Hydraulic Conductivity Calculator

Enter your constant-head permeameter test measurements (flow rate, sample length, cross-sectional area, and head loss) to solve Darcy's Law for hydraulic conductivity K, plus the hydraulic gradient and a soil permeability class.

Quick Facts

Darcy's Law
K = Q·L / (A·Δh)
Solved for hydraulic conductivity from a steady-state, constant-head permeameter test.
Hydraulic gradient
i = Δh / L
Dimensionless driving force; must be measured across the actual flow path length.
Typical soil range
~10⁻⁹ to 10¹ cm/s
Clay (~10⁻⁹ cm/s) to clean gravel (~10 cm/s) — about ten orders of magnitude.
K vs. permeability
K = k·ρ·g / μ
Hydraulic conductivity depends on the fluid too; intrinsic permeability k does not.

Your Results

Calculated
Hydraulic Conductivity (K)
-
K = QL / (AΔh), in cm/s
Hydraulic Conductivity (K)
-
Same K, in m/day
Hydraulic Gradient (i)
-
i = Δh / L (dimensionless)
Permeability Class
-
Typical soil/rock category for this K

Ready

Enter your permeameter test measurements, then press Calculate.

Formula and Method for Hydraulic Conductivity

Hydraulic conductivity (K) describes how easily water flows through a porous medium such as soil, sand, or fractured rock. It is measured directly with a constant-head permeameter test: a sample of known length and cross-sectional area is subjected to a steady head difference, and the steady-state flow rate through it is recorded. Darcy's Law connects these measurements to K: Q = K · A · (Δh / L), which rearranges to K = Q · L / (A · Δh), where Q is flow rate, L is the length of the flow path, A is the cross-sectional area, and Δh is the head loss across that length.

How the calculation works

Enter the steady flow rate collected through the sample, the length of the flow path, the cross-sectional area the water passes through, and the head loss (the drop in hydraulic head) measured across that length. The calculator converts every input to consistent SI units (m³/s, m, m²), applies K = QL / (AΔh) to get K in m/s, then reports it in the more commonly used cm/s and m/day. It also reports the hydraulic gradient i = Δh / L — the dimensionless driving force in Darcy's Law — and matches your K value to a standard soil permeability class.

Common mistakes

  • Confusing sample length with head loss: L is the physical distance water travels through the sample; Δh is the drop in hydraulic head (often measured with manometers) across that same distance — they are rarely equal.
  • Using flow rate instead of steady-state flow rate: Darcy's Law assumes steady, laminar flow. Let the outflow rate stabilize before timing your volume collection, and confirm flow stays laminar (Reynolds number typically well below 1-10 for Darcy's Law to hold).
  • Mixing unit systems: keep length, area, and flow-rate units internally consistent, or use the unit selectors here so the conversion is handled for you — a stray inch-vs-centimeter mismatch can shift K by an order of magnitude.

Real-world applications

  • Groundwater and well-yield studies use K to estimate how fast an aquifer can supply water to a pumping well.
  • Geotechnical and dam engineers use K to assess seepage rates through embankments, foundations, and earthen dams.
  • Landfill and containment liner design relies on very low K values (dense clay or geomembranes) to limit contaminant migration.
  • Agricultural drainage and septic/leach-field design use K to size drainage systems and infiltration areas.

Frequently Asked Questions

What is hydraulic conductivity?
Hydraulic conductivity (K) is a measure of how easily water moves through a porous material such as soil or rock under a given hydraulic gradient. It depends on both the properties of the medium (pore size, connectivity) and the properties of the fluid (density, viscosity), and is typically expressed in units of velocity such as cm/s, m/day, or ft/day.
How do you calculate K from a constant-head permeameter test?
Apply Darcy's Law rearranged for K: K = Q × L / (A × Δh), where Q is the steady flow rate through the sample, L is the length of the flow path, A is the cross-sectional area of the sample, and Δh is the head loss measured across that length.
What is a typical range of hydraulic conductivity values for soils?
Values span many orders of magnitude: clean gravel is roughly 1-100 cm/s, clean sand roughly 1e-1 to 1e-3 cm/s, silty sand and silt roughly 1e-3 to 1e-5 cm/s, and dense clay can be lower than 1e-7 cm/s — essentially impermeable on human timescales.
How is hydraulic conductivity different from intrinsic permeability?
Hydraulic conductivity (K) depends on the fluid as well as the medium, while intrinsic permeability (k) depends only on the medium's pore geometry. They are related by K = k × ρ × g / μ, where ρ and μ are the fluid's density and dynamic viscosity and g is gravitational acceleration — so K for water differs from K for oil in the same soil, but k stays the same.

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