How to Draw an Octagon With a Compass

Architects often draw octagons for added details.

Famously depicted on stop signs, the octagon is any eight-sided polygon, no matter its shape. Although the classification of octagon contains all eight-sided shapes, the term usually brings to mind the regular octagon, which a square that has lost its corners. A regular octagon has sides of equal length and eight internal angles, each 135 degrees. Regular octagons seem difficult to draw, but the compass allows you to use mathematics to draw perfect octagons every time.

Things You'll Need

• Ruler
• Compass
• Eraser (optional)

Instructions

1. Draw a square, using a ruler to make straight lines of equal length.

2. Mark the exact center of the square by placing the ruler on the diagonal and dividing the total length by 2.

3. Place the point of the compass on one corner of the square and stretch the other side until the pencil rests on the center of the square.

4. Draw an arc so that it crosses two sides and the center of the square. Repeat the arcs on all four corners.

5. Connect the points where the arcs intersect the square to form an octagon.

6. Erase the arcs and extra parts of the square, if desired.

Tips & Warnings

• Once you understand the concept, you can mark the intersections with the compass without drawing the entire arc to lessen the amount erased.

References

• Nrich: The Medieval Octagon

Resources

• University of South Florida: Construction of an Octagon from a Square
• Dartmouth College; Geometry in Art & Architecture; Paul Calter; 1998