The quickest, easiest and safest way to cut crown molding miters is to use a miter box and a regular hand saw. Although an electric compound miter saw may at first appear attractive, the results you can achieve using a simple miter box which you purchase or build yourself are usually superior. No complex calculations are required.
The diagrams below show you how to cut the miters for 90 degree corners (at 45 degrees.) For other wall angles, you will need to add cuts to your miter box at one-half of the required wall angle. For example, for 135 degree wall-to-wall angles, add cuts to your miter box at 67.5 degrees (up from the front edge) in both directions. A scrap length of wood quarter-round can be very useful for making test cuts.
Note that the crown molding is upside down
in the miter box - with the bottom edge of the crown molding against the side of the miter box farthest away from you. The far side of the miter box corresponds to the wall and its bottom corresponds to the ceiling.
Room measurements are usually made along the wall (which corresponds to the far side of the miter box.)