Formula and Method for Porosity and Permeability
Porosity (φ) is the fraction of a soil, sediment, or rock sample's total volume that is empty pore space — it tells you how much fluid the material can store. Permeability (k) measures how easily that pore space lets fluid flow through the material — it tells you how well the pores are connected. This calculator finds porosity from dry bulk density and grain (particle) density, φ = 1 − (ρb / ρs), then estimates intrinsic permeability from that porosity and the mean grain diameter using the Kozeny-Carman equation, k = φ³d² / [180(1 − φ)²].
How porosity is calculated
Dry bulk density (ρb) is the mass of dried soil or rock divided by its total volume, including pores — it is always lower than the grain (particle or mineral) density (ρs), which is the mass of the solid material alone divided by the volume of solids only (commonly about 2.65 g/cm³ for quartz-dominated sand or soil). Because the solid fraction of the sample is ρb/ρs, the void fraction — porosity — is the remainder: φ = 1 − (ρb/ρs). The calculator also reports the void ratio, e = φ/(1 − φ), the ratio of void volume to solid volume that geotechnical engineers use alongside porosity.
Estimating permeability with the Kozeny-Carman equation
Permeability cannot be derived from porosity alone — two materials with identical porosity can have very different permeability depending on how large and how well-connected the pores are. The Kozeny-Carman equation is a widely used semi-empirical model that adds grain size to porosity to estimate the intrinsic permeability of granular media: k = φ³d² / [180(1 − φ)²], where d is the mean grain diameter (converted to meters before use) and k comes out in square meters. The calculator also converts k to millidarcy (mD), the practical unit used in petroleum engineering and hydrogeology, using 1 darcy ≈ 9.869 × 10⁻¹³ m².
Assumptions and limitations
The Kozeny-Carman equation assumes roughly uniform, spherical grains, laminar (Darcy) flow, and that essentially all of the measured porosity is interconnected and contributes to flow. Real soils and rocks with angular grains, poor sorting, clay content, or cementation can deviate from this estimate by an order of magnitude or more, and some pore space (like isolated vugs or clay-bound water) may not conduct fluid at all. Treat the result as a reasonable first estimate for clean, unconsolidated sand-like material — for engineering design or reservoir work, confirm with a laboratory permeameter test or field pumping test.