Porosity and Permeability Calculator
This calculator solves both porosity and permeability for porous media such as soil, rock, sand, and concrete. Choose between two porosity methods (volume ratio or bulk-density approach) and two permeability methods (Darcy's law from measured flow data, or the Kozeny-Carman equation from grain size and porosity). Results include hydraulic conductivity, specific discharge, and a classification against typical material ranges.
What are porosity and permeability?
Porosity (symbol phi) is the fraction of a material's total volume that is made up of open pore space. It tells you how much fluid a rock, soil, or engineered material can hold. Permeability (symbol k) is a measure of how easily a fluid can flow through that connected pore network under a pressure gradient. High porosity does not guarantee high permeability: clay has a porosity of 40-70% but an extremely low permeability because its tiny pores are poorly connected. Conversely, a fractured granite can have low porosity but high permeability along fracture planes. Together, these two properties govern fluid storage and flow in aquifers, petroleum reservoirs, soil drainage systems, and filtration media.
Porosity methods: volume ratio and bulk density
The volume ratio method is the most direct: porosity = void volume / total volume. You measure both geometrically or by displacement. The density method is preferred when direct volume measurement is difficult: porosity = 1 - (bulk density / grain density). Bulk density is simply the mass of an undisturbed sample divided by its total volume; grain density (also called particle density) is the density of the solid mineral framework only, which is about 2.65 g/cm³ for quartz-rich soils and sedimentary rock. The void ratio (e = phi / (1 - phi)) is widely used in geotechnical engineering because it normalises pore volume against the solid volume rather than the total volume, making it additive when mixing materials.
Permeability: Darcy's law and the Kozeny-Carman equation
Darcy's law (1856) relates the volumetric flow rate Q through a sample to the pressure difference, sample geometry, and fluid viscosity: k = Q * mu * L / (A * delta-P), where mu is dynamic viscosity, L is sample length, A is cross-sectional area, and delta-P is the pressure drop. This gives the intrinsic permeability k in m², which is a property of the porous medium alone, independent of the fluid. One darcy is defined as the permeability that lets 1 cm³/s of 1 cP fluid flow through 1 cm² under 1 atm/cm gradient; in SI units, 1 D = 9.87 x 10⁻¹³ m². When no flow-test data is available, the Kozeny-Carman equation estimates k from grain diameter d and porosity phi: k = d² / 180 * phi³ / (1 - phi)². The phi³ / (1-phi)² factor rises steeply with porosity, which explains why even modest increases in porosity can dramatically raise permeability.
Hydraulic conductivity and specific discharge
Hydraulic conductivity K (m/s) combines the intrinsic permeability k with fluid properties: K = k * rho * g / mu, where rho is fluid density and g is gravitational acceleration. Unlike k, K depends on the fluid, so always specify the fluid when reporting it. Water at 20°C has a viscosity of 1.002 mPa·s and a density of 998 kg/m³; at 0°C the viscosity rises to 1.79 mPa·s, which cuts hydraulic conductivity nearly in half even for the same medium. Specific discharge (the Darcy velocity) is q = Q / A, the volumetric flux per unit cross-sectional area. It is not the actual pore-water velocity, which is higher by a factor of 1/phi because flow only occurs in the fraction phi of the cross-section that is pore space.
Typical porosity and permeability by material
| Material | Porosity range | Permeability range | Typical use |
|---|---|---|---|
| Well-sorted gravel | 25-40% | 100-1,000+ D | Drainage, rapid infiltration |
| Well-sorted sand | 25-50% | 1-100 D | Aquifers, filtration |
| Silt | 35-50% | 0.001-1 D | Fine filtration, seals |
| Clay | 40-70% | <0.001 mD | Aquitards, liners |
| Glacial till | 10-25% | 0.001-0.1 D | Mixed sediment deposits |
| Sandstone | 5-30% | 0.1-1,000 mD | Petroleum reservoirs |
| Limestone/Dolomite | 1-20% | 0.1-100 mD | Karst aquifers |
| Shale | 5-30% | <0.001 mD | Cap rock, seals |
| Granite (unfractured) | 0.1-1.5% | <0.001 mD | Hard rock foundation |
| Pumice | 50-85% | 10-1,000 mD | Volcanic tephra |
| Concrete | 8-15% | 0.001-0.1 mD | Construction material |
Representative values for common geological and engineering materials. Actual values depend on grain sorting, cementation, and depth.
Frequently asked questions
What is the difference between porosity and permeability?
Porosity measures how much empty space is in a material (expressed as a fraction or percentage of total volume). Permeability measures how easily a fluid can flow through the connected pore space under a pressure gradient. A material can be highly porous but nearly impermeable if the pores are isolated, like vesicular basalt, or it can have low porosity but high permeability if fractures create efficient flow paths.
What is Darcy's law and why is it used?
Darcy's law states that the volumetric flow rate through a porous medium is proportional to the pressure gradient and the cross-sectional area, and inversely proportional to fluid viscosity and sample length. Written as Q = kA / (mu * L) * delta-P, it lets you back-calculate permeability k from a measured constant-head or variable-head flow test. It is valid for slow, laminar (Darcian) flow, which applies to most groundwater and petroleum reservoir conditions.
When should I use Kozeny-Carman instead of Darcy's law?
Use the Kozeny-Carman equation when you have no flow-test data but you know the representative grain diameter and the porosity. It is commonly applied to unconsolidated sands and gravels in hydrogeological reconnaissance, filter design, and early-stage reservoir analysis. It can underestimate permeability in well-sorted coarse materials and overestimate it in heterogeneous or cemented media.
What units are used for permeability?
Intrinsic permeability is measured in m² (SI units) or in darcy (petroleum engineering). One darcy equals approximately 9.87 x 10⁻¹³ m². In tight reservoir rocks, millidarcy (mD) and even microdarcy are common. Hydraulic conductivity K, which folds in fluid density and viscosity, is in m/s (or cm/s) and is specific to a particular fluid at a particular temperature.
Why does clay have high porosity but low permeability?
Clay particles are flat plates with a very large surface area relative to their volume. When packed together, the pores between them are extremely small (often less than 1 micrometre). Although those pores make up 40-70% of the clay's volume (giving high porosity), the pore throats are so narrow that viscous drag prevents fluid from moving quickly, so permeability is typically less than a millidarcy. Clay layers serve as natural aquitards and engineered liners precisely because of this combination.