Darcy's Law Calculator

Free Darcy's Law Calculator — compute groundwater seepage flow rate, hydraulic conductivity, cross-sectional area, head difference, or flow path length with multi-unit support.

928.2K uses Updated · 2026-05-11 Runs locally · zero upload
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How to Use Darcy’s Law Calculator

The Darcy’s Law Calculator makes seepage flow calculations straightforward with multi-unit input and clear result breakdown.

  1. Select a Calculation Mode — Choose from five modes: calculate flow rate Q, or solve for hydraulic conductivity k, cross-sectional area A, head difference Δh, or path length L.
  2. Enter Known Parameters — Fill in the fields displayed for your chosen mode. Select appropriate units (m/s, cm/s, m/day, ft/day for k; m², cm², ft² for area; m, cm, ft for length; m³/s, m³/day, L/s, ft³/s for flow rate).
  3. Read the Result — The Darcy’s Law Calculator shows the primary result in your chosen unit plus the SI equivalent, hydraulic gradient i, and Darcy velocity q.
  4. Check the Substitution — The formula, substitution, and unit conversion panel confirm every computation step.

Formula & Theory — Darcy’s Law Calculator

The Darcy’s Law Calculator is based on Darcy’s empirical law for flow through saturated porous media:

$$Q = \frac{k \cdot A \cdot \Delta h}{L}$$

SymbolDescriptionSI Unit
QVolumetric flow ratem³/s
kHydraulic conductivitym/s
ACross-sectional area perpendicular to flow
ΔhHead difference (hydraulic head drop)m
LFlow path lengthm

Derived Quantities

Hydraulic gradient:

$$i = \frac{\Delta h}{L}$$

Darcy velocity (specific discharge):

$$q = \frac{Q}{A} = k \cdot i$$

The Darcy’s Law Calculator handles all five rearrangements of the formula, allowing any single unknown to be solved given the other four parameters.

Inverse Calculation Formulas

Solve ForFormula
kk = Q × L / (A × Δh)
AA = Q × L / (k × Δh)
ΔhΔh = Q × L / (k × A)
LL = k × A × Δh / Q

Use Cases for Darcy’s Law Calculator

The Darcy’s Law Calculator is widely used in:

  • Groundwater hydrology — estimating aquifer discharge rates, inter-layer seepage, and pumping well analysis.
  • Geotechnical engineering — calculating seepage through earth dams, embankments, and retaining walls to assess stability and filtration.
  • Soil science — measuring or inferring saturated hydraulic conductivity from field or laboratory permeability tests.
  • Environmental engineering — modeling contaminant transport in soil and evaluating remediation flow systems.
  • Civil engineering — drainage design, landfill liner performance, and construction dewatering.

The Darcy’s Law Calculator supports engineers and scientists working at any scale, from laboratory column tests to large-scale aquifer systems. Use it alongside permeameter data or slug-test results to verify conductivity estimates and design flow control systems with confidence.

Frequently asked questions about Darcy's Law Calculator

What is Darcy's Law?

Darcy's Law states that the volumetric flow rate Q through a porous medium equals the hydraulic conductivity k multiplied by the cross-sectional area A and the hydraulic gradient (Δh / L). Written as Q = k × A × Δh / L.

What is hydraulic conductivity and what are typical values?

Hydraulic conductivity k describes how easily water moves through a porous material. Gravel may have k around 1e-2 m/s, clean sand around 1e-4 m/s, silty clay around 1e-7 m/s, and unfractured rock below 1e-9 m/s.

What is the hydraulic gradient?

The hydraulic gradient i = Δh / L is the ratio of head difference to flow path length. It is dimensionless and represents the driving force for groundwater flow.

What is Darcy velocity?

Darcy velocity (specific discharge) q = Q / A = k × i is the apparent flow velocity through the bulk cross-section, not the actual pore water velocity. Actual pore velocity equals q divided by porosity.

Can I solve for unknown parameters instead of flow rate?

Yes. Use the mode buttons to switch between solving for k, A, Δh, or L given the other known parameters.

Is my data stored?

No. All calculations happen in your browser; nothing is sent to a server.