Miter & Bevel Angle Calculator
Calculate miter and bevel angles for flat frames, pyramid structures, and angled polygon assemblies given the number of sides and frame type. Ideal for picture frames, roof peaks, and decorative polygon boxes.
Last updated: September 2026
Formula below · 2 sources (fpl.fs.usda.gov, Wikipedia) · Updated Sep 2026
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About this calculator
Saw settings here are measured the usual way: miter from a square crosscut and bevel from a vertical blade. For a flat frame (picture frame) the pieces lie flat and only a miter is needed: miter = 180° / numberOfSides (45° for a square, 30° for a hexagon, 22.5° for an octagon), bevel 0°. For a box or shadow box with vertical sides, the corners are cut with the blade tilted instead: miter 0°, bevel = 180° / numberOfSides (45° for a 4-sided box). For a pyramid or splayed box whose sides lean in at a tilt T from vertical, both settings are needed: miter = atan(sin T × tan(180°/n)) and bevel = asin(cos T × sin(180°/n)). At T = 0 this reduces to the box case and at T = 90° to the flat frame. Test the settings on scrap before cutting finished stock.
How to use
Example 1 — flat hexagon picture frame (6 sides): miter = 180 / 6 = 30°, bevel 0°. Example 2 — 4-sided box with vertical sides: miter 0°, bevel 45°. Example 3 — 4-sided pyramid (or splayed box) with sides tilted 30° from vertical: miter = atan(sin 30° × tan 45°) = atan(0.5) = 26.6°; bevel = asin(cos 30° × sin 45°) = asin(0.612) = 37.8°. Set the saw to a 26.6° miter and a 37.8° bevel.
Frequently asked questions
What miter angle do I need to cut a regular octagon frame?
For a flat 8-sided (octagon) frame each cut is 180 / 8 = 22.5° from a square crosscut, which most miter saws have as a detent. The cut face then sits at 67.5° to the long edge of the board, which is why some protractor tables list 67.5°; on a standard miter saw scale, set 22.5°. Always dry-fit all eight pieces before applying glue to confirm the joints close without gaps.
How do I calculate compound miter angles for a pyramid box or tapered frame?
A pyramid or splayed box needs both a miter and a bevel because the sides lean. With the side tilt T measured from vertical and n sides: miter = atan(sin T × tan(180°/n)) and bevel = asin(cos T × sin(180°/n)). For a 4-sided piece with 30° tilt that is a 26.6° miter and a 37.8° bevel; with 45° tilt, 35.3° and 30°. Cut a test set from scrap first, because small errors repeat at every corner.
Why does a square frame need 45° miters but other polygons need different angles?
A square has four 90° corners and each corner is split between two pieces, so each piece is cut 45° from square. In general the saw setting is 180 / sides: a pentagon needs 36°, a hexagon 30° and an octagon 22.5°. The faces of the cuts sit at 90 minus that value to the board edge (54°, 60° and 67.5°), which is the number some tables quote instead.