Miter angle formula
For a closed frame with n equal sides, every corner is split evenly between two boards:
Miter saw setting = 180° ÷ n
Corner (interior) angle = 180° − 360° ÷ n
Cut angle measured from the board edge = 90° − 180° ÷ n
For a single corner of any angle (baseboard, crown molding laid flat, handrails):
Miter saw setting = 90° − corner angle ÷ 2
Miter angles for common polygons
| Sides | Shape | Miter setting | Corner angle |
|---|---|---|---|
| 3 | Triangle | 60° | 60° |
| 4 | Square / rectangle | 45° | 90° |
| 5 | Pentagon | 36° | 108° |
| 6 | Hexagon | 30° | 120° |
| 7 | Heptagon | 25.71° | 128.57° |
| 8 | Octagon | 22.5° | 135° |
| 9 | Nonagon | 20° | 140° |
| 10 | Decagon | 18° | 144° |
| 12 | Dodecagon | 15° | 150° |
| 16 | 16-sided | 11.25° | 157.5° |
Tips for tight miter joints
- Calibrate your saw. The detents on many miter saws are off by a fraction of a degree. Check them with a digital angle gauge, or cut four pieces and test-fit them.
- Cut matching pieces together. Opposite sides of a frame must be exactly the same length. Use a stop block for repeat cuts.
- Mind the long point. Measure frame pieces on the outside (long point) edge, then use the inside length from the calculator to check your work.
- Sneak up on it. Cut slightly long, test the fit, then shave the last 1/32 in.
- Measure odd corners. Walls are rarely exactly 90°. Measure the real corner with a protractor or the phone angle finder, then use corner-angle mode.
Frequently asked questions
What is the miter angle for a 4-sided (square) frame?
45°. Each corner is 90°, and it is split between two boards, so each board is cut at 45°. The general formula for a frame with n equal sides is miter angle = 180° ÷ n.
What angle do I cut for a hexagon or octagon?
A 6-sided (hexagon) frame needs 30° miters (180 ÷ 6). An 8-sided (octagon) frame needs 22.5° miters (180 ÷ 8). A 5-sided pentagon needs 36°, and a 12-sided frame needs 15°.
How do I miter a corner that is not 90°?
Measure the corner angle (for example with the online protractor or a digital angle gauge), enter it in "Corner angle" mode, and cut each board at 90° − (corner ÷ 2). A 135° corner, for example, needs two 22.5° miters.
My miter saw shows 0° for a square cut. Is that the number I set?
Yes. Most US miter saws read 0° for a square (90°) cut, and the calculator gives you the number to set on that scale. If your miter gauge or protractor measures from the board edge instead, use the "cut angle from edge" value (90° minus the saw setting).
Why do my miter joints have gaps?
Small angle errors add up: on a 4-sided frame, a 0.5° error on every cut leaves a 4° gap in the last corner. Check your saw with a digital angle gauge, make test cuts on scrap, and make sure opposite sides are exactly the same length.