How it works
Each shape has its own volume formula, but they share a common idea: multiply a cross-sectional area by a length, or in the case of a sphere, integrate that idea across every possible slice. Picking a shape swaps in the fields and formula that apply to it.
Cube: V = side³
Box: V = length × width × height
Cylinder: V = π × radius² × height
Sphere: V = (4/3) × π × radius³
Cone: V = (1/3) × π × radius² × height
Worked example
A cylinder with radius 3 and height 5.
- Square the radius: 3² = 9.
- Multiply by π: π × 9 = 28.27.
- Multiply by height: 28.27 × 5 = 141.37.
The cylinder's volume is 141.37.
Common questions
Why does a cone use ⅓ but a cylinder doesn't?
A cone tapers to a point, so on average it only fills about a third of the cylinder that shares its base and height — you can verify this by pouring water from a cone into a same-sized cylinder three times. A cylinder keeps the same cross-section all the way up, so it needs no such correction.
What if my shape isn't listed?
Many real objects can be approximated by combining these five basic shapes — a pill-shaped tank is a cylinder plus two half-spheres, for instance. For a shape that genuinely doesn't decompose this way, a more specialised formula is needed.
Why is there no unit conversion here?
These are pure geometric formulas — the answer scales directly with whatever unit you measured in, cubed. For construction-specific volume with imperial/metric switching and material quantities, see the Cubic Yard, Concrete or Gravel calculators.