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Hydraulic Conductivity Calculator

Enter flow rate, area, and gradient to find aquifer hydraulic conductivity.

How it is calculated

The tool rearranges Darcy's law to solve for conductivity: K = Q ÷ (A × i). Q is the volume of water passing per day in cubic metres per day, A is the cross-sectional area the water flows through, in square metres, and i is the hydraulic gradient, the head loss divided by the flow distance, a ratio with no unit (0.02 means 2 m of head loss over 100 m). The result is shown in metres per day to four decimals and also in metres per second, found by dividing by 86,400 and written in scientific notation (1.3889e-3 means 1.3889 × 10−3). With no result shown, check that the area is above zero and the gradient is not zero. Flow and gradient are magnitudes: a negative flow, or a gradient of zero or below, gives no result.

Worked example

In a pumping test, 120 m³ of water passes per day through a cross-section of 50 m² under a gradient of 0.02. First multiply the area by the gradient: 50 × 0.02 = 1.0. Then K = 120 ÷ 1.0 = 120.0000 m/day. Dividing by the 86,400 seconds in a day gives 1.3889e-3 m/s, about 1.4 millimetres per second. That is a very permeable material such as clean gravel; clay would give a far smaller K.

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Common mistakes

  • Entering the gradient as a percentage or an angle. It is a plain ratio of head loss to distance, so a 2% slope is entered as 0.02.
  • Using the wrong area, such as the plan area of the site instead of the cross-section at right angles to the flow. A is the face the water flows through.
  • Mixing time units. The flow must be in cubic metres per day; a flow in litres per second needs converting first (1 L/s is 86.4 m³/day).
  • Typing the head loss in metres into the gradient field. Divide by the flow distance first, since the gradient is dimensionless.
  • Reading K as flow speed. K is a property of the material; the real groundwater velocity also depends on porosity.

About this calculator

Hydraulic conductivity (K) describes how easily groundwater moves through a saturated soil or rock formation. It follows Darcy's law, Q = K·A·i, where Q is the volumetric flow rate, A is the cross-sectional area the water flows through, and i is the hydraulic gradient (the head loss per unit distance). Rearranged, K = Q ÷ (A × i), so the calculator solves directly for K once you supply the other three measured quantities.

K values span many orders of magnitude — from under 10⁻⁹ m/s in clay to over 10⁻² m/s in gravel — and that spread is exactly what determines how fast a well recharges or a contaminant plume spreads. Hydrogeologists, environmental consultants, and water-well drillers use this calculation from pumping tests or permeameter data to size wells, model aquifer yield, and assess contamination risk.

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