What miter angle for a six-sided frame?
A hexagon is cut at 30° per end — 180 divided by the number of sides. Angles for every polygon from a triangle to a 24-sided ring, and what to do when it will not close.
Every piece of a six-sided frame is cut at 30.0° on each end.
The rule is 180 ÷ sides: a square frame is 45.0°, a hexagon 30.0°, an octagon 22.5°. Both ends of every piece get the same angle.
How that is worked out
- A regular polygon with 6 sides has interior angles of 120.0°.
- Two pieces meet at each corner and split that angle between them, so each is cut at half of what is left from a straight line — the same arithmetic as any flat miter.
- (180 − 120.0°) ÷ 2 = 30.0°, which is also just 180 ÷ 6.
Miter per end, flat frames and rings
| Sides | Shape | Interior angle | Miter per end | Total cuts |
|---|---|---|---|---|
| 3 | Triangle | 60.0° | 60.0° | 6 |
| 4 | Square | 90.0° | 45.0° | 8 |
| 5 | Pentagon | 108.0° | 36.0° | 10 |
| 6 | Hexagon | 120.0° | 30.0° | 12 |
| 8 | Octagon | 135.0° | 22.5° | 16 |
| 10 | Decagon | 144.0° | 18.0° | 20 |
| 12 | Dodecagon | 150.0° | 15.0° | 24 |
| 16 | 16-sided | 157.5° | 11.3° | 32 |
| 24 | 24-sided | 165.0° | 7.5° | 48 |
Worth knowing
- This is the flat case — pieces lying in one plane, like a picture frame or a flat segmented ring. A ring whose staves lean inward is a compound miter and needs a bevel as well; that is the segmented ring calculator.
- Error multiplies. Every joint has two cuts, so a 12-sided ring is 24 chances to be wrong, and an error too small to read on a protractor is not too small to see in the finished ring.
- The fix for a ring that will not close is almost never the arithmetic. Cut a test ring from scrap, measure the gap, and adjust the saw by a fraction of the total error divided by the number of cuts.
- More sides means a shallower angle and a longer, weaker glue surface. Above about sixteen sides the joint is nearly edge grain to edge grain and wants splines or a spline-and-groove.
Work out your own numbers
- Miter angle calculator
The miter for baseboard, casing or chair rail at any corner angle — flat trim, so there's no bevel to set.
- Segmented rings and columns
Miter and bevel for any number of sides, flat or flared, and how long each segment has to be.
- Picture frame miter cuts
Cut lengths, long point to long point, for a rectangular mitered frame, and how much molding to buy.
Related questions
- What angle do you cut a hexagon at?
- 30° on each end of each of the six pieces. That is 180 divided by six. Set the saw to 30° and cut every piece the same way, flipping the stock rather than swinging the saw, so that any error in the setting cancels rather than compounds.
- What is the miter angle for an octagon?
- 22.5° per end. Eight pieces, sixteen cuts, and 180 ÷ 8 = 22.5. It is the second most common frame angle after 45° and most miter saws have a detent for it.
- Why won't my segmented ring close?
- Because the error at every cut is multiplied by twice the number of segments. A twelve-segment ring with each cut 0.1° over leaves 2.4° of the 360° unaccounted for, and that is a visible gap. Cut a full test ring from scrap and dry-fit it: the size of the gap tells you exactly how much to take off the saw setting, divided over all the cuts.