Carr index

The Carr index (Carr's index[1] or Carr's Compressibility Index[2]) 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 ${\displaystyle C=100{\frac {\rho _{T}-\rho _{B}}{\rho _{T}}}}$, where ${\displaystyle \rho _{B}}$ is the freely settled bulk density of the powder, and ${\displaystyle \rho _{T}}$ is the tapped bulk density of the powder after "tapping down". It can also be expressed as ${\displaystyle C=100(1-\rho _{B}/\rho _{T})}$.

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.[3] A Carr index greater than 25 is considered to be an indication of poor flowability, and below 15, of good flowability.[4]

Another way to measure the flow of a powder is the Hausner ratio, which can be expressed as ${\displaystyle H=\rho _{T}/\rho _{B}}$.

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.