Volume Percent Calculator

Concentration by Volume

Volume percent (often denoted as %v/v) is heavily used when mixing two liquids together, such as alcohol and water, or different liquid fuels. It expresses the concentration of a solute as a percentage of the total final volume.

A $40\%$ by volume solution of ethanol means that for every $100 \, \text{mL}$ of the final mixture, there is exactly $40 \, \text{mL}$ of pure ethanol.

The Complication of Liquid Mixing

Unlike mass, which is always perfectly additive (10g + 10g always equals 20g), volume is not always additive.

If you mix $50 \, \text{mL}$ of pure water with $50 \, \text{mL}$ of pure ethanol, you will actually end up with about $96 \, \text{mL}$ of total solution, not $100 \, \text{mL}$. This happens because the smaller water molecules physically fit into the empty spaces between the larger ethanol molecules, causing the mixture to shrink slightly.

Therefore, true volume percent must be calculated using the actual final measured volume of the mixture, rather than simply adding the initial volumes together.

The Formula

Example Calculation

You pour $30 \, \text{mL}$ of rubbing alcohol into a beaker, and then add enough water until the final mixture reaches exactly the $150 \, \text{mL}$ mark on the glass.

1. Identify Solute Volume: $30 \, \text{mL}$.
2. Identify Total Final Volume: $150 \, \text{mL}$.
3. Calculate: $(30 / 150) \cdot 100 = \mathbf{20\%}$.

The resulting mixture is $20\%$ rubbing alcohol by volume.