The miter angle formula
For a regular polygon, the miter angle is constant at every joint:
Miter = 90° − (180° ÷ N)
Where N is the number of sides. Square = 45°, pentagon = 54°, hexagon = 60°, octagon = 67.5°.
For irregular polygons (a rectangular picture frame, for example), there are two joint angles: the long-side joints use one angle, the short-side joints use another. Use our Picture Frame Miter calculator for that case.
Compound cuts for crown molding
Crown molding sits on the wall at an angle (the "spring angle") and meets the ceiling at another angle. To cut crown on a flat miter saw, you tilt the molding so it lays like it's against the wall — and the saw cuts in two planes simultaneously. The miter angle on the saw is different from the wall-angle.
The formula for spring-angle compound cuts:
Saw Miter = arctan(sin(half-wall-angle) × tan(spring-angle))
Saw Bevel = arctan(cos(half-wall-angle) × tan(spring-angle))
Where "wall angle" is the corner angle (90° inside corner, 270° outside corner).
Common mistakes that ruin crown jobs
- Molding flipped upside down. Lay it on the saw with the ceiling edge against the fence and the wall edge against the table. Right-side up for inside corners, right-side up for outside corners, but mirrored.
- Right vs left bevel confusion. Cut a test piece, hold it against the wall in the corner. If it's wrong, flip the molding — don't move the saw.
- Sprung walls. No house has a true 90° inside corner. Test-cut each corner — you'll often need to split the difference.
Reading the diagram
The polygon visualization shows the inside-edge shape of your frame. The miter angle you set on the saw cuts the outside-edge joints. To preview how the joints will look, sketch the polygon and angle your eye along the joints — if it looks like the joint "opens" instead of "closes," your angle is mirrored.
Frequently asked questions
Should I cut a few degrees off the miter for a snug fit?
Often, yes — especially for hardwood. A "fudge factor" of 0.5–1° under the calculated miter makes joints close tightly on the inside face. Test on scrap first.
Why does my compound miter saw read 31.6° for a 45° corner?
Because 45° is the corner angle, not the miter. The miter saw's "miter" is the angle of the cut. For a 45° corner with 38° spring angle, the saw should be set to 31.6° miter and 33.9° bevel. The corner closes correctly when the math is right.
Can I cut octagons on a regular miter saw?
Yes — the miter is 67.5° from straight (or 22.5° on the saw scale, depending on which side you measure from). Octagons are easier with a stop block on the miter saw fence.