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Geometry

Volume of a box (cuboid)

Length times width times height: the space inside a rectangular box.

V=lwh
Cube of side sV=s3

Calculator

The live calculator needs JavaScript. The worked example below shows the same steps it would.

See it move

l = 5w = 3h = 2
  • Volume = lwh = 30
  • Surface area = 2(lw + lh + wh) = 62
  • Space diagonal = √(l² + w² + h²) = 6.1644

What the symbols mean

V
the volume, in cubic units (cm³, m³)
l
the length
w
the width
h
the height

When to use it

Use it for rooms, boxes, tanks, shipping containers, bricks and anything with rectangular faces. 1 litre is 1000 cm³ and 1 m³ is 1000 litres, so a tank's capacity follows straight from its volume.

Worked example

A box is 5 cm long, 3 cm wide and 2 cm high. What is its volume? (l = 5, w = 3, h = 2)

  1. Start from the formula.

    V=l⁢w⁢h

  2. Substitute l = 5, w = 3, h = 2 and work it out.

    V=5·3·2
    =15·2
    =30

Answer V = 30 cm³

Why it works

Each layer of the box holds l×w unit cubes, and there are h layers.

Common mistakes

  • Mixing units, such as metres and centimetres, in the same product.
  • Converting cubic units like plain ones: 1 m³ is 1,000,000 cm³, not 100.