Electrical Resistivity of Earth Layers Calculator
Find apparent ground resistivity from a Wenner four-electrode survey reading, with a plain-language soil/rock classification note.
⚡ What is Electrical Resistivity of Earth Layers?
Electrical resistivity surveying is a geophysical prospecting method that measures how strongly the ground resists the flow of electrical current, then uses that measurement to infer what lies beneath the surface. The most common field layout is the Wenner array, four equally spaced electrodes driven into the ground in a straight line, with current injected through the outer two and voltage measured across the inner two. This calculator applies the standard Wenner formula, rho_a = 2*pi*a*(V/I), to turn a field reading into an apparent resistivity value in ohm-meters (Ω·m).
Hydrogeologists use resistivity surveys to locate groundwater aquifers and map their depth and extent before drilling a well, since saturated, porous ground typically reads a distinctly lower resistivity than dry ground above it. Geotechnical and civil engineers use it to estimate bedrock depth ahead of foundation design, since bedrock almost always reads far more resistive than the overlying soil. Environmental consultants use resistivity mapping to trace contamination plumes and landfill boundaries, since many contaminants change the ground's ionic content and therefore its resistivity. Archaeologists use small-scale resistivity grids to detect buried walls, foundations, and ditches that contrast electrically with the surrounding, undisturbed soil.
A common point of confusion is treating the calculated result as the exact resistivity at the electrode spacing's depth. It is not. The formula returns apparent resistivity, the resistivity a single uniform half-space of ground would need to have to produce the same voltage and current reading. Real ground is layered, and the current from a single reading passes through a broad, roughly hemispherical volume that touches multiple layers at once, so apparent resistivity is really a depth-weighted blend, not a sharp reading at one exact depth.
This calculator is useful because it does the geometric-factor arithmetic instantly and consistently, converts realistic millivolt and milliamp field readings without manual unit juggling, and adds a plain-language classification note comparing the result against typical published resistivity ranges for common earth materials, giving a fast first-pass read on whether a site looks clay-like, sand-like, or rock-like before any formal interpretation begins.
📐 Formula
ρa is directly proportional to both a (at fixed V/I) and to the ratio V/I (at fixed a), a single multiplication with no curve, threshold, or fold in either relationship, so this page does not include a chart, per the same reasoning used for other single-multiplication relationships on this site: a straight-line "vs" plot adds no shape a reader couldn't already see from the formula itself.
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 — Typical Silty/Clay Soil Survey
a = 10 m, V = 50 mV, I = 100 mA
Example 2 — Sand and Gravel Deposit
a = 20 m, V = 150 mV, I = 30 mA
Example 3 — Crystalline Bedrock
a = 10 m, V = 800 mV, I = 5 mA
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Wenner array formula for apparent resistivity?
Apparent resistivity is rho_a = 2*pi*a*(V/I), where a is the equal spacing between the four electrodes in meters, V is the voltage measured between the inner two electrodes in volts, and I is the current injected between the outer two electrodes in amps. The result comes out in ohm-meters (Ω·m).
Why is it called apparent resistivity instead of true resistivity?
Apparent resistivity is the resistivity a single, perfectly uniform half-space of ground would need to have to produce the exact same voltage and current reading. Real ground is layered and heterogeneous, so the true resistivity varies with depth and position, apparent resistivity is only a weighted average of whatever the current path actually crossed.
What do the inputs a, V, and I represent in a Wenner survey?
a is the equal spacing between all four electrodes, laid out in a straight line. Current I is injected into the ground through the two outer electrodes, and the resulting voltage V is measured between the two inner electrodes. All three values are read directly off field survey equipment.
How deep does a Wenner array actually probe?
As a rough rule of thumb, a Wenner array's effective investigation depth is on the order of the electrode spacing a itself, so a 10-meter spacing samples roughly the top 10 meters of ground. This is only an approximation since the current actually flows through a broad, roughly hemispherical volume beneath the array, not a sharp depth cutoff.
What is a typical resistivity value for clay compared to sand or bedrock?
Clay and wet, silty soil typically read roughly 1 to 100 Ω·m, sand, gravel, and dry sandy soil typically read roughly 100 to 1000 Ω·m, and unfractured crystalline bedrock typically reads 1000 Ω·m or higher, sometimes far higher when very dry. These ranges overlap in practice and should be treated as illustrative, not definitive.
Why is the geometric factor 2*pi*a used in the Wenner configuration?
The 2*pi*a factor, formally called the geometric factor, converts a raw voltage-over-current reading into a resistivity value by accounting for how current spreads out from a point electrode into the ground. It comes from solving the current-flow equations for four equally spaced, collinear electrodes on a uniform half-space, and it changes for other electrode layouts like the Schlumberger or dipole-dipole arrays.
Can apparent resistivity alone tell me exactly what material is underground?
No, not with certainty. Apparent resistivity narrows down the likely material family (clay-like, sand-like, or rock-like) using typical published ranges, but many other factors, including moisture content, salinity, porosity, and mineral composition, can shift a material's real resistivity well outside its typical range. Full interpretation needs geological context and, often, a calibration borehole.
What is the difference between resistivity and conductivity in this context?
Resistivity (Ω·m) and conductivity (siemens per meter) are reciprocals of each other, conductivity = 1/resistivity. Geophysicists commonly report the same underlying property as either resistivity or conductivity depending on the survey method and target, this calculator reports resistivity, the more common convention for Wenner DC resistivity surveys.
Why does wet soil have lower resistivity than dry soil?
Electrical current in soil and rock mostly flows through the water and dissolved ions filling the pore spaces, not through the dry mineral grains themselves. More water and more dissolved salts mean more available charge carriers, so wetter, more saline ground conducts better and reads a lower resistivity.
What is electrical resistivity surveying used for in practice?
Common applications include locating groundwater aquifers and estimating their depth, mapping bedrock depth for foundation and geotechnical engineering, detecting buried utilities, voids, or contamination plumes, and archaeological prospecting for buried structures or features that contrast electrically with surrounding soil.
Are there other electrode configurations besides the Wenner array?
Yes. The Schlumberger array keeps the current electrodes wide and the voltage electrodes close together near the center, the dipole-dipole array separates the current and voltage electrode pairs entirely, and each layout has its own geometric factor and trade-offs in depth sensitivity, noise resistance, and field logistics. The Wenner array is popular for its simple equal-spacing geometric factor and strong signal.
Do I need more than one reading to profile resistivity with depth?
Yes. A single Wenner reading at one spacing gives only a single apparent-resistivity number representative of roughly that depth scale. Real vertical resistivity profiling requires a sounding, repeating the measurement at a range of increasing electrode spacings, then running the resulting curve through an inversion model to estimate true layer resistivities and thicknesses.