Pharmaceutics
Powder Flowability Index Calculator
Works out Carr's index and the Hausner ratio from a powder's bulk and tapped density, and says how well it will flow.
Carr's index
Enter the bulk and tapped density to see Carr's index and the Hausner ratio.
Powder density values
Mass of powder divided by its bulk (poured, untapped) volume.
Mass of powder divided by its tapped volume. Always higher than bulk density.
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Flowability scale
Carr's index bands used to describe powder flow.
Carr's Index = (ρₜ − ρᵦ) / ρₜ × 100
Hausner Ratio = ρₜ / ρᵦ
ρₜ = tapped density, ρᵦ = bulk density (both in the same units, e.g. g/mL).
Both numbers describe the same thing — how much the powder consolidates when tapped. Carr's index expresses the loss of volume as a percentage; the Hausner ratio expresses it as a ratio. A free-flowing powder barely settles, so its index is low and its ratio is close to 1.
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References
- Aulton ME, Taylor KMG, editors. Aulton's Pharmaceutics: The Design and Manufacture of Medicines. 6th ed. Edinburgh: Elsevier; 2022.
- Sinko PJ, editor. Martin's Physical Pharmacy and Pharmaceutical Sciences. 8th ed. Philadelphia: Wolters Kluwer; 2023.
Common questions
Pour a weighed amount of powder gently into a graduated cylinder and read the volume — mass ÷ that volume is the bulk density. Then tap the cylinder a set number of times (USP uses a mechanical tapper, typically 500–1250 taps) until the volume stops changing; mass ÷ the tapped volume is the tapped density.
No. Both formulas divide one density by the other, so the units cancel. Any unit works as long as both values use the same one.
Tapping removes air from between particles, so the same mass occupies less volume and the density can only rise. Equal or reversed values usually mean the two readings were swapped or mistyped.
The powder is cohesive and will flow unevenly, causing tablet or capsule weight variation. Adding a glidant such as colloidal silica, or granulating the powder, are the usual fixes.
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