What miter angle for an octagon?
An octagon needs a miter of 22.5 degrees on both ends of all eight pieces, and each corner is 135 degrees. With 12 in sides and 2 in wide stock, the frame is 29 in (2 ft 5 in) across the flats and 31-3/8 in (2 ft 7-3/8 in) corner to corner.
How to work it out
- 180° ÷ 8 sides = 22.5 degrees on both ends of every piece (16 cuts)
- Long point − short point = 2 × 2 in × tan 22.5° = 1.657 in → long 12 in, short 10-5/16 in
- Table-saw miter gauge setting (only if your gauge reads 90° for a square cut): 90° − 22.5° = 67.5°
Octagons are the shape of gazebo floors, game-table aprons, clock surrounds and window-seat frames. Sixteen cuts go into one ring, so a tenth of a degree off at the saw becomes a 1.6° gap at the last joint.
Adjust for your project
- Corner angle where the pieces meet
- 135 degrees
- Long-point (outside) length
- 12 in
- Short-point (inside) length
- 10.34 in
- Outside size, corner to corner
- 31-3/8 in (2 ft 7-3/8 in)
- Outside size, flat to flat
- 29 in (2 ft 5 in)
- Total stock (before kerf and waste)
- 96 in (8 ft) (8 ft)
Octagon short point by stock width (12 in sides)
| Stock width | Short-point (inside) length | Outside size, flat to flat |
|---|---|---|
| 1 in | 11.17 in | 29 in (2 ft 5 in) |
| 1.5 in | 10.76 in | 29 in (2 ft 5 in) |
| 2 in | 10.34 in | 29 in (2 ft 5 in) |
| 3.5 in | 9.1 in | 29 in (2 ft 5 in) |
| 5.5 in | 7.44 in | 29 in (2 ft 5 in) |
What to know about cutting an octagon
Many miter saws have a positive stop at 22.5°, which makes the angle the easy part. Getting eight identical lengths is harder: cut all eight against one stop block, and if you have to move it, recut every piece. On a table-saw miter gauge that reads 90° at square, set 67.5°.
Twelve-inch sides add up to exactly 96 in at the long point, so one 8 ft board looks as if it should work and does not once you allow for kerfs and squaring the end. Flip a plain board end for end between cuts so the pieces nest, and the ring needs only about 91 in with a 1/8 in kerf, which does fit.
To size an octagon from the width you want, multiply the flat-to-flat width by 0.4142 (tan 22.5°) for the long point. A 48 in octagon tabletop frame needs sides of about 19-7/8 in.
Every corner of an octagon is 135°, the same as a bay window, so crown in a bay uses the same 22.5° when cut nested: see Crown molding angles for a 135° bay window corner. For six sides, What miter angle for a hexagon has the numbers.
Different size? Use the full Miter Angle Calculator.
What you’ll need
- Compound miter sawPremium price
Fast, repeatable crosscuts, miters and bevels for trim, frames and cut lists. A sliding model handles wider boards.
See options on Amazon (opens in a new tab) - Digital angle finderBudget price
Reads angles to a tenth of a degree — blade-to-fence, blade tilt and existing corners — so saw settings match the calculator.
See options on Amazon (opens in a new tab) - Band clamp with cornersBudget price
Pulls all the corners of a frame, hexagon or octagon together at once — the easiest way to glue a mitered ring.
See options on Amazon (opens in a new tab)
As an Amazon Associate we earn from qualifying purchases. Links to products are affiliate links — they cost you nothing extra and help keep these calculators free.
Frequently asked questions
What side length for a 48 in octagon tabletop frame?
About 19-7/8 in at the long point: 48 in across the flats × 0.4142. Check it in the calculator with your stock width to get the short point too.
How big is an octagon with 24 in sides?
57-15/16 in (4 ft 9-15/16 in) across the flats and 62-11/16 in (5 ft 2-11/16 in) corner to corner, with a short point of 22-5/16 in when cut from 2 in stock, and 192 in (16 ft) of stock at the long point.
What is the short point of an octagon cut from a 2×4 on the flat?
A 2×4 is 3-1/2 in wide, so with 12 in outside sides the short point is 9.1 in (9-1/8 in).
Other common sizes
- What miter angle for a hexagon — 30 degrees