Regular Polygon Circumcircle Calculator

Find the circumscribed circle radius and area of a regular polygon from its side count and side length, plus polygon area and fill ratio.

Input

Enter the number of sides and side length of a regular polygon to compute its circumcircle radius, area, and fill ratio.

Number of sides n

Side length a

Circumcircle radius R

Circumcircle area

314.159265

Polygon area

259.807621

Fill ratio (area)

82.699334%

Enter lengths in the same unit. Areas are in that unit squared.

The circumradius is R＝a÷（2×sin（π÷n）），where n is the number of sides and a is the side length.
The circumcircle area is π×R×R and the regular polygon area is （n×a×a）÷（4×tan（π÷n））.
The fill ratio is polygon area divided by circumcircle area, approaching 100 percent as n grows.
Enter an integer of 3 or more for the number of sides and a positive value for the side length.

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