Volume calculator
Volume of eight common solids, with the formula, and the answer in cubic units, litres and US gallons.
Volume formulas
| Solid | Formula |
|---|---|
| Cube | V = a³ |
| Rectangular box | V = l × w × h |
| Cylinder | V = π r² h |
| Sphere | V = (4/3) π r³ |
| Cone | V = (1/3) π r² h |
| Square pyramid | V = (1/3) a² h |
| Hemisphere | V = (2/3) π r³ |
| Triangular prism | V = ½ b h × l |
One idea behind most of these formulas
Any prism or cylinder is its base area stacked up to its height: V = base area × height. A box is a rectangle stacked, a cylinder a circle stacked. Anything that tapers to a point (cone, pyramid) holds exactly one third of the matching prism: V = ⅓ × base area × height.
Questions people ask
How do I convert cubic units to litres?
1 litre = 1,000 cm³ = 0.001 m³. One cubic foot is about 28.32 litres. The result box converts to litres and US gallons automatically.
Why is a cone exactly one third of a cylinder?
A cone with the same base and height as a cylinder holds exactly one third as much. Archimedes proved the related result for the sphere: a sphere fills two thirds of the cylinder that just contains it.
How do I find the volume of a tank or pool?
A rectangular pool is a box (length × width × average depth). A round tank is a cylinder. Enter the dimensions in the same unit and read the litres or gallons from the result box.
What if my measurements are in different units?
Convert them to one unit first, for example all in centimetres, then pick that unit. Mixing inches and feet is the most common source of wrong volumes.