Polygon Circumscribed About a Circle

From a circle radius and side count, compute the area, side length, perimeter, and area ratio of the regular polygon circumscribed about the circle.

Input

Enter the inscribed circle radius and side count to compute the area, side length, and perimeter of the polygon circumscribed about the circle.

Circle radius r

Number of sides n

Polygon area

86.60254

Side length

5.773503

Perimeter

34.641016

Area ratio to circle

1.102658 times

Lengths use the same unit as the radius, and areas use that unit squared.

The side length is a = 2r tan(pi divided by n), where r is the inscribed circle radius and n is the number of sides.
The area is S = n r squared tan(pi divided by n).
The perimeter equals the side length multiplied by the number of sides.
The area ratio is the polygon area divided by the inscribed circle area pi r squared.
As n increases, the regular polygon approaches the inscribed circle and the area ratio approaches 1.

Tell us what you think of this calculator.