# Volume fraction

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In chemistry, the volume fraction φi is defined as the volume of a constituent Vi divided by the volume of all constituents of the mixture V prior to mixing:[1]

$\phi_i = \frac {V_i}{\sum_j V_j}$

Being dimensionless, its unit is 1; it is expressed as a number, e.g., 0.18. It is the same concept as volume percent (vol%) except that the latter is expressed with a denominator of 100, e.g., 18%.

The volume fraction coincides with the volume concentration in ideal solutions where the volumes of the constituents are additive (the volume of the solution is equal to the sum of the volumes of its ingredients).

The sum of all volume fractions of a mixture is equal to 1:

$\sum_{i=1}^{N} V_i = V ; \qquad \sum_{i=1}^{N} \phi_i = 1$

The volume fraction (percentage by volume, vol%) is one way of expressing the composition of a mixture with a dimensionless quantity; mass fraction (percentage by weight, wt%) and mole fraction (percentage by moles, mol%) are others.

## References

1. ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "volume fraction".