# 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.[1] Another name for this shape is spherocylinder.[2]

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

## Formulas

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

The surface area formula is ${\displaystyle SA=2\pi r(2r+a).}$.[3]

## References

1. ^
2. ^ Dzubiella, Joachim; Matthias Schmidt; Hartmut Löwen (2000). "Topological defects in nematic droplets of hard spherocylinders". Physical Review E. 62: 5081. doi:10.1103/PhysRevE.62.5081.
3. ^ "Capsule Calculator". Calculatorsoup.com. Retrieved 2013-02-18.