Cube: side³. Box: length × width × height. Cylinder: π × r² × h. Sphere: 4/3 × π × r³. Cone: 1/3 × π × r² × h.
Volume is the amount of three-dimensional space an object occupies — how much it can hold, or how much material it contains. It is measured in cubic units: cubic centimetres (cm³), cubic metres (m³), cubic inches, or litres for liquids (1 litre = 1,000 cm³). A volume calculator applies the right geometric formula for each shape instantly, so you don't have to memorise five different equations or fumble with π on a hand calculation.
Volume calculations are everywhere: concrete for a foundation, water for a swimming pool or fish tank, soil for a garden bed, the capacity of a cylindrical storage tank, or the displacement of a grain silo.
| Shape | Formula | What to measure |
|---|---|---|
| Cube | V = s³ | One side length (s) |
| Rectangular box | V = l × w × h | Length, width, height |
| Cylinder | V = π × r² × h | Radius (r) and height (h) |
| Sphere | V = ⅔ × π × r³ | Radius (r) |
| Cone | V = ⅓ × π × r² × h | Radius (r) and height (h) |
Notice the elegant pattern: a cone holds exactly one-third the volume of a cylinder with the same base and height, because Vcone = (1/3)πr²h while Vcylinder = πr²h. And the sphere formula is no coincidence either — a sphere's volume is exactly two-thirds of the cylinder that encloses it, a result Archimedes was so proud of that he had it carved on his tomb.
How much water does a cylindrical tank with radius 3 m and height 5 m hold?
Volume is the amount of three-dimensional space an object occupies, measured in cubic units.
Multiply π by the radius squared and then by the height: V = π × r² × h.
