Volume Calculator

How the volume of each solid is found

Prisms and cylinders multiply the area of the base by the height. Cones and pyramids take one third of the matching prism or cylinder, and a sphere depends only on its radius.

The pyramid assumes a rectangular base with the apex directly above its center, which is the usual textbook case; its surface area includes the base and the four triangular faces.

Formulas used

Cube = s³
Box = length × width × height
Cylinder = π × r² × h
Sphere = 4⁄3 × π × r³
Cone = ⅓ × π × r² × h
Pyramid = ⅓ × length × width × height

Worked example

A box 5 long, 4 wide and 3 high:

Volume: 5 × 4 × 3 = 60
Surface: 2 × (5×4 + 5×3 + 4×3) = 2 × 47 = 94

5 × 4 × 3 = 60 cubic units.

Assumptions and limits

Solids are exact and solid; walls, slopes and truncated shapes are not modeled.
Liters are shown only for units with a standard capacity equivalent.
Values up to one million are accepted.

Common questions

What is the difference between volume and capacity?

Volume is the amount of space a solid occupies, measured in cubic units, while capacity is how much a container can hold, often given in liters or gallons. One liter equals 1,000 cubic centimeters, which is why the calculator adds liters for common units.

Why does a cone hold one third of a cylinder?

A cone with the same base and height as a cylinder has exactly one third of its volume. The same relationship links a pyramid to a prism with the same base and height.

Your solid

Result