# 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 adding the volume of the two hemispheres (a sphere of radius ${\displaystyle r}$) to the volume of the cylindrical part: ${\textstyle V={\frac {4}{3}}\pi r^{3}+(\pi r^{2}a)}$, where ${\displaystyle r}$ is the cylindrical radius and ${\displaystyle a}$ is the cylindrical height.

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

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

## References

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