Polygon Inscribed in a Circle Calculator

Find the area, side length, perimeter, and circle area ratio of a regular polygon inscribed in a circle from its circumradius and number of sides.

Input

Enter the circumradius and the number of sides to compute the area of a regular polygon inscribed in the circle.

Circumradius R

Number of sides n

Polygon area

259.807621

Side length

Perimeter

Area ratio to circle

82.699334%

Apothem

8.660254

Circle area

314.159265

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

The side length is a = 2R sin(pi / n), where R is the circumradius and n is the number of sides.
The area is (1/2) n R squared sin(2 pi / n).
The apothem (distance to a side) is R cos(pi / n) and the perimeter is n times a.
As the number of sides n grows, the polygon area approaches the circle area pi R squared.

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