Darcy's Law states that the volumetric flow rate (Q) of a fluid through a porous medium is proportional to the hydraulic conductivity (K), the hydraulic gradient (i), and the cross-sectional area (A): Q = K × i × A. It was formulated by Henry Darcy in 1856.

What is hydraulic conductivity?

Hydraulic conductivity (K) measures how easily water moves through a porous material. It depends on both the aquifer material (grain size, porosity) and fluid properties (viscosity). Gravels have K up to 1 m/s; clays can be as low as 10⁻¹⁰ m/s.

How is the hydraulic gradient calculated?

The hydraulic gradient (i) equals the difference in hydraulic head (Δh) between two points divided by the distance (L) between them along the flow path: i = Δh / L. It is dimensionless.

Does Darcy's Law apply to all groundwater flow?

Darcy's Law is valid for laminar (slow) flow through porous media, which covers most natural groundwater conditions. It breaks down in very high-velocity flow (e.g., karst conduits or coarse gravels near pumping wells) where turbulent flow occurs.

What units does this calculator support?

Hydraulic conductivity can be entered in m/s, m/day, cm/s, or ft/day. Cross-sectional area can be in m², cm², or ft². Results are displayed in m³/s, m³/day, and L/s.

Groundwater Flow Calculator

Name: Groundwater Flow Calculator
Availability: InStock
Author: Nham Vu

Compute groundwater discharge using Darcy's Law: Q = K × i × A, with unit conversion and result breakdown.

Darcy's Law Inputs

Q = K × i × A

Hydraulic Conductivity (K)

Common values: gravel 10⁻² m/s, sand 10⁻⁴ m/s, clay <10⁻⁸ m/s

Hydraulic Gradient (i)

Dimensionless — head difference / flow path length (Δh / L)

Cross-sectional Area (A)

Area perpendicular to the direction of flow

Typical K Values

Material	K (m/s)
Gravel	10⁻²
Coarse sand	10⁻⁴
Fine sand	10⁻⁶
Silt	10⁻⁹
Clay	10⁻¹¹

Click a row to use that K value.

Enter values on the left and click Calculate

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Summary

Compute groundwater discharge using Darcy's Law: Q = K × i × A, with unit conversion and result breakdown.

How it works

Enter the hydraulic conductivity (K) of the aquifer material and select its unit (m/s, m/day, cm/s, or ft/day).
Enter the hydraulic gradient (i), which is the head difference divided by the flow path length (dimensionless).
Enter the cross-sectional area (A) perpendicular to the flow direction and choose the unit (m², cm², or ft²).
Click "Calculate" to apply Darcy's Law: Q = K × i × A.
View the discharge result in multiple units along with a parameter summary.

Use cases

Estimate aquifer discharge rates for water supply planning.
Assess contaminant transport speed through saturated soil.
Design dewatering systems for construction sites.
Size drainage structures and groundwater extraction wells.
Validate field pump tests against theoretical Darcy predictions.
Teach hydrogeology concepts in academic settings.
Support environmental impact assessments for landfills or spills.
Calculate seepage rates through earth dams and embankments.

Frequently Asked Questions

Last updated: 2026-06-09 · Reviewed by Nham Vu