carr index carr index the carr index (also: carr's index or carr's compressibility index) is an indicator of the compressibility of a powder. it is named after the scientist ralph j. carr, jr. the carr index is calculated by the formula c = 100 ρ t − ρ b ρ t -\rho _ , where ρ b is the freely settled bulk density of the powder, and ρ t is the tapped bulk density of the powder after "tapping down". it can also be expressed as c = 100 ( 1 − ρ b / ρ t ) /\rho _)} . the carr index is frequently used in pharmaceutics as an indication of the compressibility 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 h = ρ t / ρ b /\rho _ . 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.