TOPICS
Search

Rounded Rectangle


RoundedRectangle

A rounded rectangle is the shape obtained by taking the convex hull of four equal circles of radius r and placing their centers at the four corners of a rectangle with side lengths a and b.

A filled rounded rectangle with b=0 (or a=0) is called a stadium.

The rounded rectangle has perimeter

 p=2(a+b+pir).
(1)

A filled rounded rectangle has area

 A=ab+2r(a+b)+pir^2.
(2)

For a rounded square with (center) length and width x, the corner radius can be determined by measuring the generalized diameter d from the edge of one rounded corner to the diagonally opposite corner. From the Pythagorean theorem, the diagonal distance x from the rounded corner to the corner of the circumscribed square is

 s=1/2(sqrt(2)x-d)
(3)

and the corner radius r is related to the edge length of the square circumscribing the corner circle by

 2r^2=(r+s)^2.
(4)

Combining gives

r=s(1+sqrt(2))
(5)
=1/2(1+sqrt(2))(sqrt(2)x-d).
(6)

See also

Circle, Disk, Ellipse, Oval, Rectangle, Rectellipse, Stadium

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Rounded Rectangle." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RoundedRectangle.html

Subject classifications