Miter and crown angle calculator
The miter and bevel to set on a miter saw for a picture frame or any polygon, two boards meeting at any corner, crown molding cut laid flat or nested, and boxes with sloped sides. The answers are geometry, so they are exact; the reasoning shows each step.
Miter
45°
Bevel
0°
Geometry: exact by definition
Read on a miter saw whose miter scale shows 0° at a square cut and whose bevel scale shows 0° with the blade upright. A table saw miter gauge that reads 90° at square needs 90° minus the miter.
Why: Four equal sides turn 360° in all, so each end is cut at 180° ÷ 4 = 45°.
Why these numbers?
The situation
A flat frame with 4 equal sides.
From your input: number of sides
The number
180° ÷ 4 = 45° miter on each end, bevel 0°.
Arithmetic: exact by definition
How the angles work
A miter saw has two scales. The miter scale swings the blade left or right across the board and reads 0° for a square cut. The bevel scale tilts the blade and reads 0° when it stands upright. Flat work, like a picture frame, needs only a miter: a frame with n equal sides turns a full 360° in n corners, so each end is cut at 180° ÷ n. Two boards meeting at a corner of any angle each take half of the turn, 90° minus half the corner angle.
Work that leans needs both. Crown molding laid flat on the saw table is tilted from the wall by its spring angle, and the sides of a hopper or a sloped box lean out from vertical. For a lean t and a corner that turns each piece through a, the bevel is asin(cos t × sin a) and the miter is atan(sin t × tan a). With no lean that is a plain bevel of a, which is how baseboard laid flat is cut.
Miter angles for frames and polygons
Each end of each piece, stock flat on the saw, bevel at 0°. This is where 22.5° on a miter saw comes from: an octagon.
| Shape | Sides | Miter |
|---|---|---|
| Triangle | 3 | 60° |
| Square or rectangle | 4 | 45° |
| Pentagon | 5 | 36° |
| Hexagon | 6 | 30° |
| Octagon | 8 | 22.5° |
| Decagon | 10 | 18° |
| Dodecagon | 12 | 15° |
Crown molding angle chart
Crown laid flat on the saw, for the two common spring angles. Nested crown, held upside down against the fence at its spring angle, needs only the miter in the first column and no bevel. Inside and outside corners take the same numbers; the direction of the cut changes, so follow the crown table in your saw's manual for which way to swing and tilt.
| Corner | Nested: miter | 52/38 flat: miter / bevel | 45/45 flat: miter / bevel |
|---|---|---|---|
| 90° | 45° | 31.62° / 33.86° | 35.26° / 30° |
| 120° | 30° | 19.57° / 23.2° | 22.21° / 20.7° |
| 135° | 22.5° | 14.31° / 17.55° | 16.32° / 15.7° |
The 90° row matches the crown tables printed in the Makita LS1216 and RIDGID R4121 manuals. Setup, safety and the difference between nested and flat crown are in the miter saw guide.