Compound Mitre Angle
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A simple mitre cuts an angle in one plane (rotating the blade horizontally). A compound mitre combines that horizontal mitre angle with a blade tilt (the bevel angle), needed when the piece being joined is both angled in plan view and tilted out of vertical, like a picture frame moulding tilted against a wall or a pyramid-shaped box side.

The two settings work together to produce a single compound cut: the mitre angle handles the corner's rotation in plan, while the bevel angle handles the workpiece's slope or splay. Changing either input changes both output angles, since they're derived together from the shape's geometry.

Typically the number of sides (or the corner angle) of the shape and the slope or splay angle of the sides from vertical. From those two values, trigonometric formulas resolve the actual mitre and bevel settings to dial into the saw.

Crown moulding sits at a spring angle against both the wall and ceiling rather than lying flat, so cutting an inside or outside corner requires simultaneously angling the cut across the moulding's length and tilting the blade, which is exactly what a compound mitre setting solves.

Because two angles must both be correct at once, an error in either the mitre or bevel setting compounds with the other, and the mismatch often isn't obvious until the pieces are test-fit. Cutting scrap test pieces at the calculated settings before committing good stock is standard practice for compound work.