A volume of a rectangular prism calculator finds how much space a box-shaped object occupies. Rectangular prisms are everywhere: shipping boxes, rooms, aquariums, bricks, and storage containers. Volume answers a different question from area or perimeter. Area covers a surface, perimeter measures an outline, and volume measures the three-dimensional space inside.
The calculation is a direct extension of area. The area of the rectangular base is length times width, and multiplying by height stacks that base through the third dimension. That is why volume uses three lengths and why the result is in cubic units. A box that is 6 units long, 4 units wide, and 3 units high contains 6 x 4 = 24 square units in its base layer, and 3 such layers, for 72 cubic units in total.
What this calculator does
The formula is volume = length x width x height. All three measurements must be in the same unit before multiplying. If length is in metres, width in centimetres, and height in metres, the width must be converted first, or the result will be off by a factor of 100. The calculator below multiplies the three inputs as entered, so unit consistency is the user’s responsibility and the most important check.
Cubic units follow from the inputs: centimetres give cubic centimetres, inches give cubic inches, and metres give cubic metres. Converting between cubic units is not the same as converting linear units. One cubic metre equals 1,000,000 cubic centimetres, because the linear factor of 100 is cubed, not used once.
Formula
Volume = length x width x height, with all three lengths in the same unit. Result is in cubic units.
How to use it
- Measure length, width, and height of the prism.
- Convert all three to the same unit if they differ.
- Multiply length by width to get the base area.
- Multiply the base area by height to get volume.
- Label the result in cubic units and check that it is larger than any single dimension product that omits a dimension.
Try the calculator
Worked example
Find the volume of a rectangular prism with length 6 units, width 4 units, and height 3 units. Base area = 6 x 4 = 24 square units. Volume = 24 x 3 = 72 cubic units. As a check, the prism can be thought of as 3 layers, each containing 24 unit cubes, for 3 x 24 = 72 unit cubes in total. That layer picture confirms the multiplication and shows why volume counts cubes, not squares.
A second example with different units in mind: a box 2 metres long, 1.5 metres wide, and 1 metre high has volume 2 x 1.5 x 1 = 3 cubic metres. If the same box were measured in centimetres, 200 x 150 x 100 = 3,000,000 cubic centimetres, which is the same volume expressed differently, since 1 cubic metre = 1,000,000 cubic centimetres.
How to check your answer
Count unit cubes in layers if possible. Layers times cubes per layer must equal the volume.
Check unit consistency before multiplying. Mixed units are the most common error.
Compare volume with base area. Volume must be base area times height, so a volume smaller than base area with height greater than 1 signals an error.
Common mistakes
- Multiplying only two dimensions and reporting an area as a volume.
- Mixing units, such as metres for length and centimetres for width, without converting.
- Confusing volume with surface area, which for a prism is 2(lw + lh + wh), a different formula.
- Forgetting that cubic conversion factors are cubed, not linear.
Frequently asked questions
What is the difference between volume and capacity?
Volume is the space an object occupies. Capacity is how much a container can hold, which is closely related but may subtract wall thickness or unusable space.
Do length, width, and height have to be in a particular order?
No. Multiplication is commutative, so any order gives the same volume, as long as all three are in the same unit.
How do I convert cubic metres to cubic centimetres?
Multiply by 1,000,000, because 1 metre = 100 centimetres and 100^3 = 1,000,000. Linear conversion factors must be cubed for volume.
