Darcy’s Law Calculator
Compute groundwater flow through porous media: Q = k · A · i. Four modes: discharge (Q), hydraulic conductivity (k), hydraulic gradient (i), and true pore velocity — complete with k unit conversion and intrinsic permeability.
Material presets (optional)
Preset values are typical; actual values vary with grain gradation, compaction, and water temperature.
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Sign convention
The full form of Darcy’s law is Q = −k · A · (dh/dl). The negative sign means flow moves toward decreasing hydraulic head (from high head to low head). This calculator treats the gradient i as a flow-direction quantity, so Q appears positive.
Not this tool? Scope limits
This calculator is specifically for groundwater flow through porous media (hydrogeology). For head loss of flow inside pressurized pipes — a different problem that happens to share the “Darcy” name — use:
Frequently asked questions
What is Darcy’s law?
Darcy’s law states that groundwater discharge Q is proportional to the hydraulic conductivity k, cross-sectional area A, and hydraulic gradient i — that is, Q equals k times A times i. The negative sign in the full form of the equation indicates flow moves toward decreasing hydraulic head.
What is hydraulic conductivity (k)?
Hydraulic conductivity measures how easily water flows through a porous medium under a unit hydraulic gradient. Its units can be m/s, cm/s, m/day, or ft/day. Its value depends on the material type, pore size, and water temperature, because temperature affects viscosity.
What is the difference between Darcy velocity and true pore velocity?
Darcy velocity v equals Q divided by A; it is a fictitious velocity as if water flowed through the entire cross-section. Water actually moves only through the pores, so the true pore velocity v_pore equals v divided by porosity n, and is always greater than v.
What is the hydraulic gradient (i)?
The hydraulic gradient is the change in hydraulic head per unit distance of flow, dh/dl, and is dimensionless. A positive value means head decreases in the direction of the flow being considered; the negative sign in Darcy’s equation confirms flow moves from high head to low head.
How does this calculator differ from the Darcy-Weisbach calculator?
This calculator computes groundwater flow through porous media (hydrogeology). The Darcy-Weisbach calculator computes head loss for flow inside pressurized pipes — a completely different problem. For pipe flow, use the Darcy-Weisbach head loss, pipe flow, or friction loss calculators linked on this page.
What is intrinsic permeability?
Intrinsic permeability kappa is a property of the porous medium alone, independent of the fluid, computed as kappa equals k times viscosity divided by density times gravity. Its units are m² or darcy; this calculator shows both for water at 20 degrees Celsius.
What are typical hydraulic conductivity values for sand, silt, and clay?
Typical values: gravel about 1e-2 to 1 m/s, coarse sand 1e-4 to 1e-2, fine sand 1e-6 to 1e-4, silt 1e-9 to 1e-6, and clay 1e-11 to 1e-9 m/s. These are typical ranges; actual values can differ with gradation, compaction, and temperature.
What is a worked example of Darcy’s law?
For k equal to 0.0001 m/s, cross-sectional area A equal to 2 m², and hydraulic gradient i equal to 0.01, discharge Q equals k times A times i equals 0.000002 m³/s, or 0.1728 m³/day. Darcy velocity v equals 0.000001 m/s, and the true pore velocity at porosity 0.35 is 0.2469 m/day.
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