Circumcircle of a Polygon

Definition: The circle that passes through each vertex of the regular polygon.
Also - circumscribed circle.
Try this Adjust the polygon below by dragging any orange dot, or alter the number of sides. Note the behavior of the polygon's circumcircle.

For Regular Polygons

The circumcircle of a regular polygon is the circle that passes through every vertex of the polygon. If the number of sides is 3, then the result is an equilateral triangle and its circumcircle is exactly the same as the one described in Circumcircle of a Triangle.

Finding the radius

The radius of the circumcircle (the circumradius) of a regular polygon is exactly the same as the radius of the polygon. For more on the radius and formulas to calculate it see Radius of a Polygon.

Irregular Polygons

Irregular polygons are not usually considered as having a circumcircle. If you draw a polygon at random, it is unlikely there will be a circle that passes through every vertex.

An alternative view
Sometimes you may see an alternative definition of the circumcircle: "the smallest circle that will enclose the polygon" For this definition it is possible for an irregular polygon to have a circumcircle, since the circle need not pass through every vertex, as shown above.

Other polygon topics


Types of polygon

Area of various polygon types

Perimeter of various polygon types

Angles associated with polygons

Named polygons