inadequate sensitivity, or electrode polarization can invalidate or distort measurements.
• The complete field procedure remains a conditional Method and is not published by this Calculation.

Worked calculation

Given: equal pin spacing a = 5 ft; measured resistance R = 10 Ω.

ρa(Ω·cm) = 191.5 × 5 × 10

ρa = 9,575 Ω·cm

Equivalent metric resistivity: 9,575 Ω·cm ÷ 100 = 95.75 Ω·m.

Result: 9,575 Ω·cm = 95.75 Ω·m

Interpretation

This is the apparent resistivity associated with the valid Wenner geometry and spacing. In nonuniform soil it is a weighted subsurface response; it is not necessarily the resistivity of a discrete layer at 5 ft depth. No universal corrosivity class or CP design rule is assigned from this value.

Limitations

The basic form is not valid for arbitrary four-electrode geometry. Pin spacing must not be relabeled as literal measurement depth. One spacing does not establish a complete layered-earth model. Barnes layer analysis is blocked as a governing Corrosion Authority calculation/tool under current authority and is not implemented here. Soil resistivity is also distinct from groundbed or anode resistance.

Common mistakes

• Reporting measured resistance in Ω as though it were resistivity.
• Entering spacing in feet into the direct 2πaR form and labeling the result Ω·cm without conversion.
• Using the 191.5 form with spacing in metres.
• Treating Ω·cm and Ω·m as interchangeable.
• Treating pin spacing as literal depth.
• Treating one apparent-resistivity value as a discrete layer value or universal corrosivity classification.
• Assuming the calculated result proves field-measurement quality.
• Treating soil resistivity as equivalent to groundbed/anode resistance.

Technical visuals

Next action

Preserve each spacing/resistance/result pair when measurements are made at multiple spacings. If resistivity changes substantially with spacing, route the data to controlled layered-earth interpretation rather than forcing a Barnes result. If the field geometry does not meet the Wenner assumptions, this basic calculation is non-applicable.