Stadium

A stadium, also called a discorectangle, obround, or sausage body, is a geometric figure consisting of a rectangle with top and bottom lengths whose ends are capped off with semicircles of radius . The area of a stadium is therefore given by

(1)

and the perimeter by

(2)

Defining the ratio gives the alternate forms

(3)

and

(4)

The term is most commonly encountered in the context of stadium billiards.

The stadium is implemented in the Wolfram Language as StadiumShape[lbrx1, y1, x2, y2, r].

A stadium of revolution might be termed a capsule.