Miter & Bevel (Angle) Calculator
Slope convention: this calculator measures slope from the horizontal (0° is a flat frame). Some published compound-miter tables measure the workpiece's tilt from the vertical instead — the same physical cut, described from the other axis. If a number here looks different from a table you're cross-checking, confirm which axis that table is measuring from before assuming either one is wrong.
Enter the number of sides for a flat frame, or add a slope angle for compound (sloped) work, to get the miter and bevel angles to set on the saw. The state lives in the URL, so the exact combination you're looking at is always a link you can share.
How this works
For a flat frame, each of the two boards meeting at a corner is cut at half the angle between adjacent sides of the polygon — miter angle = 180 / N, where N is the number of sides. A square (4 sides) needs 45° at each end; a five-sided planter needs 36°; a hexagon needs 30°. That's the whole formula for flat work, and it's exact for any regular polygon.
Sloped (compound) work — a flared planter, a canted-leg stool, a raised panel — needs two saw settings instead of one: the miter angle (rotation in the horizontal plane) AND a bevel angle (blade tilt). Both are derived from the actual 3D geometry of a regular N-sided frustum: each side panel's face normal is computed from its plan angle and slope, then solved for the saw settings that cut the panel's edge flush against its neighbour. At zero slope, the compound formula reduces exactly to the flat-frame formula above — that internal consistency is one of the checks this calculator's math is tested against.
The slope convention, restated
This calculator measures slope from the horizontal — 0° is a flat frame, and the angle grows as the sides tilt or flare up out of that flat plane. Several published shop tables and crown-molding charts instead measure the workpiece's tilt from the vertical. Both describe the same physical cut; they just read differently on paper. If a number you get here doesn't match a printed chart you're comparing against, check which axis that chart uses before assuming either one is wrong — this is the single most common way people end up second-guessing a correct compound-miter setup.
A caveat about testing this kind of formula
A 4-sided box is a poor test case for a compound-angle formula, because at 45° half-corner angle, sine and cosine are numerically equal — a formula with the sine and cosine terms swapped would still pass a 4-sided check while being wrong for every other side count. This site's compound-angle math was verified against an independently-built 3D geometry model across side counts other than 4 specifically because of that blind spot, and the compound miter angles for sloped work page has the full derivation if you want to check the math yourself.
Reading the result
Miter is the angle you set on the saw's miter gauge or sliding table, measured from a square (90°) crosscut. Bevel is the blade's tilt from vertical. At zero slope, bevel is always 0° — you're only rotating, never tilting. As slope increases at a fixed side count, both numbers move together; changing either the side count or the slope changes both saw settings, never just one. For segmented turning specifically (built-up rings for bowls and vessels), the math is the same flat-frame formula applied per segment — see segmented turning angle basics for that specific case, or miter vs. bevel, explained if the two terms themselves are the part that's unclear.