Regular hexagon, given one side
Geometry construction using a compass and straightedge

How to construct a regular hexagon given one side. The construction starts by finding the center of the hexagon, then drawing its circumcircle, which is the circle that passes through each vertex. The compass then steps around the circle marking off each side.

Printable step-by-step instructions

The above animation is available as a printable step-by-step instruction sheet, which can be used for making handouts or when a computer is not available.

Explanation of method

This construction is very similar to Constructing a hexagon inscribed in a circle, except we are not given the circle, but one of the sides instead. Steps 1-3 are there to draw this circle, and from then on the constructions are the same.

The center of the circle is found using the fact that the radius of a regular hexagon (distance from the center to a vertex) is equal to the length of each side. See Definition of a Hexagon.


The image below is the final drawing from the above animation.

  Argument Reason
1 ABCDEF is a hexagon It is a polygon with six sides. See Definition of a Hexagon.
2 AB, BC, CD, DE, EF, FA are all congruent. Drawn with the same compass width AF.
3 A, B, C, D, E, F all lie on the circle O By construction
4 ABCDEF is a regular hexagon From (1), (2). All its vertices lie on a circle, and all sides are congruent. This defines a regular hexagon. See Regular polygon definition and properties

  - Q.E.D

Try it yourself

Click here for a printable worksheet containing two problems to try. When you get to the page, use the browser print command to print as many as you wish. The printed output is not copyright.
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 constructions pages on this site




Right triangles

Triangle Centers

Circles, Arcs and Ellipses


Non-Euclidean constructions