Darcy's law states that flow rate Q through a porous medium equals the product of hydraulic conductivity K, cross-sectional area A, and hydraulic gradient (dh/dL): Q = K × A × (dh/dL). It is valid for laminar, slow flow through saturated porous media.

What is hydraulic conductivity?

Hydraulic conductivity (K) measures how easily water flows through a porous material. It depends on both the medium (pore size, porosity) and the fluid (viscosity, density). Units are length/time (m/s, cm/s, ft/day).

What is intrinsic permeability?

Intrinsic permeability (k) is a property of the porous medium alone, independent of the fluid. Measured in m² or darcy (1 darcy ≈ 9.869×10⁻¹³ m²). K = k × ρg/μ, where ρ is fluid density, g is gravity, and μ is dynamic viscosity.

What is a millidarcy (mD)?

A millidarcy is 0.001 darcy, commonly used in petroleum engineering for tight rock formations. 1 mD ≈ 9.869×10⁻¹⁶ m². Reservoir sandstones typically range from 1–1000 mD; tight gas sands below 0.1 mD.

When does Darcy's law not apply?

Darcy's law breaks down at high flow velocities (turbulent flow, Reynolds number > 1–10), in fractured media with non-linear flow paths, or in unsaturated (partially wetted) conditions where capillary effects dominate.

Permeability Calculator

Enter any three of the four Darcy's law variables (Q, K, A, dh/dL) and instantly compute the fourth. Supports SI and field units with reference values for common materials.

Darcy's Law Calculator

Solve For:

Q — Flow Rate

K — Hydraulic Conductivity

darcy/mD assume water at 20 °C (ρg/μ ≈ 9.61×10⁶ s⁻¹·m⁻¹)

A — Cross-Sectional Area

i — Hydraulic Gradient (dh/dL, dimensionless)

m/m

Head difference divided by flow path length. Dimensionless.

Select what to solve for, enter the three known values, then click Calculate.

Q = K × A × i

Result

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Conversions

Typical Hydraulic Conductivity Values

Material	K (m/s)	K (cm/s)

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Summary

Compute any Darcy's law variable — flow rate (Q), hydraulic conductivity (K), cross-sectional area (A), or hydraulic gradient (dh/dL) — given the other three. Includes unit conversions across SI and field units and a reference table of typical K values for common geological and engineering materials.

How it works

The tool applies Darcy's law in the form Q = K × A × (dh/dL). All inputs are converted to SI base units (m³/s, m/s, m², dimensionless) before calculation, then the result is converted back to your chosen output unit. The hydraulic gradient is dimensionless (head loss divided by flow path length).

Use cases

Estimate groundwater flow rate through an aquifer layer.
Determine hydraulic conductivity from pump test or lab data.
Calculate required cross-sectional area for a drainage filter.
Convert between m/s, cm/s, darcy, and millidarcy permeability units.
Verify soil compaction compliance for engineering projects.

Frequently Asked Questions

Last updated: 2026-05-23 · Reviewed by Nham Vu