Porosity and Permeability Calculator
Compute porosity permeability using validated scientific equations. See step-by-step derivations, unit analysis, and reference values.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
n = Vv/Vt = 1 - (bulk density / grain density)
Porosity n equals the void volume divided by total volume, or equivalently 1 minus the ratio of bulk density to grain density. Void ratio e = n/(1-n). Permeability is estimated using the Hazen formula K = C * d10^2 for clean sands, or the Kozeny-Carman equation which relates permeability to porosity cubed divided by (1-n) squared times grain diameter squared divided by 180.
Worked Examples
Example 1: Sand Sample Porosity and Permeability
Problem:A 100 cm3 sand sample contains 35 cm3 of void space. Grain density is 2.65 g/cm3, bulk density is 1.72 g/cm3, and mean grain diameter is 0.5 mm.
Solution:Porosity (volume) = 35/100 = 35%\nPorosity (density) = 1 - 1.72/2.65 = 35.1%\nVoid ratio = 0.35/(1-0.35) = 0.538\nHazen K = 0.01 * 0.5^2 = 0.0025 cm/s\nKozeny-Carman K from porosity and grain size.
Result:Porosity = 35%, void ratio = 0.538, moderate sand
Example 2: Clay Soil Porosity Analysis
Problem:A clay sample has grain density 2.70 g/cm3 and bulk density 1.35 g/cm3.
Solution:Porosity = 1 - 1.35/2.70 = 50%\nVoid ratio = 0.5/0.5 = 1.0\nHigh porosity but very low permeability due to small pore sizes.
Result:Porosity = 50%, void ratio = 1.0, high porosity clay
Frequently Asked Questions
What is the difference between porosity and permeability?
Porosity is the fraction of void space in a material relative to its total volume, expressed as a percentage. It describes how much fluid a material can hold. Permeability, on the other hand, measures how easily fluids can flow through the connected pore spaces. A material can have high porosity but low permeability if the pores are not well connected, like clay which has 40 to 60 percent porosity but very low permeability. Conversely, fractured rock may have low porosity but high permeability along the fractures.
How is porosity measured in the laboratory?
There are several methods to measure porosity. The direct method involves saturating a dry sample with water and measuring the volume of water absorbed. The density method calculates porosity from the grain density and bulk density of the sample using the formula n = 1 minus bulk density divided by grain density. Gas pycnometry uses helium gas to measure the true volume of solid grains. For rocks, mercury injection porosimetry forces mercury into pores at increasing pressures to map the pore size distribution and total porosity.
What factors affect the porosity of soil and rock?
Grain size distribution is one of the biggest factors, where well-sorted (uniform) soils have higher porosity than poorly sorted soils because small grains fill the voids between larger ones. Grain shape matters too, as angular grains pack less efficiently than rounded ones, creating more void space. Compaction and cementation reduce porosity over time. Depth of burial increases overburden pressure which compresses pores. Biological activity and root growth can create secondary porosity, while mineral precipitation can reduce it.
How do porosity and permeability relate to groundwater availability?
A good aquifer needs both high porosity and high permeability. Porosity determines the total volume of water that can be stored, while permeability controls how fast that water can be extracted. Specific yield, which is the fraction of water that drains by gravity, is typically 60 to 80 percent of total porosity for sand and gravel aquifers. Clean sand and gravel make excellent aquifers because they have moderate porosity (25 to 40 percent) combined with high permeability, allowing wells to produce large volumes of water sustainably.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy