Calculate an Arena

Calculator for the perimeter and size of an arena or stadium with different units. An arena has the shape of a bisected circle, where between the two semicircles a matching rectangle in inserted. To calculate the perimeter and area, the irrational number pi is needed, which is written with the Greek letter π. Please enter length and width of the arena and choose the units. The length must be larger than the width. Perimeter and area will be calculated.

Length:		cmdmmkminftydmi
Width:		cmdmmkminftydmi
Perimeter:		cmdmmkminftydmi
Area:		cm²dm²m²km²ahasq insq ftsq ydacsq mi

Units of measurement: cm=centimeter, dm=decimeter, m=meter, km=kilometer, in=inch, ft=foot, yd=yard, mi=mile, ²,sq=square, a=are, ha=hectare, ac=acre

Formulas:

Length l, width w
Perimeter p = πw + 2(l-w)
Area A = πw²/4 + w(l-w)

An arena or stadium shaped field.

The name for this geometric shape is indeed a stadium. The calculator linked here works with different specifications, namely the length of the rectangle and the radius of the circle. Depending on the values ​​available, one calculator or the other will be more suitable.
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.

This shape has no corners or vertices, even though it has two straight edges. The straight sides are parallel and therefore do not intersect. They are connected by two circular arcs, with the ends of the arcs transitioning smoothly into the straight edges. This is only possible if the arcs are exact semicircles.
The three-dimensional equivalent of such a shape is called a capsule.

Last updated on 01/12/2026. Author: Jürgen Kummer

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