Craft & Design
Miter Angle for Polygons
Saw-blade angle for cutting a regular polygon — picture frames, hexagons, octagons, pipe sections.
Miter Angle for Polygons
Inputs
Common polygons
Results
Miter-saw cut angle
Set saw to this from 90°
30.00°
Interior angle
120.00°
Segmented bevel angle
For pipe staves / segmented rings
30.00°
| Shape | Sides | Miter cut |
|---|---|---|
| Triangle | 3 | 60.00° |
| Square | 4 | 45.00° |
| Pentagon | 5 | 36.00° |
| Hexagon | 6 | 30.00° |
| Heptagon | 7 | 25.71° |
| Octagon | 8 | 22.50° |
| Decagon | 10 | 18.00° |
| Dodecagon | 12 | 15.00° |
Selected: Hexagon
How to use this
A closed regular polygon with N sides has an interior angle of 180 × (N − 2) ÷ N. For a picture-frame-style miter, each of the two mating pieces gets cut at half the exterior angle — which is 180 ÷ N. That’s the number you dial into the miter gauge.
For segmented constructions like barrels, columns, or turned rings, use the bevel angle (360 ÷ N ÷ 2) on the edge of each stave so they meet flat around the circumference.
Formula
interior_angle = 180 × (N − 2) ÷ N
miter_cut = 180 ÷ N (each piece)
segmented_bevel = 360 ÷ N ÷ 2
Related calculators
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Formula
miter_cut = 180 ÷ N; interior = 180 × (N − 2) ÷ N