How to make a protractor. 1. Per Hand method 1 Draw a square of 11.5cm sides. (Or of course any multiple. And of course any other decimal base measurement can be substituted for cm.) Draw a circle of 11.5cm diameter exactly on the square. Draw the 45°, 90°, 135° etc diagonals in using the square. Now 20 and 10 and 5 degree marks may be made - 20° points are 2cm apart on the circle (measured as a line between the 2 points, and not as an arc on the circle). 10° - 1cm, 5° - 0.5cm. 1° points are now made, 1mm apart. Cut out the circle/half circle/quarter circle. Accuracy: 1° 0.1004cm 5° 0.5016cm 10° 1.0023cm 20° 1.997cm 45° should measure 4.4009cm 90° should measure 8.132cm This works because the sine is nearly linear for small values. 2. Per Hand method 2, with graph paper: protractor.gif The errors in the angle using the given approximations are: angle per cent error approximation used 5 -0.605 2/23 10 0.080 3/17 15 0.122 11/41 20 -0.084 4/11 25 0.068 7/15 30 -0.061 15/26 35 -0.023 7/10 40 -0.033 26/31