Constructing a square
Geometry construction using a compass and straightedge

This page shows how to construct (or draw) a square given the length of a side.

It starts with a given line segment AB. It then erects a perpendicular at one end of the line, which will become the second side of the square. The compass is then set to the length of the given side, and the other three sides are marked off.

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.


  Argument Reason
1 Angle ABC is 90° (a right angle) By construction. See Constructing a perpendicular to a line at a point for the proof.
2 Segments BC, CD and DA are the same length as AB They were all drawn with the same compass width - AB
3 Therefore ABCD is a square. Four congruent sides and interior angles are 90°

  - Q.E.D

Try it yourself

Click here for a printable construction worksheet containing two square constructions 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