Get Accurate Angles Without a Protractor

It is hard to get an accurate angle even with a protractor. Old time woodworkers traditionally did not have protractors so they used the ratio of two unit values to set an angle. They just remembered the ratios for the angles they used the most. It is easy to set an angle with a carpenter square. The angle set in the photos is 20°. I know this because the table included with this Instructable shows that for an angle of 20° the ratio is 4 units high and 11 units long, or 4:11. You can see in the photos that the straight edge is clamped 8" high and 22" long for a ratio of 4:11. The table gives you the ratios for angles from 1° to 45° in 1° increments. (22.5° is also included) As you can see the error is never more than 5/100s of a degree.

Suppose you want 15°. The table says that is a ratio of 15:56. Set the length to 14" (56/4) and the height to 3¾" (15/4), clamp a straight edge to the square, and you have 15°. You could also set the length to 21" (56*3/8) and the height to 5⅝" (15*3/8"). Choose the values that best fit your application making sure to keep the ratio to 15:56 for 15°.