To draw an octagon to scale, first determine how big the octagon is to be. Draw the top line of the octagon to the desired length using a ruler. Use a protractor to determine a 135-degree angle from the end of the top line, and then use the ruler to draw a line the same length as the first at that angle. Repeat the process for all eight sides of the octagon.
Octagons can also be drawn using a compass and straightedge ruler, although the process is more complex. Use a compass to draw a circle 4 inches in diameter, and then use the straightedge to divide the circle into four equal quarters with two perpendicular lines. Draw a second circle around the first, this time measuring a diameter of 4 1/2 inches. Extend the perpendicular lines to intersect the second circle as well.
Keeping the compass at the 4 1/2-inch diameter, draw a vertical arc near the center of the circle that extends across both sides of the circle. Draw a mirroring arc on the other side. Use the straightedge to draw two lines through the places where the arcs intersect. Repeat the arc process by adding horizontal arcs and drawing lines through their intersections.
Looking at the circle, there appears to be two intersecting eyes with a square around them. To form the octagon, start at the top left-hand corner, and use the straightedge to draw a line from the edge of the square to the top of the inner circle. Repeat this process for all eight sides, and erase all lines but the newly drawn octagon.