What is volume?
The volume of a 3D shape measures the space it takes up in three dimensions: length, width AND height. It's the "3D version" of area, which only measures a surface in two dimensions.
Counting unit cubes
The simplest way to understand volume: build a solid shape out of identical small cubes (called "unit cubes"), then count them one by one. Volume is simply the number of unit cubes needed to fill the shape.
A cuboid 3 cubes long, 2 wide and 2 high
3 × 2 × 2 = 12 unit cubes → the volume is 12
The volume of a cuboid
Rather than counting the cubes one by one, you multiply the cuboid's three dimensions directly.
Volume = length × width × height
Example: a cuboid 5 cm long, 3 cm wide and 4 cm high.
5 × 3 × 4 = 60 cm³
- First multiply two dimensions together: 5 × 3 = 15.
- Multiply that result by the third dimension: 15 × 4 = 60.
- Don't forget the cubed unit: 60 cm³.
The volume of a cube
A cube is a very special cuboid: its three dimensions (length, width, height) are all identical. This single dimension is called the cube's side length.
Volume = side × side × side
A cube with a 4 cm side has a volume of: 4 × 4 × 4 = 64 cm³.
Units of volume
Volume is measured in "cubed" units: cm³ (cubic centimetre), m³ (cubic metre)… The small 3 is a reminder that three lengths were multiplied together — just like the small 2 in cm² (for an area) is a reminder that two were multiplied.
Mistakes to avoid
- Forgetting one of the three dimensions and only multiplying two numbers together (which would give an area, not a volume).
- Forgetting the small 3 in the unit (writing cm instead of cm³).
- Mixing units: all the dimensions need to be in the same unit before multiplying.
Worked exercises
What is the volume of a cuboid 6 cm × 4 cm × 2 cm?
What is the volume of a cube with a 5 cm side?
A solid shape is made of 18 unit cubes. What is its volume?
Now it's your turn!
On EasyMaths, your child practises calculating volumes with exercises that never repeat and instant marking.
Start the exercises →Frequently asked questions
What is the formula for the volume of a cuboid?
Volume = length × width × height. You simply multiply the three dimensions of the cuboid together to get its volume.
What is the formula for the volume of a cube?
Volume = side × side × side. Since a cube's three dimensions are all identical, you simply multiply the length of one side by itself three times.
What is the unit for volume?
Volume is measured in "cubed" units: cm³ (cubic centimetre), m³ (cubic metre)… The small 3 is a reminder that three lengths were multiplied together, just like the small 2 in cm² is a reminder that two were multiplied for an area.