Hydraulic Conductivity Calculator — Constant & Falling Head Permeameter
Calculate hydraulic conductivity (K) from lab permeameter test data — choose constant-head for permeable soils (sand, gravel) or falling-head for less permeable soils (silt, clay), enter the sample geometry and measurements, and get K in m/s, cm/s, and m/day with a soil-type classification.
Test method
cm
cm²
s
mL
cm
Permeability of the soil sample — how fast water moves under a unit hydraulic gradient
Flow rate Q
Apply Darcy: K = Q·L / (A·h·t)
K (cm/s)
- 1
Hydraulic gradient i = Δh ÷ L
30 ÷ 15 = 2Head loss per unit length of sample. - 2
K = Q × L ÷ (A × Δh × t)
150 × 15 ÷ (20 × 30 × 60) = 0.0625 cm/s - 3
Convert to m/s (÷ 100)
0.0625 ÷ 100 = 0.000625 m/s
How does this calculator work?
Hydraulic conductivity K = Q·L/(A·Δh·t) for constant-head tests, or (a·L/(A·t))·ln(h₁/h₂) for falling-head tests, both derived from Darcy's law. Results span 10⁻¹¹ m/s (clay) to ~1 m/s (gravel). Enter your permeameter geometry and measurements for K in m/s, cm/s, and m/day.
Formula
How this is calculated
Hydraulic conductivity (also called coefficient of permeability) describes how readily water flows through a porous medium under a hydraulic gradient. It is the proportionality constant in Darcy's law: the discharge velocity q equals K times the hydraulic gradient i (head loss ÷ sample length). Typical values span twelve orders of magnitude — from ~1 m/s for clean gravel to 10⁻¹¹ m/s for dense clay.
The constant-head test is used for more permeable soils (sand, gravel). A steady hydraulic head difference Δh is maintained across the sample of length L and cross-sectional area A; the volume Q collected over time t gives K = Q·L / (A·Δh·t). The falling-head test is used for less permeable soils (silt, clay) where maintaining a constant head is impractical. Water drains through the sample from a standpipe of area a; measuring the head drop from h₁ to h₂ over time t gives K = (a·L / (A·t)) × ln(h₁/h₂), which comes from integrating Darcy's law as the head falls.
Both methods assume laminar (low Reynolds number) Darcian flow, homogeneous and saturated soil, and no gas bubbles. Real field-scale conductivity may differ from lab measurements due to anisotropy, macro-pores, and sample disturbance. Results are appropriate for preliminary engineering assessments; critical applications (seepage, dewatering, landfill liners) require multiple tests and often field pump tests.
Frequently asked questions
Use the constant-head test for permeable soils (K > 10⁻⁵ m/s) such as sand and gravel where measurable flow rates can be sustained under a fixed head. Use the falling-head test for finer soils (K < 10⁻⁵ m/s) such as silt and clay where flow rates are too low for the constant-head approach.
Gravel: 10⁻² to 1 m/s; coarse sand: 10⁻⁴ to 10⁻² m/s; fine sand / silty sand: 10⁻⁶ to 10⁻⁴ m/s; silt: 10⁻⁸ to 10⁻⁶ m/s; clay: 10⁻¹¹ to 10⁻⁸ m/s. These are approximate ranges; real soils vary with density, fabric, and saturation.
K depends primarily on pore size and connectivity. Gravel has large, well-connected pores; clay has extremely small pores and a high surface area that strongly attracts and retards water. The Kozeny–Carman equation formalises this: K ∝ (pore radius)² — halving the pore radius reduces K by a factor of four.
Also known as
TG we-Calculate Editorial Team. (2026). Hydraulic Conductivity Calculator — Constant & Falling Head Permeameter [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/hydraulic-conductivity-calculator
TG we-Calculate Editorial Team. "Hydraulic Conductivity Calculator — Constant & Falling Head Permeameter." TG we-Calculate. 2026. https://we-calculate.com/calculator/hydraulic-conductivity-calculator.
TG we-Calculate Editorial Team, "Hydraulic Conductivity Calculator — Constant & Falling Head Permeameter," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/hydraulic-conductivity-calculator
@misc{wecalculate_hydraulic_conductivity_calculator, title = {Hydraulic Conductivity Calculator — Constant & Falling Head Permeameter}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/hydraulic-conductivity-calculator}}, year = {2026}, note = {TG we-Calculate} }
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