Get the saw settings for a polygon: the flat miter for a picture frame, octagon or segmented ring, and the compound miter and bevel when the sides tilt, as on a tapered planter or a splayed box.
For a flat frame — a square picture frame, a hexagonal mirror, an octagonal tabletop apron lying on the bench — every corner is a simple miter of 180° ÷ number of sides: 45° for four sides, 30° for six, 22.5° for eight. The saw blade stays vertical.
Tilt the sides and the joint becomes compound. A planter or a tapered box needs both a miter (the saw’s turntable or miter gauge angle) and a bevel (the blade tilt), and neither is the obvious number. The calculator handles both cases with one input: how far the sides are tilted up from lying flat.
The tilt input T is measured from flat. A frame lying on the bench is T = 0. A box with perfectly vertical sides would be T = 90. Most project plans describe splayed boxes by how far the sides lean out from vertical — call that S — so enter T = 90 − S. Sides leaning 15° from vertical are entered as 75.
flat miter = 180° ÷ N
miter = atan(cos T × tan(180°/N)) · bevel = asin(sin T × sin(180°/N))
Miter is measured from square on the saw’s miter scale; bevel is blade tilt from vertical.
| Sides | Shape | Miter per corner |
|---|---|---|
| 3 | triangle | 60° |
| 4 | square / rectangle | 45° |
| 5 | pentagon | 36° |
| 6 | hexagon | 30° |
| 8 | octagon | 22.5° |
| 10 | decagon | 18° |
| 12 | dodecagon | 15° |
Segmented turners use the same numbers: a 12-segment ring needs 15° on each end of each segment.
Settings for sides that lean out from vertical by S degrees (entered as T = 90 − S). Miter / bevel, both in degrees.
| Lean from vertical S | 4 sides | 6 sides | 8 sides |
|---|---|---|---|
| 5° (T = 85) | 4.98 / 44.78 | 2.88 / 29.87 | 2.07 / 22.41 |
| 10° (T = 80) | 9.85 / 44.14 | 5.73 / 29.5 | 4.11 / 22.14 |
| 15° (T = 75) | 14.51 / 43.08 | 8.5 / 28.88 | 6.12 / 21.69 |
| 20° (T = 70) | 18.88 / 41.64 | 11.17 / 28.02 | 8.06 / 21.08 |
| 30° (T = 60) | 26.57 / 37.76 | 16.1 / 25.66 | 11.7 / 19.35 |
| 45° (T = 45) | 35.26 / 30 | 22.21 / 20.7 | 16.32 / 15.7 |
An octagonal mirror frame. N = 8, T = 0: 22.5° miter, blade at 0°. Cut all sixteen miters with the same setting and stop block so the opposite sides match.
A four-sided planter with sides leaning 15°. Enter N = 4 and T = 75. The calculator returns a miter of 14.51° and a bevel of 43.08°. These match the long-published compound-miter tables for a 15° four-sided box (about 14½° miter, 43° bevel).
A six-sided splayed box at 30°. N = 6, T = 60: miter 16.1°, bevel 25.66°.
Compound cuts put the blade at an angle to both the fence and the table, which makes it easier for small offcuts to be trapped and thrown. Keep hands well clear of the blade path, use a hold-down on the miter saw, and let the blade stop before lifting it out of the cut.
At T near 90 the joint is mostly a bevel: a vertical-sided four-sided box is a straight 45° bevel with no miter. As the sides lean out, the work shifts from bevel to miter.
Some saws and miter gauges read from the blade face rather than from square. On those, set 90 − 14.51 = 75.49.
Yes. Flat rings use T = 0. Staved or tapered segments use the tilted case.
Yes, three or more. Irregular polygons need each corner worked out separately.