Capsule (geometry)

File:Capsule geometry.svg

A two-dimensional orthographic projection of a capsule

A capsule (from Latin capsula, "small box or chest"), or stadium of revolution, is a basic three-dimensional geometric shape consisting of a cylinder with hemispherical ends. Another name for this shape is spherocylinder.

The shape is used for containers for pressurised gasses and for pharmaceutical capsules.

Formulas

The volume of a capsule is calculated by the formula $V = \pi r^2 \left (\frac{4}{3}r + a \right )$ where $r$ is the radius of the cylinder and hemispheres and $a$ is the height of the cylindrical part.

The surface area formula is $SA = 2 \pi r (2r + a).$.