Volume of Cuboids

In a Nutshell

Volume measures the space inside a 3D shape. For a cuboid, multiply the length by the width by the height.

Volume is measured in cubic units such as cm3\text{cm}^3, m3\text{m}^3 or mm3\text{mm}^3. A cuboid (rectangular prism) has three dimensions:

Volume=l×w×h\text{Volume} = l \times w \times h

You can think of it as layers of unit cubes: the base layer has l×wl \times w cubes, and there are hh layers stacked up.

A cube is a special cuboid where all three dimensions are equal, so V=s3V = s^3.

Explore: cuboid volume

Volume of a cuboid A 3D cuboid with length 4 cm, width 3 cm and height 2 cm. Volume = 4 × 3 × 2 = 24 cm³. l = 4 cm w = 3 cm h = 2 cm Volume = 4 × 3 × 2 = 24 cm³

Change the length, width and height, then press Update to see the cuboid and its volume recalculated.

Watch it work

Question: A box is 6 cm6 \, \text{cm} long, 4 cm4 \, \text{cm} wide and 3 cm3 \, \text{cm} tall. Find its volume.

Have a go

Q1. Find the volume of a cuboid with l=5 cml = 5 \, \text{cm}, w=3 cmw = 3 \, \text{cm} and h=2 cmh = 2 \, \text{cm}.

Q2. A cube has side length 4 cm4 \, \text{cm}. Find its volume.

Q3. A fish tank is 60 cm60 \, \text{cm} long, 30 cm30 \, \text{cm} wide and 40 cm40 \, \text{cm} deep. Find its volume in cm3\text{cm}^3.

Q4. The volume of a cuboid is 120 cm3120 \, \text{cm}^3. Its length is 10 cm10 \, \text{cm} and width is 4 cm4 \, \text{cm}. Find the height.

Q5. How many 1 cm1 \, \text{cm} cubes fit inside a box that is 8×5×3 cm8 \times 5 \times 3 \, \text{cm}?