What this calculator does
Hydraulic conductivity describes how easily water moves through soil or rock. It is a core figure in hydrogeology, well design and drainage work, because it tells you whether a material lets water pass quickly (like coarse gravel) or barely at all (like dense clay).
The calculation comes straight from Darcy’s Law: conductivity equals flow rate multiplied by the length of the flow path, divided by the cross-sectional area the water moves through and the head difference driving that flow. Get the units consistent and the result is directly comparable to published tables of typical values for different soil types.
The formula
Darcy’s Law states that flow rate through a porous medium is proportional to the cross-sectional area and the hydraulic gradient (head difference over length), with hydraulic conductivity as the constant of proportionality. Rearranging for K gives K = (Q × L) ÷ (A × Δh), so K rises whenever more flow is produced for the same driving head, and falls whenever it takes more head to push the same flow through.
| Term | Meaning |
|---|---|
| K | Hydraulic conductivity, in metres per second: how readily water moves through the material. |
| Q | Flow rate through the sample or aquifer section, in cubic metres per second. |
| L | Length of the flow path the water travels, in metres. |
| A | Cross-sectional area perpendicular to flow, in square metres. |
| Δh | Head difference (hydraulic head loss) driving the flow, in metres. |
The inputs explained
| Field | What to enter |
|---|---|
| Flow rate (m³/s) | The volume of water passing through per second, from a permeameter test or field measurement. |
| Flow path length (m) | The distance the water travels along the flow path, measured between the two points where head is recorded. |
| Cross-sectional area (m²) | The cross-sectional area of the sample or aquifer section that the flow passes through. |
| Head difference (m) | The difference in hydraulic head between the inflow and outflow points. |
When to use it
Laboratory permeameter testing
A constant-head or falling-head permeameter test measures flow rate through a soil sample of known dimensions, and this formula converts that directly into a conductivity value for the material.
Assessing drainage or infiltration
A low hydraulic conductivity signals poor drainage, relevant for septic system design, stormwater infiltration basins and foundation drainage.
Estimating aquifer yield
Combined with an aquifer’s thickness and gradient, conductivity feeds into estimates of how much water a well field can sustainably produce.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How hydraulic conductivity changes with flow rate at fixed geometry
The same sample geometry, at a range of measured flow rates.
| Flow rate | Hydraulic conductivity (K) | Darcy velocity (Q/A) |
|---|---|---|
| 0.0005 m³/s | 0.002500 m/s | 0.001000 m/s |
| 0.0010 m³/s | 0.005000 m/s | 0.002000 m/s |
| 0.0020 m³/s | 0.010000 m/s | 0.004000 m/s |
| 0.0040 m³/s | 0.020000 m/s | 0.008000 m/s |
| 0.0080 m³/s | 0.040000 m/s | 0.016000 m/s |
| 0.0160 m³/s | 0.080000 m/s | 0.032000 m/s |
How hydraulic conductivity changes with head difference at fixed flow
A fixed flow rate and geometry, against a range of head differences.
| Head difference | Hydraulic conductivity (K) | Darcy velocity (Q/A) |
|---|---|---|
| 0.2 m | 0.040000 m/s | 0.004000 m/s |
| 0.4 m | 0.020000 m/s | 0.004000 m/s |
| 0.8 m | 0.010000 m/s | 0.004000 m/s |
| 1.6 m | 0.005000 m/s | 0.004000 m/s |
| 3.2 m | 0.002500 m/s | 0.004000 m/s |
| 6.4 m | 0.001250 m/s | 0.004000 m/s |
Questions
What is a typical hydraulic conductivity for soil?
It varies by orders of magnitude: clean gravel can exceed 1 cm/s, sand is often around 10⁻³ to 10⁻⁵ m/s, and dense clay can be below 10⁻⁹ m/s. Comparing a measured K against these ranges is a quick sanity check on a test result.
Is hydraulic conductivity the same as permeability?
They are related but not identical. Intrinsic permeability depends only on the material itself, while hydraulic conductivity also depends on the properties of the fluid moving through it, usually water, so it changes with fluid viscosity and density.
Why does the head difference matter so much?
Darcy’s Law assumes flow is proportional to the hydraulic gradient. A larger head difference over the same path length drives more flow through the same material, so it has to be accounted for to isolate the material property, K, from the test conditions.
Does this formula work for both saturated and unsaturated soil?
This is the standard saturated hydraulic conductivity calculation from Darcy’s Law. Unsaturated conductivity varies with moisture content and needs a different, more involved approach.
For the geometry of open-channel flow rather than flow through a porous material, see the hydraulic radius calculator.