Why 31.6 degrees for crown molding?
31.6° is the miter for 52/38 crown in a 90° corner when the molding lies flat on the saw table. It comes from the compound-miter formula: miter = arctan(sin 38° ÷ tan 45°) = arctan(0.6157) = 31.6°. Some saws stop at it: DeWalt’s DWS780 manual lists miter latch points at 31.62° left and right.
What is 33.9 on a miter saw?
33.9° is the matching bevel for 52/38 crown in a 90° corner, cut flat: bevel = arcsin(cos 38° × cos 45°) = arcsin(0.5572) = 33.9°. DeWalt’s DWS780 has a bevel stop at 33.86° and a mark on its bevel scale at 33.9°; other saws may not.
Crown molding spring angles
52/38 crown is the one the DeWalt manual calls “standard (U.S.) crown molding”; Jon Eakes’s settings cover it and 45/45 crown. The formulas use the 38° or 45° figure, the spring angle, and the chart has a table for each.
Inside and outside corners
The formula uses only the corner angle and the spring angle, so an outside corner takes the same two numbers as an inside one; what changes is the direction of each cut. For example, DeWalt’s manual sets the left piece of an inside corner with the bevel to the left at 33.9°, the miter to the right at 31.62°, and keeps the left end. Saws differ, so follow your saw’s own crown table for the directions.
Corners that are not 90°
Walls are rarely exactly square. Measure the corner with an angle finder and use its row: a 95° corner takes a 29.4° miter and 32.2° bevel for 52/38 crown; an 85° corner takes 33.9° and 35.5°. A 135° corner, like each corner of a regular octagon, takes 14.3° and 17.6°.
The crown formula
Construction Calculator 1.1.1 works out crown settings with miter = arctan(sin S ÷ tan(C ÷ 2)) and bevel = arcsin(cos S × cos(C ÷ 2)), where C is the wall corner and S the spring angle, rounded to 0.1°.