By Zencalcy Editorial TeamLast reviewed About us
A miter joint splits the angle between two pieces. For a regular polygon the exterior angle is 360 ÷ n, so each piece is cut at half that — 22.5° for an octagon, 30° for a hexagon. Crown moulding adds a bevel because the moulding sits at an angle to the wall.
Miter and bevel settings for polygons and trim.
miter = 180° ÷ sides included angle = 360° ÷ sides
Saw scales differ: some read 0° at the square cut and others read 90°. Most compound mitre saws read 0° at square, so an octagon is set to 22.5°. Always test on scrap.
| Symbol | Meaning |
|---|---|
| n | Number of sides. |
| θ | Miter angle at each end. |
180 ÷ 8 = 22.5°, so each end is cut at 22.5° to make a 135° corner.
Continue with the Angle Cut Calculator, Angle of Depression Calculator, Bolt Circle Calculator, or the Bowl Segment Calculator — or browse more layout & geometry and all construction calculators.
22.5° on the saw, giving a 135° included corner.
Results use standard construction estimating arithmetic: volumes from measured area and depth, unit weights from published material densities, and code-referenced spans or clearances where the page names a code. Quantities are rounded up to whole saleable units and include the stated waste allowance. These tools are planning aids, not structural design, and do not replace a licensed engineer, a local code check, or a contractor's site measurement.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
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Content updated: September 2026