Radius of a regular polygon (also Circumradius)
Definition: The distance from the center of a regular polygon to any vertex .
Try this Adjust the polygon below by dragging any orange dot, or alter the number of sides. Note the behavior of the polygon's radius.

The radius of a regular polygon is the distance from the center to any vertex. It will be the same for any vertex. The radius is also the radius of the polygon's circumcircle, which is the circle that passes through every vertex. In this role, it is sometimes called the circumradius.

Irregular polygons are not usually thought of as having a center or radius.

Radius given the length of a side

By definition, all sides of a regular polygon are equal in length. If you know the length of one of the sides, the radius is given by the formula:

s  is the length of any side
n  is the number of sides
sin  is the sine function calculated in degrees
(see Trigonometry Overview)

Radius given the apothem (inradius):

If you know the apothem (or inradius) (distance from the center to the midpoint of a side):

a  is the apothem (inradius)
n  is the number of sides
cos  is the cosine function calculated in degrees
(see Trigonometry Overview)

While you are here..

... I have a small favor to ask. Over the years we have used advertising to support the site so it can remain free for everyone. However, advertising revenue is falling and I have always hated the ads. So, would you go to Patreon and become a patron of the site? When we reach the goal I will remove all advertising from the site.

It only takes a minute and any amount would be greatly appreciated. Thank you for considering it!   – John Page

Become a patron of the site at

Other polygon topics


Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons