Radius of the inscribed circle in a regular polygon

Radius of the inscribed circle in a regular polygon. This online calculator is designed to determine the radius of the inscribed circle in a regular polygon. When entering the number of sides n and the length of the side a, the calculator instantly calculates the radius of the inscribed circle, providing accurate results for various polygons.

For a regular n-gon (all sides and angles are equal), inscribed circle with radius r, and side length a, the formula for the radius of the inscribed circle is as follows:
\[ r = \frac{a}{2 tan ( \frac{π}{n} ) } \]
where:
π - is the number pi (approximately 3.14159),
n - number of sides in the polygon,
tan - tangent.

This formula is based on the fact that the angle in a regular n-gon is equal to \[ \frac{2π}{n} \] ​