Darcy's Law Calculator
Groundwater flow through a porous medium: hydraulic gradient, Darcy flux, total flow rate Q = KiA, and the seepage velocity and travel time that actually govern how fast water — and anything dissolved in it — moves.
Defaults: clean sand, K = 1×10⁻³ cm/s (2.835 ft/day), 0.5 ft of head loss over 100 ft, 500 ft² of aquifer cross-section, effective porosity 0.30.
Darcy flux is not how fast the water moves
The most common Darcy's law mistake is using the flux q as a velocity. The flux divides flow by the whole cross-section, grains included. Water can only travel through connected pore space, so its average speed is q divided by effective porosity. With nₑ = 0.30 the seepage velocity is 3.3 times the Darcy flux. For contaminant plumes, capture-zone sizing and well-head protection travel times, seepage velocity is the number that matters — and it is still only an average, since dispersion spreads a real plume ahead of it.
Hydraulic conductivity varies over more than ten orders of magnitude between gravel and unfractured clay, which makes K by far the most uncertain input. A factor-of-ten error in K is a factor-of-ten error in Q. Use pumping-test, slug-test or permeameter values where you have them; see the soil permeability reference card for typical ranges by soil type.
Hydraulic conductivity unit conversions
| 1 unit of | cm/s | m/day | ft/day | gpd/ft² |
|---|---|---|---|---|
| cm/s | 1 | 864 | 2,834.6 | 21,205 |
| m/day | 1.157×10⁻³ | 1 | 3.2808 | 24.542 |
| ft/day | 3.528×10⁻⁴ | 0.3048 | 1 | 7.4805 |
| gpd/ft² | 4.716×10⁻⁵ | 0.040746 | 0.13368 | 1 |
gpd/ft² is gallons per day through one square foot under unit gradient ("Meinzer unit"), common in US water-well work. Hydraulic conductivity K includes the fluid's density and viscosity; intrinsic permeability (darcys, m²) does not.
Worked examples
Example 1 — Flow and travel time through a sand aquifer
Example 2 — Seepage under a cutoff (SI)
Where Darcy's law applies — and where it doesn't
- Valid: laminar flow through granular soils, sandstones and most aquifers; seepage through embankments, foundations and levees; flow toward drains and wells away from the well bore.
- Not valid: turbulent flow in coarse gravel, karst conduits and open fractures, or immediately around high-rate pumping wells. As a check, keep the grain Reynolds number ρ·q·d₁₀/μ below about 1 to 10.
- Single-direction only: this calculator treats one straight flow path of constant area. Flow nets or a numerical model are needed for two- and three-dimensional seepage.
Not to be confused with the Darcy-Weisbach equation, which describes friction head loss for flow in pipes.
References: Darcy, H. (1856). Les Fontaines Publiques de la Ville de Dijon. Freeze, R.A., Cherry, J.A. (1979). Groundwater. Prentice-Hall. Fetter, C.W. (2001). Applied Hydrogeology, 4th ed.
Related tools
- Soil permeability (k) by soil type
- Embankment seepage — Casagrande phreatic line and seepage rate
- Seepage exit gradient — critical gradient and heave
- Filter criteria — Sherard / NRCS filter design
- Darcy-Weisbach — pipe friction (a different Darcy equation)