Pharmaceutics

Porosity Calculator

Calculates the porosity (ε), void fraction and solid fraction of a powder, granule or tablet from its densities or volumes.

Porosity

Enter the true and bulk density to see the porosity.

Inputs

True density (ρ_true)

g/mL

Density excluding pores (helium pycnometry).

Bulk density (ρ_bulk)

g/mL

Mass ÷ bulk volume, including voids. Must not exceed the true density.

Try a sample material

Porosity scale

0–10%Very Low

10–25%Low

25–40%Medium

40–60%High

60–100%Very High

ε = (1 − ρ_bulk / ρ_true) × 100%

ε = (V_total − V_solid) / V_total × 100%

ε = porosity; ρ_bulk and ρ_true = bulk and true density (same units); V_total = bulk volume of the sample; V_solid = volume of the solid alone.

Void fraction is porosity as a fraction (ε ÷ 100), and solid fraction is what is left (1 − void fraction). Both methods give the same answer for the same sample, because bulk ÷ true density equals solid ÷ total volume.

When you'd use this

A micromeritics practical gives you the helium-pycnometer (true) density of a powder and its poured bulk density, and asks for the porosity of the powder bed.

You have measured a tablet's diameter and thickness, weighed it, and want its porosity to explain why it disintegrates faster or slower than another batch.

Comparing granules before and after a change in granulation or compression force, where a drop in porosity points to a denser, harder product.

Checking a reported porosity in a lab record: entering the two densities or volumes shows whether the stated figure follows from them.

Worked example: porosity of a granule bed from its densities

Granules prepared for tableting have a true density of 1.48 g/mL (helium pycnometer). A weighed sample poured gently into a measuring cylinder gives a bulk density of 0.68 g/mL. What is the porosity of the bed? (Illustrative values for a practical.)

True density, ρ_true: 1.48 g/mL
Bulk density, ρ_bulk: 0.68 g/mL
Calculator mode: Density Method

Write the equation
ε = (1 − ρ_bulk ÷ ρ_true) × 100%
Ratio of the densities (the solid fraction)
0.68 ÷ 1.48 = 0.4595
Porosity
ε = (1 − 0.4595) × 100 = 54.05 %
Void and solid fractions
Void fraction = 54.05 ÷ 100 = 0.5405 Solid fraction = 1 − 0.5405 = 0.4595

Porosity ε = 54.05 % (void fraction 0.5405, solid fraction 0.4595).

The calculator prints 54.05 % and classes it as High Porosity. Just over half of the bed's volume is air — mostly the spaces between granules, because a poured bulk density counts those voids. Tapping the cylinder would raise the bulk density and lower this figure, so always state which bulk density you used.

Worked example: porosity of a compressed tablet from its volumes

A flat-faced tablet measures 10.0 mm in diameter and 3.60 mm thick, weighs 0.360 g, and is made from a blend with a true density of 1.50 g/cm³. What is its porosity? (Illustrative values for a practical.)

Total (bulk) volume, V_total: π × 0.50² × 0.360 cm³ = 0.2827 → entered as 0.283 mL
Solid volume, V_solid: 0.360 g ÷ 1.50 g/cm³ = 0.240 mL
Calculator mode: Volume Method

Tablet volume from its dimensions (1 cm³ = 1 mL)
V_total = π r² h = π × (0.50 cm)² × 0.360 cm = 0.2827 cm³ ≈ 0.283 mL
Volume of the solid alone
V_solid = mass ÷ true density = 0.360 ÷ 1.50 = 0.240 mL
Write the equation
ε = (V_total − V_solid) ÷ V_total × 100%
Substitute
ε = (0.283 − 0.240) ÷ 0.283 × 100 = 0.043 ÷ 0.283 × 100 = 15.19 %
Void and solid fractions
Void fraction = 0.1519 Solid fraction = 1 − 0.1519 = 0.8481

Porosity ε = 15.19 % (void fraction 0.1519, solid fraction 0.8481).

The calculator prints 15.19 % and classes it as Low Porosity, a typical range for a compressed tablet. Rounding V_total to 0.283 mL matters: with the unrounded 0.2827 mL the porosity is 15.12 %, so carry enough figures from your measurements. A solid fraction of 0.85 is also called the tablet's relative density.

Density CalculatorWork out the true or bulk density from a mass and a volume before entering them here.Powder Flowability CalculatorUse the same bulk density with the tapped density to judge how the powder flows.

References

Sinko PJ, editor. Martin's Physical Pharmacy and Pharmaceutical Sciences. 8th ed. Philadelphia: Wolters Kluwer; 2023.
Aulton ME, Taylor KMG, editors. Aulton's Pharmaceutics: The Design and Manufacture of Medicines. 6th ed. Edinburgh: Elsevier; 2022.

Common questions

Use whichever you measured. Densities are the usual route for powders (true density from a pycnometer, bulk density from a cylinder); volumes suit a tablet or compact whose dimensions and solid volume you know.

They are the same quantity in different forms: porosity is a percentage (40%), void fraction is the fraction (0.40). Solid fraction, sometimes called relative density, is 1 minus the void fraction.

Open pores let fluid into the particle or tablet, speeding disintegration and dissolution. But a very porous powder is usually light and fluffy, packs unevenly and flows poorly.

No. In each formula the units cancel, so any unit works as long as both densities, or both volumes, use the same one.

Prepared by the PharmaWallah student team. Verify results with your textbook or instructor. Report an error · Editorial policy