The Carr Index and the Hausner Ratio are both meant as being indicators of the flowability of bulk solids. The flowability of solids is complex and linked to many parameters, it is thus not always obvious to characterize the solid flowability with the few set of data that Engineers usually have in hand during design or troubleshooting.

Both Carr and Hausner attempted just that : assuming that the compressibility of a solid is related to its flowability, they proposed to measure the bulk and tapped density of bulk materials and calculate a ratio in order to estimate how the material will flow.

The lower the Carr Index or Hausner Ratio, the more flowable is a material.

The Carr's Index of a material is calculated with the following formula :

Carr_Index = (ρtapped-ρbulk)/ρtapped*100

With

ρtapped : the tapped bulk density of the material (kg/m3) ρbulk : the loose bulk density of the material (kg/m3)

It is possible to relate the Carr's Index and the Hausner ratio with the following formula :

H = 100/(100-Carr_Index)

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The Hausner Ratio of a material is calculated with the following formula :

H = ρtapped/ρbulk

With

There are other methods to define the flowability of powders or granules (click for more infos) :

The flowability of a bulk solids is estimated by 1st calculating the ratio, then referring to the table below to determine in which class is the powder studied :

The table was determined by the authors of the method, by testing different material flowability, and calculating the compressibility ratio associated.

Note that Carr's Index and Hausner Ratio are approximate methods, the characterization of the flowability and the determination of physical parameters allowing the design of hoppers would require more measurement using powder rheometers or full shear cell testing.

An Engineer wishes to have an idea of the probable flowability of a powder. He measures the bulk loose density as 600 kg/m3 and the tapped density as 660 kg/m3. He can then calculate the Carr Index :

Carr_Index = (ρtapped-ρbulk)/ρtapped*100 = (660-600)/660*100 = 9.1

Refering to the table above, the Engineer concludes the powder is probably free flowing.

With the data above, the Engineer also wishes to define the Hausner ratio, he then makes the following calculation :

H = ρtapped/ρbulk = 660/600 = 1.1

The table above is also used, the powder is indeed probably free flowing.

Please access here the Free Excel calculator for Carr Index and Hausner ratio : calculator download (click here)