Math Checkup: Converting Units of Area and Volume

Converting units of volume is necessary when calculating volumes of concrete.  For example, if you measure dimensions of concrete in feet and inches, you need to calculate volume in decimal inches, and convert to cubic yards.  Concrete is not ordered in cubic feet.  Similarly, millimetres need to be converted to metres because concrete is ordered in cubic metres.  Finally, it may be necessary to convert cubic metres to cubic yards or cubic yards to cubic metres.

Remember, the volume of a right rectangular prism (box) is the length X width X height.

Example Convert Cubic Feet to Cubic Yards

In general, when converting any cubic measurement to another cubic measurement, use the linear conversion cubed.

For example, a box 3 ft by 3 ft by 3 ft has a volume of 27 ft³.  The same box, with measurement in yards is 1 yd by 1 yd by 1 yd has a volume of 1 yd³.  To convert a unit of volume, you must convert each dimensional measurement.  That is, convert 3 ft to yards for each side.

Alternatively, you can take the final volume in ft³ and divide by 3³ or 27.

Convert 45.678 ft³ to yd³:

Using your calculator, it is a shortcut to use the  button.  Press 3, followed by , followed by .

Example Calculate Volume in Imperial

To calculate a volume, all dimensions must be expressed in decimal form first.

Calculate the volume:

First, convert all dimensions to decimal feet:

Multiply the dimensions in decimal feet to get a volume in cubic feet:

Convert the measurement in cubic feet to cubic yards:

Calculate the volume:

Convert all the measurements to metres:

Multiply the dimensions in metres to get the final volume in metres cubed: