Carr Index ⃒ Hausner Ratio
How is Carr Index calculated ? What is Carr's Index ? What is Carr's index formula ?
How is Hausner ratio calculated ? What is Hausner ratio ? What is Hausner ratio formula ?
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| Section summary |
|---|
| 1. Powder
flowability characterization : Carr Index and Hausner
Ratio |
| 2. Calculation
formula of Carr Index |
| 3. Calculation
formula of the Hausner Ratio |
| 4. Interpretation and relation to flowability of Carr index and Hausner Ratio |
| 5. Carr Index and Hausner ratio Excel calculation tool |
1. Powder flowability characterization : Carr Index and Hausner
Ratio
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.
Interactive Powder Flowability Estimator
FOR PRELIMINARY ESTIMATION ONLY — ALWAYS CONSULT A REPUTABLE SUPPLIER1. Angle of Repose Sizer
Calculated Angle: - °
Flowability Class: -
2. Density Compressibility Sizer
Carr Index: - %
Hausner Ratio: -
Flowability Class: -
2. Calculation formula of Carr Index
How to calculate the Carr Index ? What is Carr's index formula ?
The Carr's Index of a material is calculated with the following formula :
Carr's Index 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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3. Calculation formula of the Hausner Ratio
How to calculate the Hausner Ratio ? What is the Hausner Ratio formula ?
The Hausner Ratio of a material is calculated with the following formula :
Hausner ratio formula
H = ρtapped/ρbulk
With
H : Hausner Ratioρtapped : the tapped bulk density of the material (kg/m3)
ρbulk : the loose bulk density of the material (kg/m3)
There are other methods to define the flowability of powders or granules (click for more infos) :
4. Interpretation and relation to flowability of Carr index and Hausner Ratio
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 :
| Flowability expected | Hausner Ratio | Carr's Index |
| Excellent / Very Free Flow | 1.00 - 1.11 | <10 |
| Good / Free Flow | 1.12 - 1.18 | 11-15 |
| Fair | 1.19 - 1.25 | 16-20 |
| Passable | 1.26 - 1.34 | 21-25 |
| Poor Flow / Cohesive | 1.35 - 1.45 | 26-31 |
| Very Poor Flow / Very Cohesive | 1.46 - 1.59 | 32-37 |
| Approximatively no flow | > 1.60 | > 38 |
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.
Example of calculation of Carr Index
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.
Example of calculation of Hausner Ratio
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.
5. Carr Index and Hausner ratio Excel calculation tool
Please access here the Free Excel calculator for Carr Index and Hausner ratio : calculator download (click here)
Download Powder Flowability Excel Sizing Spreadsheet
Get the professional bulk testing template offline. Evaluate both Angle of Repose and Compressibility Ratios (Carr Index, Hausner ratio) with built-in standard flowability rating comparisons.
Frequently Asked Questions (FAQ)
What is the difference between the Carr Index and the Hausner Ratio?
The Carr Index measures the compressibility percentage of a bulk solid, while the Hausner Ratio is the direct proportion of tapped density to loose density. Although both indicators are derived from the exact same loose bulk and tapped bulk density measurements, the Carr Index evaluates flowability on a scale from 0 to 100 percent, whereas the Hausner Ratio runs from 1.00 upward to represent cohesive structural consolidation.
How do you calculate the Carr Index of a powder?
To calculate the Carr Index, subtract the loose bulk density from the tapped bulk density, divide the result by the tapped density, and multiply by 100. This ratio, also called the compressibility index, establishes how easily a bulk solid collapses under tapping. A high index (e.g., above 25%) indicates a cohesive powder with poor flow properties, while a low index (e.g., below 15%) indicates a free-flowing, stable material.
What is the relation between the Carr Index and the Angle of Repose?
Both the Carr Index and the Angle of Repose are indicators of powder flowability, where lower values represent superior powder flow and higher values represent cohesive behaviors. Generally, a powder with an excellent Carr Index of less than 10% will form a flat pile with an angle of repose between 25 and 30 degrees, while a cohesive, non-flowing powder with a Carr Index above 32% will stack steeply, forming an angle greater than 55 degrees.