How to calculate volume for any shape

Start with the right measurements

Measure inside dimensions for capacity, outside dimensions for the space an object takes up. For round things, measuring across (the diameter) is easier than finding the center, so measure across and halve it.

Write every measurement in the same unit before multiplying. 3 feet 6 inches is 3.5 feet, not 3.6.

Worked example: a raised garden bed

A bed 8 ft long, 4 ft wide and 10 inches deep holds 8 × 4 × 0.833 = 26.7 cubic feet. Divide by 27 to get 0.99 cubic yards. Soil companies sell in whole or half yards, so order 1 cubic yard, or 1.1 to allow for settling.

Worked example: a round pool

An above-ground pool 15 ft across filled to 48 inches holds π × 7.5² × 4 = 707 cubic feet, which is 707 × 7.48 = 5,288 gallons. That number tells you how much chlorine or shock to add, since doses are given per 10,000 gallons.

Worked example: a carton for a courier

A box 20 × 14 × 10 inches is 2,800 cubic inches. Divided by 139 that is 20.1, so the carrier bills 21 lb even if the box weighs 8 lb. A smaller box that fits the item more tightly can cut the shipping price noticeably.

Common mistakes

• Using the diameter as the radius, which makes a cylinder four times too big.
• Mixing inches and feet in one multiplication.
• Forgetting that US and imperial gallons are different sizes.
• Using outside tank dimensions, which overstates capacity by the wall thickness.