Calculations at a stadium. A stadium in geometry is a bisected circle of the radius r with a matching rectangle of the size a*2r between the two halfs. The length of the rectangle a can be arbitrary.
Enter rectangle length and circle radius and choose the number of decimal places. Then click Calculate.
Formulas:
l = a + 2r
b = 2r
p = 2 * ( πr + a )
A = r * ( πr + 2a )
pi:
π = 3.141592653589793...
Radius, lengths, breadth and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).
A stadium halved lengthwise is a half-stadium, a stadium halved vertically is an elongated semicircle. The three-dimensional equivalent of the stadium is a capsule. If you rotate the stadium around its perpendicular bisector, you get a rounded disc as solid of revolution.
The name stadium probably comes from the Roman or Greek shape of these arenas. The horse racing tracks, called hippodromes or simply circuses, were very long facilities with sharp curves at their ends, which were formed by semicircles. Even today, this shape can be found in many stadiums, for example in a 400-meter track around a football field; these tracks are shorter and wider than the ancient horse racing tracks.
The stadium is axially symmetrical to the perpendicular bisector through the two parallel sides. It is also axially symmetrical to the straight line with the greatest length, which bisects the semicircles again. In addition, it is point-symmetrical to the intersection of these two axes. It is rotationally symmetrical to this point at an angle of 180 degrees and multiples thereof.
If you use a stadium as the base for a (hypothetical) billiard table, you get what is known as a Bunimovich stadium. This is a dynamic system in which the billiard balls follow chaotic trajectories, so a ball follows a completely different trajectory with slightly different starting conditions (force and direction).