Capsule - surface area

The Surface Area of a Capsule calculator computes the surface area of a capsule,            Capsule also known as a spherocylinder.  

INSTRUCTIONS: Choose units (e.g. meters or feet) and enter the following:

• (r) - This is the radius (half the diameter) of the spherical ends of the capsule.
• (l) - This is the overall length of the capsule.  Note, the length must be equal to or greater than two times the radius (2xr).

Capsule Surface Area (A): The calculator computes the surface area in square meters.  However this can be automatically converted in the many other area units (e.g. square feet) via the pull-down menu.  

Related Calculators

• For the Volume of a Capsule, CLICK HERE.  
• For the Mass or Weight of a Capsule, CLICK HERE.

Note: the formula assumes hemispheres (half spheres) on either side of the capsule cylinder.

The Math

Geometrically, a capsule is a cylinder of any length (l) with two hemispheres on either end where the radius (r)  of the cylinder is equal to the radius of the hemispheres.  See diagram.

The formula may seem simple, but it's the correct reduction of the surface area of a sphere plus the lateral surface area of a cylinder:

SA_sphere = 4 π r²
SA_cylinder =  2πr * (l-2r)
SA_capsule = 4 π r² + 2πr * (l-2r)
               = 4 π r² + 2πrl - 4πr²
               =  2πrl

Uses

Spherocylinders are found in many applications. The most common are in capsule containers such small pills and large containers such as liquid or gas transport containers.