# 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.

## 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 $SA = 2 \pi r (2r + a)$ where $r$ is the radius of the cylinder and hemispheres and $a$ is the length of the cylindrical part.[3]

## References

1. ^ "Capsule". Mathworld.wolfram.com. 2005-10-20. Retrieved 2013-01-31.
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.