Soil Permeability Calculator
Falling-head permeability k = (a × L) ÷ (A × t) × ln(h₁ ÷ h₂), reported in cm/s; a constant-head method is included too. A 1 cm² standpipe on a 10 cm, 30 cm² sample, head falling from 60 to 30 cm in 300 s, gives k ≈ 7.70 × 10⁻⁴ cm/s. Related: Atterberg Limits Calculator.
How it's calculated: Falling head: k = (a × L) ÷ (A × t) × ln(h₁ ÷ h₂); constant head: k = (Q × L) ÷ (A × h × t). a = standpipe area, L = sample length, A = sample area, t = elapsed time, h = head, Q = volume collected.
Result appears here
Fill in the fields and press Calculate.
Formula, calculation, assumptions and sources
Falling head: k = (a·L) ÷ (A·t) × ln(h₁ ÷ h₂)
Constant head: k = (Q·L) ÷ (A·h·t)
a = standpipe area, L = sample length, A = sample area, t = elapsed time, h₁/h₂ = initial/final head, h = constant head, Q = volume collected
Run the calculation to see each step with your own numbers.
Falling-head test: 1 cm² standpipe, 10 cm sample length, 30 cm² sample area, head drops 60→30 cm in 300 s.
k = (1 × 10) ÷ (30 × 300) × ln(60/30) = 0.0011111 × 0.6931 ≈ 7.70 × 10⁻⁴ cm/s
- Water and sample at (or corrected to) a consistent temperature — permeability is temperature-sensitive through water's viscosity; ASTM standards allow a temperature correction to 20°C that this calculator does not apply.
- Fully saturated sample with no entrapped air, and laminar (Darcian) flow throughout the test — both required for the underlying formulas to hold.
- Falling head suits fine-grained, low-permeability soils (k roughly below 10⁻⁴ cm/s); constant head suits granular, free-draining soils (k roughly above 10⁻⁴ cm/s) — using the wrong method for the soil type gives an unreliable reading in practice, independent of this calculator's arithmetic.
- Which method should I use for my soil?
- Constant head for free-draining, granular soils (sand and gravel) where flow is fast enough to measure a steady discharge. Falling head for fine-grained, low-permeability soils (silt and clay) where flow is too slow for a practical constant-head reading. The wrong choice for a given soil type tends to give a less reliable — not necessarily wrong-formula — result.
- Why is k shown to 8 decimal places?
- Hydraulic conductivity values for soil routinely span many orders of magnitude, from around 1 cm/s for clean gravel down to 10⁻⁹ cm/s or smaller for intact clay. Fixed decimal places are the least confusing way to show that range without a specialised scientific-notation display; for very small values, read the leading zeros as the order of magnitude.
- Does temperature really matter?
- Yes, meaningfully — water's viscosity (and so how easily it flows through the same soil) changes noticeably with temperature. ASTM standards correct measured k to a standard 20°C reference; if your lab report already applies that correction, your reading is ready to enter as-is.
- How do you calculate the coefficient of permeability?
- For a falling-head test, multiply (a × L) ÷ (A × t) by the natural log of the initial head over the final head. With a = 1 cm², L = 10 cm, A = 30 cm² and the head falling from 60 to 30 cm in 300 s, k ≈ 7.70 × 10⁻⁴ cm/s.
- What is the constant-head permeability formula?
- k = (Q × L) ÷ (A × h × t): the volume of water collected times the sample length, divided by the sample area, the constant head and the elapsed time. 500 mL through a 10 cm, 78.5 cm² sample under 30 cm of head in 60 s gives about 0.0354 cm/s.
Falling-head method
ASTM D5084, 'Standard Test Methods for Measurement of Hydraulic Conductivity of Saturated Porous Materials Using a Flexible Wall Permeameter' (falling-head form of the calculation).
Constant-head method
ASTM D2434, 'Standard Test Method for Permeability of Granular Soils (Constant Head)'.
About the Soil Permeability Calculator
The Soil Permeability Calculator gives the coefficient of permeability (hydraulic conductivity, k) from either a falling-head test (ASTM D5084 — used for fine-grained, low-permeability soils) or a constant-head test (ASTM D2434 — used for granular, free-draining soils). One tool with a method selector, since both report the same property from the same permeameter geometry, just a different head condition. Results are given in cm/s, the conventional unit for reporting hydraulic conductivity in geotechnical practice worldwide.
What you enter
- Test method
- Standpipe cross-section area, a
- Sample length, L
- Sample cross-section area, A
- Initial head, h₁
- Final head, h₂
- Elapsed time, t
- Sample length, L
- Sample cross-section area, A
- Constant head difference, h
- Water collected, Q
- Elapsed time, t
What you get back
- Coefficient of permeability, k — cm/s — the conventional reporting unit for hydraulic conductivity regardless of measurement system.
The formula, a worked example, the assumptions behind it and the sources are shown in full below the calculator.
Related calculators
- Atterberg Limits Calculator — Liquid limit (one-point method), plastic limit and plasticity index of a fine-grained soil.
- In-Situ Dry Density Calculator — Field bulk density, dry density and percent compaction of compacted soil from a drive-cylinder (core cutter) sample.
- California Bearing Ratio (CBR) Calculator — California Bearing Ratio of a subgrade or base sample at 2.5 mm and 5.0 mm penetration, against the ASTM standard loads.
Related articles
- What Is Soil Permeability? — Permeability describes how readily water flows through a soil — a property that drives drainage design, seepage analysis, and foundation decisions.
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