Porosity and Permeability Calculator. Enter your porous media parameters — void volume, total volume, flow rate, dynamic viscosity, cross-sectional area, pressure drop, and sample length — and the Porosity and Permeability Calculator returns porosity (φ) and permeability (k) using Darcy's law. Switch between calculating porosity from volumes or permeability from flow data depending on what you know. Also try the Wind Load Calculator.
Ever wondered how water, oil, or gas really move through soil, rocks, or engineered materials? With the porosity and permeability calculator, you gain precise insight into a material’s ability to store or transport fluids. Whether you’re a geologist striving for more accurate groundwater models, an engineer optimizing filter design, or a scientist evaluating construction materials, knowing both porosity and permeability directly impacts your project's safety, efficiency, and sustainability. Gaining clarity on these essential parameters empowers you to tackle everything from groundwater management to designing innovative energy systems and even improving construction durability. See also our Knudsen Number Calculator.
Darcy’s law describes the steady-state flow of a fluid through a porous structure driven by a pressure gradient. It is the cornerstone of hydrology, petroleum science, and environmental earth sciences.
The classic Darcy’s law equation is:
$$Q = \frac{k A}{\mu L}\Delta p$$
$$k = \frac{Q \mu L}{A \Delta p}$$
The permeability unit in SI is m², but in practice, darcy (d) and millidarcy (md) are often used:
The coefficient of permeability (also known as hydraulic permeability or simply "k"), quantifies how well a structure transmits a particular liquid under a differential force. It is a property intrinsic to the substrate, influenced by porosity, pore size, fluid type, and temperature.
The coefficient of permeability unites fundamental properties of the fluid and the structure of the porous medium. For fluids, viscosity and density matter; for matrices, factors include pore geometry and connectivity.
The larger the pressure gradient and the more connected the voids, the greater the flow rate for a given matrix.
Porosity is a relative measure of a structure’s void fraction—the openings or voids between solid particles—which allows storage of water, oil, and gas. It is expressed as a dimensionless number between 0 and 1, representing the fraction of void relative to the total specimen volume (solid plus void):
Porosity = (open volume) / (sample size)
This property is crucial in hydrology, petrophysics, environmental analysis, and material science, because it directly affects fluid storage and the capacity for fluid movement in geological or synthetic matrices.
$$\phi = \frac{V_v}{V_t}$$
| Material | Typical Porosity (\(\phi\), dimensionless) | Practical Implication |
|---|---|---|
| Sandy soils | 0.36–0.43 | Higher porosity, good for groundwater movement |
| Clay-rich soils | 0.51–0.58 | High porosity but often lower permeability due to poor connectivity |
| Granite/igneous rocks | 0.01–0.03 | Very low porosity, poor fluid storage |
| Sandstones | 0.10–0.30 | Variable, highly dependent on cementation and compaction |
| Peaty soils/organic substance | 0.70–0.90 | Extremely high porosity; very soft, can retain much water |
Porosity and permeability are related terms—but not identical. Porosity quantifies the fraction of void a substance contains, while permeability describes how easily fluids can move through those voids. Only connected pores allow fluid movement, so a high porosity material can still be impermeable if its pores are disconnected.
In energy reservoirs, knowing the porosity of soils and stone layers directly impacts oil extraction planning and subsurface fluid management. For example, in civil design, porosity is crucial when designing drainage layers or evaluating the suitability of aggregate for roads and foundations.
Ensure all input fields use consistent systems—SI (meters, pascals, seconds), unless another measurement is specifically required for your application (e.g., darcy for geology).
This digital tool is powered by verified math and delivers step-by-step solutions for clarity and traceability. You might also find our calculate Lift Coefficient (C_L), Dynamic Pressure (q) & Fluid Density Used (ρ) — Lift Coefficient useful.
The output provides both porosity (dimensionless or as a percent) and permeability (in m², darcy, or millidarcy). Use these results to assess drainage, fluid transmission, or suitability for your specific design, hydrology, or infrastructure application.
| Parameter | Symbol | Typical Soil Example (Sand) | Typical Rock Example (Granite) |
|---|---|---|---|
| Porosity | \(\phi\) | 0.38 | 0.02 |
| Permeability (m²) | k | 1 × 10-11 | 1 × 10-20 |
| Permeability (darcy) | k | 0.01 | 1.0 × 10-8 |
| Permeability (millidarcy) | k | 10 | 1.0 × 10-5 |
Porosity (φ) is the fraction of a material's total volume that consists of void (pore) spaces. It is calculated as φ = Vᵥ / Vₜ, where Vᵥ is the void volume and Vₜ is the total bulk volume. It is often expressed as a percentage and ranges from near 0% (very dense rock) to over 50% (loose sand or gravel).
Darcy's law states that the flow rate Q through a porous medium equals k·A·ΔP / (μ·L), where k is permeability, A is cross-sectional area, ΔP is the pressure drop, μ is dynamic viscosity, and L is sample length. Rearranging gives k = Q·μ·L / (A·ΔP), allowing permeability to be determined from measured flow data.
k is the intrinsic permeability of the porous medium, measured in m² or in darcies. It quantifies how easily a fluid flows through the material, independent of the fluid's properties. Higher k values mean the medium allows fluid to pass through more readily.
Porosity describes how much empty space exists within a material (its capacity to store fluid), while permeability describes how easily a fluid can flow through that material (its ability to transmit fluid). A material can have high porosity but low permeability if the pores are not well connected — for example, pumice stone.
Darcy velocity (also called specific discharge) is defined as q = Q / A — the flow rate divided by the total cross-sectional area of the sample. It is not the actual velocity of fluid through the pores (which would be higher), but a useful bulk flux parameter that simplifies porous media flow calculations.
Soil permeability varies widely by type. Gravel can have permeability of 10⁻⁸ to 10⁻⁶ m², sandy soils range from 10⁻¹² to 10⁻⁹ m², silts are around 10⁻¹⁵ to 10⁻¹² m², and clays can be as low as 10⁻²⁰ m². In practical units, reservoir rocks in petroleum engineering are typically measured in millidarcies (1 mD ≈ 9.87×10⁻¹⁶ m²).
Soil porosity depends on grain size, packing, and compaction. Loose sands typically have porosity of 25–50%, clay soils 40–70%, and consolidated sandstone 5–30%. Compact crystalline rocks may have porosity below 1%, while highly fractured rocks or gravel can exceed 30%.
Henry Darcy originally verified his law through experiments on sand-filled columns in Dijon, France in 1856. Since then, it has been extensively confirmed in groundwater aquifer studies, petroleum reservoir testing, and laboratory permeameter experiments worldwide. It remains valid for slow (laminar) flow conditions where the Reynolds number is low, typically Re < 1 for porous media.