How to Calculate Volume
Formulas for every common 3D shape — and the difference between a US gallon and a UK gallon.
Key formulas: Cube = s³. Rectangular box = l × w × h. Cylinder = πr²h. Sphere = (4/3)πr³. Cone = (1/3)πr²h. Example: cylinder radius 5 cm, height 12 cm → Volume = π × 25 × 12 = 942.5 cm³ ≈ 0.94 litres.
Step-by-Step: Volume of a Cylinder
A cylinder needs the radius of its circular base and its height. Example: radius = 5 cm, height = 12 cm.
The volume of a cylinder = π × r² × h, where r is the base radius and h is the height.
Plug in the numbers: π × 5² × 12 = π × 25 × 12 = 942.5 cm³.
1 litre = 1,000 cm³, so 942.5 cm³ ≈ 0.94 litres.
Volume Formulas
| Shape | Formula | Variables | Example |
|---|---|---|---|
| Cube | s³ | s = side length | s=4m → V=64 m³ |
| Rectangular prism | l × w × h | l=length, w=width, h=height | 3×4×5 = 60 m³ |
| Cylinder | πr²h | r=radius, h=height | r=3, h=10 → 282.7 cm³ |
| Sphere | (4/3)πr³ | r=radius | r=5 → 523.6 cm³ |
| Cone | (1/3)πr²h | r=base radius, h=height | r=3, h=9 → 84.8 cm³ |
| Pyramid | (1/3) × base area × h | h=perpendicular height | Square base 4×4, h=6 → 32 m³ |
Liquid Volume: Litres, Gallons, and the US vs UK Difference
One of the most confusing international differences: a US gallon and a UK (imperial) gallon are different amounts.
| Unit | In litres | In US gallons | Used in |
|---|---|---|---|
| 1 US gallon | 3.785 L | 1 gal | USA (fuel, milk) |
| 1 UK (Imperial) gallon | 4.546 L | 1.201 US gal | UK (mostly historical; now litres used for fuel) |
| 1 litre | 1 L | 0.264 US gal | Most of the world |
| 1 US fl oz | 0.02957 L | 1/128 gal | USA (beverages) |
| 1 UK fl oz | 0.02841 L | — | UK (slightly smaller than US fl oz) |
Important: "1 pint" = 0.473 L (US) vs 0.568 L (UK). A UK pint of beer is 20% larger than a US pint.