Volume calculator
Volume of 13 solids, from cubes and cylinders to capsules, frustums, spherical caps and pipes, 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 |
| Capsule | V = πr²a + (4/3)πr³ |
| Conical frustum | V = (1/3) π h (r² + rR + R²) |
| Spherical cap | V = (1/3) π h² (3r − h) |
| Ellipsoid | V = (4/3) π a b c |
| Tube (pipe) | V = π (R² − r²) h |
| 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.
How do I calculate volume in gallons?
Work out the volume in cubic units, then convert: 1 US gallon = 231 in³ exactly, so divide cubic inches by 231. From cubic feet, multiply by about 7.48052; from litres, divide by 3.785411784. The result box above shows US gallons for every shape automatically.
How do I calculate volume in cubic feet?
Measure every dimension in feet (convert inches by dividing by 12), choose “ft” as the unit and read the ft³ result. Example: a 10 ft × 12 ft area filled 4 in (0.333 ft) deep is 10 × 12 × 0.333 ≈ 40 ft³, or about 1.48 cubic yards (27 ft³ = 1 yd³).
How do I find the volume of a liquid?
Either measure the container it fills and use the matching shape here (a box for a tank, a cylinder for a drum or pipe, a frustum for a bucket), or read it from a graduated container. Liquid volume is usually quoted in litres, millilitres or gallons rather than cubic units.
How do I find the volume of an irregular object?
Use water displacement: submerge it in a measuring container and read how much the level rises. That rise is the object’s volume (1 mL = 1 cm³). Archimedes is credited with this method.
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.