Carr index
The Carr index (also: Carr's index or Carr's Compressibility Index) is an indication of the compressibility of a powder. It is named after the scientist Ralph J. Carr, Jr. The Carr index is calculated by the formula formula_1, where formula_2 is the freely settled bulk density of the powder, and formula_3 is the tapped bulk density of the powder after "tapping down". It can also be expressed as formula_4. The Carr index is frequently used in pharmaceutics as an indication of the compresiblity of a powder. In a free-flowing powder, the bulk density and tapped  density would be close in value, therefore, the Carr index would be small. On the other hand, in a poor-flowing powder where there are greater interparticle interactions, the difference between the bulk and tapped density observed would be greater, therefore, the Carr index would be larger. A Carr index greater than 25 is considered to be an indication of poor flowability, and below 15, of good flowability. Another way to measure the flow of a powder is the Hausner ratio, which can be expressed as formula_5. Both the Hausner ratio and the Carr index are sometimes criticized, despite their  relationships to flowability being established empirically, as not having a strong theoretical basis. Use of these measures persists, however, because the equipment required to perform the analysis is relatively cheap and the technique is easy to learn.