Multiply the
three sides.
The volume of a rectangular box is the product of its length, width, and height — provided all three are in the same unit. That's the whole story.
Why it works.
A rectangular box (also called a cuboid or rectangular prism) is built from a base of area l × w stacked to a height of h. Picture a stack of identical paper sheets: each sheet has area length × width, and you stack h sheets to fill the box.
The total enclosed space — the volume — is therefore (l × w) × h, which is the same as l × w × h.
The result is always in cubic units — cubic centimeters, cubic inches, cubic meters — because you've multiplied three lengths together.
Try the math by hand.
Watch the substitution, step by step
Type three numbers below and the formula will substitute them one symbol at a time. This is how to think about it on paper.
1 · A shoebox
A shoebox is 30 cm long, 20 cm wide, and 15 cm high.
V = 9,000 cm³
V = 9 liters
2 · An aquarium
A tank measures 90 cm × 45 cm × 50 cm.
V = 202,500 cm³
V ≈ 53.5 US gallons
3 · A shipping box
A package is 18 in × 12 in × 10 in.
V = 2,160 in³
V = 1.25 ft³
4 · Mixed units
A crate is 2 ft × 50 cm × 18 in. Convert all to cm first.
18 in = 45.72 cm
V = 60.96 × 50 × 45.72
V ≈ 139,355 cm³
Volume unit conversions.
| From | To | Multiply by |
|---|---|---|
| 1 m³ | cm³ | 1,000,000 |
| 1 m³ | liters | 1,000 |
| 1 m³ | ft³ | 35.3147 |
| 1 m³ | US gallons | 264.172 |
| 1 ft³ | in³ | 1,728 |
| 1 ft³ | liters | 28.3168 |
| 1 ft³ | US gallons | 7.4805 |
| 1 liter | cm³ | 1,000 |
| 1 liter | US gallons | 0.2642 |
| 1 US gallon | UK gallons | 0.8327 |
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