Converting Units of Volume

Property To convert units of volume, you must convert the units for length, width, and height. This requires multiplying by the unit ratio three times, once for each of the three dimensions. You can also cube the unit ratio. $$ \left(\frac{1 \text{ ft}}{12 \text{ in}}\right)^3 = \frac{1 \text{ ft}^3}{1728 \text{ in}^3} $$.

Examples Convert 3 cubic yards to cubic feet: $3 \text{ yd}^3 \cdot \left(\frac{3 \text{ ft}}{1 \text{ yd}}\right)^3 = 3 \text{ yd}^3 \cdot \frac{27 \text{ ft}^3}{1 \text{ yd}^3} = 81 \text{ ft}^3$.

Convert 5000 cubic millimeters to cubic centimeters: $5000 \text{ mm}^3 \cdot \left(\frac{1 \text{ cm}}{10 \text{ mm}}\right)^3 = 5000 \text{ mm}^3 \cdot \frac{1 \text{ cm}^3}{1000 \text{ mm}^3} = 5 \text{ cm}^3$.