Capsule (geometry)

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 gases and for pharmaceutical capsules.

Formulas

• a is the letter used for cylindrical height here

The volume of a capsule is calculated by adding the volume of the two hemispheres (a sphere of radius $r$) to the volume of the cylindrical part: ${\textstyle V={\frac {4}{3}}\pi r^{3}+(\pi r^{2}a)}$

This simplifies to the formula $V=\pi r^{2}\left({\frac {4}{3}}r+a\right)$.

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