What Is a Stadium Shape?
A stadium — also called a discorectangle — is a two-dimensional geometric figure made of a rectangle with two semicircular ends. It gets its name from the running tracks of athletic stadiums, which trace this exact outline. This calculator finds the area and perimeter of a stadium from two measurements: the radius r of the semicircular ends and the length a of each straight side.
How to Use It
Enter the radius r of the rounded ends and the straight side length a (the length of the flat top and bottom). Both values must use the same unit. Click calculate to see the enclosed area in square units and the total perimeter in linear units.
The Formula Explained
A stadium is simply a rectangle of dimensions a × 2r with a semicircle stuck on each short end. The two semicircles together form one complete circle of radius r, so:
Area = \(\pi r^2 + 2ra\) — the circle (\(\pi r^2\)) plus the rectangle (length a, height 2r).
Perimeter = \(2\pi r + 2a\) — the full circle's circumference (\(2\pi r\)) plus the two straight sides (\(2a\)).
Worked Example
Suppose r = 5 and a = 10. $$A = \pi(5^2) + 2(5)(10) = 25\pi + 100 \approx 78.5398 + 100 = 178.5398 \text{ square units.}$$ $$P = 2\pi(5) + 2(10) = 10\pi + 20 \approx 31.4159 + 20 = 51.4159 \text{ units.}$$
FAQ
What if a = 0? The stadium becomes a full circle: area = \(\pi r^2\) and perimeter = \(2\pi r\).
Is the width of a stadium 2r? Yes — the total height (short dimension) equals the diameter of the semicircles, which is \(2r\).
What units does it use? Any consistent unit. If r and a are in meters, area is in square meters and perimeter in meters.
