Volume of a Cube and a Cuboid: Quick Guide

The volume of a cuboid formula is V = l × w × h. A cube is a cuboid with equal sides, so its volume is V = a³.

Example 1: a shoebox

A box is 30 cm long, 20 cm wide and 12 cm tall.

• V = l × w × h
• V = 30 × 20 × 12
• V = 7,200 cm³ = 7.2 liters

Example 2: a cube

A cube has sides of 5 cm.

• V = a³
• V = 5 × 5 × 5
• V = 125 cm³

Example 3: a fish tank in liters

A tank is 60 cm × 30 cm × 40 cm. How many liters does it hold?

• V = 60 × 30 × 40 = 72,000 cm³
• Litres = 72,000 ÷ 1,000 = 72 L

Example 4: find a missing side

A box holds 480 cm³. It is 10 cm long and 8 cm wide. How tall is it?

• 480 = 10 × 8 × h
• 480 = 80 × h
• h = 6 cm

Cuboid or rectangular prism?

In the United States a cuboid is usually called a rectangular prism. It is the same shape, a box with six rectangular faces, so the volume of a rectangular prism uses the same formula: V = l × w × h.

Example 5: a moving box in cubic feet

A moving box is 18 in long, 18 in wide and 24 in tall. What is its volume in cubic feet?

• V = 18 × 18 × 24 = 7,776 in³
• 1 ft³ = 12 × 12 × 12 = 1,728 in³
• V = 7,776 ÷ 1,728 = 4.5 ft³

Example 6: soil for a raised garden bed

A raised bed is 8 ft long, 4 ft wide and 1 ft deep. How much soil does it need?

• V = 8 × 4 × 1 = 32 ft³
• Soil is often sold by the cubic yard: 1 yd³ = 27 ft³
• 32 ÷ 27 ≈ 1.19 yd³, so buy about 1¼ cubic yards

Common mistakes

• Mixing units: convert every length to the same unit before you multiply.
• Forgetting the cube: volume is in cubic units, such as cm³, in³ or ft³, never cm or cm².
• Confusing volume and surface area: volume is the space inside; surface area is the outside, 2(lw + lh + wh).

Surface area formulas are on the cuboid formulas and cube formulas pages.