Rounded Rectangle


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


A filled rounded rectangle has area


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


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


Combining gives


See also

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

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Cite this as:

Weisstein, Eric W. "Rounded Rectangle." From MathWorld--A Wolfram Web Resource.

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