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

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

The rounded rectangle has perimeter (1)

A filled rounded rectangle has area (2)

For a rounded square with (center) length and width , the corner radius can be determined by measuring the generalized diameter from the edge of one rounded corner to the diagonally opposite corner. From the Pythagorean theorem, the diagonal distance from the rounded corner to the corner of the circumscribed square is (3)

and the corner radius is related to the edge length of the square circumscribing the corner circle by (4)

Combining gives   (5)   (6)

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. https://mathworld.wolfram.com/RoundedRectangle.html