Volume Calculator
Volume of a cube, box, cylinder, sphere, cone, or pyramid
Frequently Asked Questions
Volume for a cube, box, cylinder, sphere, cone, or pyramid each requires a genuinely different formula — and while volume and surface area are related measurements for the same shapes, they answer fundamentally different questions (space enclosed versus external area), which means the two require entirely separate calculations even for the identical shape and dimensions.
Why each shape's volume formula is structurally different
A cube's volume is simply its side length cubed. A rectangular box multiplies its three distinct edge lengths together. A cylinder's volume is its circular base area multiplied by its height. A sphere's volume uses a distinct formula (4/3 πr³) with no simple base-times-height decomposition, since a sphere has no flat base at all. A cone's volume is exactly one-third of a cylinder with the same base and height — a factor that surprises people who expect a cone to hold roughly half a comparable cylinder's volume rather than a third. A pyramid follows the same one-third relationship relative to a prism with the same base and height. These aren't variations on one universal 3D-volume formula — each shape's specific geometry requires its own distinct derivation.
A worked example
A cone and a cylinder sharing the identical base radius and height don't have a volume relationship of "roughly half" as casual intuition might suggest — the cone's volume is precisely one-third of the cylinder's, a clean mathematical relationship rather than an approximate rule of thumb, and the same one-third relationship holds between any pyramid and a prism sharing its base and height.
How this connects to your other geometry calculations
Volume and surface area are related but distinct measurements for the same three-dimensional shapes — the Surface Area Calculator covers the external-area side of the same shape set this calculator handles for enclosed space, and a complete practical description of a container or solid object typically needs both figures for different purposes (volume for capacity, surface area for material needed to construct or cover it).
Common mistakes
Assuming a cone holds roughly half the volume of a same-base-and-height cylinder, rather than the mathematically exact one-third, is a common intuitive misconception — the one-third relationship is precise, not approximate, and the same exact ratio applies to any pyramid compared against a same-base-and-height prism.