Crown molding encapsulates a large family of moldings which are designed to gracefully flare out to a finished top edge. Crown molding is generally used for capping walls, pilasters, and cabinets, and is used extensively in the creation of interior and exterior cornice assemblies and door and window hoods.
Crown molding is typically applied along the seams where ceiling meets wall. Usually it is not placed flush against the wall nor against the ceiling. Instead, when viewed from the molding's end (or as a cross-section), it, the ceiling, and the wall form a "hollow" triangle. This adds a difficulty to the installation process, namely the need for complex cuts to form corners where two walls meet.
There are two common ways to fashion inside corners. One is to use a compound miter saw to cut the ends of the corner pieces along two axes simultaneously. The other, called coping, is a two step process, first to cut a simple miter and then to use a coping saw to undercut the miters.
Using a coped joint for interior corners saves you the trouble of having to determine and cut the exact inside degree measurement since most corners are not exactly 90/45 degrees. Outside corners must be mitered, but use care because not all outside corners measure true. Measure and cut accordingly. If the angle is not exactly 45/22.5 degrees use a corner measuring device or piece of scrap crown molding to obtain the right measurement before you make your final cut.
Angle calculations 
Fitting crown molding requires a cut at the correct combination of miter angle and bevel angle. The calculation of these angles is affected by two variables: (1) the spring angle (or crown angle, typically sold in 45 degree and 38 degree formats), and (2) the wall angle.
Pre-calculated crown molding tables or software can be used to facilitate the determination of the correct angles. Given the spring angle and the wall angle, the formulas used to calculate the miter angle and the bevel angle are:
- Miter angle
- Bevel angle
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