Hydraulic conductivity calculator

How this calculator works

Measured saturated-flow tests usually provide a stronger basis than a grain-size correlation. Constant-head testing divides collected volume by time; falling-head testing integrates the declining head using the natural logarithm. Grain models assume granular material and should not be applied to clay or fractured rock. Kozeny-Carman here uses the ideal spherical-grain coefficient 1/180. Hazen exposes its empirical coefficient and is intended for clean uniform sand. Beyer uses base-10 logarithms. The USBR correlation is a fixed water-temperature calibration, roughly 10 C, without viscosity correction. Fluid defaults are rounded water properties near 20 C; replace them for other conditions.

Formula

Darcy K = Q/(Ai). Constant head K = VL/(Aht). Falling head K = aL ln(h1/h2)/(At). Intrinsic relation K = k rho g/mu. Kozeny-Carman K = (g/nu) d10^2 n^3/[180(1-n)^2]. Hazen K_cm/s = C(d10_cm)^2. Beyer K = (g/nu) 6e-4 log10(500/U) d10_m^2. USBR K_m/s = 0.0036(d20_mm)^2.3.

Worked example

Discharge 1e-5 m3/s through 0.01 m2 at gradient 0.1 gives K = 0.01 m/s. A constant-head test collecting 0.001 m3 in 100 s through the same area, with length 0.1 m and head 0.2 m, gives K = 0.0005 m/s.

Frequently asked questions

Does conductivity depend on temperature?

Yes. Viscosity changes strongly with temperature, so conductivity changes even if the pore structure does not.

Which logarithm does falling head use?

Use the natural logarithm. The Beyer empirical correlation instead uses base 10.

Are grain estimates laboratory measurements?

No. They are material-dependent estimates and may differ substantially from measured conductivity.

Sources

Written byAmira MansourCalculator writer. Builds and tests Mathulate calculators against published sources.

Reviewed byMarc LefebvreMathematics teacher. Checks each formula and worked example by hand.

Last updated November 1, 2026.