The Volume Of A Rectangular Prism Calculator

The formula this calculator uses

V = l x w x h

l

Length — one edge of the base, in the chosen unit

w

Width — the other edge of the base, in the same unit

h

Height — how far the solid rises, in the same unit

V

Volume in cubic units; divide by 1000 to reach litres

How to check the result by hand

1. 1

   Decide whether you need inside or outside measurements

   Capacity questions need internal dimensions; clearance and packing questions need external ones. The 40 x 30 x 20 box only holds 24000 cubic centimetres if those figures are the clear space inside it, because walls, lids and internal fittings all eat into what actually fits. Decide this before measuring, since re-measuring afterwards is far more work than choosing correctly at the start.

2. 2

   Express all three measurements in the same unit

   Length, width and height must share a unit before any multiplication happens. A box quoted as 40 centimetres by 300 millimetres by 0.2 metres is a 40 x 30 x 20 centimetre box, and only in that form does the product mean anything. Converting first is safer than converting the cubic answer, because unit conversions for volume apply the factor three times over.

3. 3

   Multiply length by width to get the footprint, then by height

   The footprint is 40 x 30 = 1200 square centimetres, and raising that layer twenty times gives 1200 x 20 = 24000 cubic centimetres. Splitting the work this way keeps the intermediate number small enough to check by eye, and it makes the counting interpretation of volume obvious.

4. 4

   Convert to litres or gallons if capacity is what you need

   Divide cubic centimetres by 1000 for litres: 24000 / 1000 = 24. Divide by 3785.411784 for US gallons: 24000 / 3785.411784 = 6.34012926. Keep the unrounded value if anything downstream uses it, and remember that an Imperial gallon of 4.54609 litres gives a different count for the same box.

5. 5

   Compute surface area separately, and round once at the end

   Add the three distinct face areas and double: 2 x (1200 + 800 + 600) = 5200 square centimetres. Never report that figure as a volume, and never report the volume as an area. Round the final displayed numbers to a precision the original measurements can support, rather than rounding at each stage and letting the error accumulate.