Hydraulic Conductivity Calculator
Calculate the hydraulic conductivity of a soil or porous medium using five established methods. Choose between laboratory permeameter tests (Constant Head, Falling Head), grain-size empirical equations (Kozeny-Carman, Hazen, USBR), and switch the output unit between m/s, m/day, cm/s, and ft/day. Every step of the math is shown below the result.
Formula
Worked example
Constant Head example: Q = 2.5e-5 m3/s, A = 0.005 m2, L = 0.1 m, head loss = 0.05 m. Gradient i = 0.05/0.1 = 0.5. K = 2.5e-5 / (0.5 x 0.005) = 1.0e-2 m/s, typical of coarse sand or gravel.
What is hydraulic conductivity?
Hydraulic conductivity (K) is a measure of how easily water can move through a porous medium such as soil, sand, or rock. It appears in Darcy's Law as the constant of proportionality between the Darcy flux (volumetric flow rate per unit area) and the hydraulic gradient (head loss per unit length). K depends on both the properties of the medium (pore size, tortuosity, connectivity) and of the fluid (viscosity, density). For water at 20 degC, K ranges from around 10^-11 m/s in dense clay to over 10^-1 m/s in clean gravel. Engineers and hydrogeologists use K to design drainage systems, model groundwater flow, assess contaminant transport, and size dewatering pumps.
Which method should I use?
The right method depends on what data you have. If you have a soil sample in a permeameter, use the Constant Head method for sands and gravels (it is fast and accurate for high-K material) or the Falling Head method for silts and fine sands where the constant head cannot be maintained long enough. If you only have a grain-size curve from a sieve analysis, empirical equations are your best option: the Kozeny-Carman equation is the most general and works for sands and gravels (d10 below 3 mm); the Hazen equation is well-established for well-sorted medium sands (d10 0.1 to 3 mm, uniformity coefficient below 5); and the USBR equation is a simpler alternative for fine sands. All empirical methods can be off by a factor of two to five even for clean sands, and should not be used for silts, clays, or poorly sorted soils.
How temperature affects the result
Water viscosity decreases by roughly 2 percent per degC, so K increases with temperature. At 10 degC the kinematic viscosity is about 1.31e-6 m2/s, while at 25 degC it falls to about 0.89e-6 m2/s, a difference of nearly 50 percent. For the grain-size methods this calculator applies the temperature correction automatically by computing the viscosity at your entered temperature and scaling accordingly. For the laboratory methods (Constant Head and Falling Head), the temperature of the permeant water during the test should be recorded, and if necessary, the measured K should be corrected to the standard reference temperature of 20 degC using K_20 = K_T x (nu_T / nu_20).
Intrinsic permeability and the link to K
Hydraulic conductivity is a fluid-dependent property. The fluid-independent equivalent is intrinsic permeability (k, SI unit m2), related to K by k = K x (mu / (rho x g)) where mu is dynamic viscosity and rho is fluid density. For water at 20 degC this gives k (m2) = K (m/s) x 1.02e-7. Intrinsic permeability is useful when comparing results across different fluids (oil and gas engineering) or temperatures, or when converting between laboratory results (usually water) and field conditions involving a different fluid.
Typical hydraulic conductivity values by soil type
| Soil / Material | K (m/s) | K (m/day) | Drainage class |
|---|---|---|---|
| Gravel | 10⁻¹ to 10¹ | 8,640 to 864,000 | Very well drained |
| Coarse sand | 10⁻⁴ to 10⁻² | 0.86 to 86 | Well drained |
| Medium sand | 10⁻⁵ to 10⁻³ | 0.086 to 8.6 | Well drained |
| Fine sand | 10⁻⁶ to 10⁻⁴ | 0.0086 to 0.86 | Moderately drained |
| Silt | 10⁻⁷ to 10⁻⁵ | 8.6e-4 to 0.086 | Poorly drained |
| Silty clay | 10⁻⁹ to 10⁻⁶ | 8.6e-5 to 8.6e-3 | Very poorly drained |
| Clay | 10⁻¹¹ to 10⁻⁹ | <8.6e-5 | Impermeable |
| Fractured rock | 10⁻⁷ to 10⁻³ | 8.6e-4 to 86 | Highly variable |
| Unfractured rock | <10⁻¹¹ | <8.6e-7 | Impermeable |
Order-of-magnitude ranges from Fetter, Applied Hydrogeology (2001) and Freeze & Cherry (1979). Use these to sense-check computed results.
Frequently asked questions
What is a typical hydraulic conductivity for sand?
Clean, coarse sand typically has K values of 10^-4 to 10^-2 m/s (roughly 0.9 to 900 m/day). Fine sand falls lower, around 10^-6 to 10^-4 m/s. The wide range reflects variations in grain size distribution, sorting, and compaction. Always cross-check a measured K value against the reference table for the soil type.
What is the difference between the Constant Head and Falling Head methods?
In a Constant Head test, water flows through the sample under a fixed head difference maintained throughout the test, and K is computed from the steady-state flow rate. In a Falling Head test, no flow is maintained externally; instead, water drains from a standpipe through the sample and the rate at which the head falls is recorded. The Falling Head method is preferred for fine-grained, low-permeability soils where maintaining a constant head is impractical, while the Constant Head method is faster and more straightforward for coarser material.
When should I use the Kozeny-Carman vs Hazen equation?
The Kozeny-Carman equation is more physically based and performs better across a wider range of grain sizes, provided d10 is below 3 mm and the soil is reasonably clean and well-sorted. The Hazen equation is simpler and widely used for medium sands (d10 of 0.1 to 3 mm, uniformity coefficient below 5). In practice, the two equations give similar results for medium sands under those conditions. Neither should be used for clays, silts, or poorly graded soils.
How do I estimate porosity for the grain-size methods?
Porosity depends on particle shape and packing. Loose, uniform sands have porosities of about 0.40 to 0.50; dense, well-graded sands are closer to 0.25 to 0.35; gravels are typically 0.25 to 0.40. You can measure porosity directly from undisturbed core samples (bulk density vs particle density) or estimate it from the uniformity coefficient using published correlations. The Kozeny-Carman and Hazen equations are sensitive to porosity, so use a measured value when you have one.
What units are most commonly used for hydraulic conductivity?
Groundwater modelers and hydrogeologists most often use m/s or m/day. Geotechnical engineers frequently use cm/s. US practice often uses ft/day. This calculator supports all four. A useful conversion: 1 m/s = 86,400 m/day = 100 cm/s = 283,465 ft/day.
Why is my computed K so different from the published range for my soil?
Empirical equations can be off by a factor of two to ten even for clean sands. Common causes are poorly sorted soil (empirical methods assume uniform grading), the sample not being representative of the in-situ soil, incorrect grain-size input (for example, using d50 instead of d10), and temperature effects if the water in your test was not at the standard reference temperature. Check that your d10 and porosity are correct and that the method is appropriate for your grain-size range.