The octagon is a basic polygonal shape consisting of eight sides. A regular octagon consists of eight equal sides and angles. The stop sign is a common and recognisable regular octagon. You can draw a regular octagon on graph paper according to a straightforward step-by-step process. You can also draw an irregular octagon in one simple step.

Choose a centre point for the octagon at an intersection on the grid. It should be somewhere near the centre of the area in which you want to draw the octagon.

Draw a circle around the central point using the compass. The radius is the distance from the centre of a circle to its edge. For ease and precision, choose a radius length equal to a whole number of grid boxes. For example, you can choose a length of four grid boxes for your radius, which will create a circle whose diameter is eight.

Draw a vertical diameter and a horizontal diameter with the ruler. A diameter is a straight line connecting two opposite points on a circle that passes through the centre point. This will create a cross shape and will mark four corners of the regular octagon.

Draw two more diameters that bisect, or cut in half, the angles created by the first two. This will create eight 45-degree angles.

Connect the end points of the eight radii to their adjacent radii. This step will create your regular octagon.

Draw a straight line segment with the ruler. It can be anywhere on the paper, in any direction and of any length. This is the first side. Throughout this section you technically do not have to pay any attention to the underlying grid.

Draw another straight line segment that ends at the same point as an end of the first line segment. It can also be of any length and direction. It must not overlap the first line segment.

Draw six more line segments that connect at the ends to form an enclosed shape with eight sides. The lines must not overlap or cross, and only two lines must meet at each corner. The lines do not have to be in any particular direction or form any particular angles. This gives you an eight-sided polygon, or octagon.