Capsule (geometry)

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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.


The volume of a capsule is calculated by adding the volume of the two hemispheres (a sphere of radius ) to the volume of the cylindrical part: , where is the cylindrical radius and is the cylindrical height.

This simplifies to the formula .

The surface area formula is .[3]


  1. ^ Weisstein, Eric W. "Capsule". MathWorld. 
  2. ^ Dzubiella, Joachim; Matthias Schmidt; Hartmut Löwen (2000). "Topological defects in nematic droplets of hard spherocylinders". Physical Review E. 62: 5081. arXiv:cond-mat/9906388Freely accessible. Bibcode:2000PhRvE..62.5081D. doi:10.1103/PhysRevE.62.5081. 
  3. ^ "Capsule Calculator". Retrieved 2013-02-18.