Polygon Miter and Bevel Angle Calculator
Find the cut angles and piece widths for a frame, stave box or tapered form.
8 upright sides · 0 at square
Blade bevel
Miter
67.5° on a scale marked 90 at square.
Your polygon
Bevel both long edges of each upright stave.
Saw scale
An octagon answer of 67.5° measures from the face; 22.5° measures off square. They describe the same cut.
Size (optional)
Editable example: 12 in across flats, 3/4 in stock. Clear the size to work with angles alone.
| Cut | 0 at square · selected | 90 at square |
|---|---|---|
| Blade bevel | 22.5° | 67.5° |
| Miter | 0° | 90° |
- Angle per cut off square, in top view
- 22.5°
- Interior angle, in top view
- 135°
- Joint angle: face to cut edge, in top view
- 67.5°
- Total turn around all joints
- 360°
For tapered sides, these are top-view angles. Use the bevel and miter settings above for the cuts.
Piece sizes
- Outside face width · long point to long point
- 4.971 in
- Outside width across flats
- 12 in
- Outside width across corners
- 12.989 in
- Inside face width · short point to short point
- 4.349 in
- Inside width across flats
- 10.5 in
- Outside perimeter
- 39.765 in
With an odd number of sides, there are no opposite flats or corners. These widths are the diameters of the inner and outer circles.
Inch fractions are rounded to the nearest 1/32. Keep the decimal values when laying out repeated pieces.
On a flat or upright octagon, every cut 0.5° off in the same direction adds 8° of closure error across 16 cut faces. Cut test pieces and dry-fit the whole ring first.
Your specifications
8 upright sides; scale 0 at square; 12 in across flats; 3/4 in stock thickness.
How to read the angles
The cut angle is how far you move from a square cut. Most saw scales call square 0°. A gauge that calls square 90° shows the other reading: subtract the cut angle from 90°.
The interior angle is the corner inside the finished polygon. The glue-up angle is between a piece’s face and its cut edge. Two matching cut faces meet at each corner. All the turns around the ring add to 360°.
Frame, upright staves or tapered sides?
Flat frame: the pieces lie in one plane. Miter each end and keep the blade square to the board’s face. The size field for thickness becomes rail width, measured across the frame piece’s face.
Upright sides or staves: the boards stand up to form a box or column. Bevel their long edges so the faces meet around the ring.
Tapered sides: the boards lean from vertical, as in a hopper, bucket or tapered lighthouse. Enter that tilt. With the board lying flat for cutting, each side joint needs both a blade bevel and a miter. Mirror the cuts on its two sides. The listed sizes are at the base only.
Octagon example: 22.5°, 67.5° and 135°
Eight sides need a 22.5° cut off square. On a scale marked 90 at square, the same cut reads 67.5°. The finished corner is 135° inside. For a flat octagon frame, miter each end at 22.5°. For an upright octagonal column, bevel each long edge at 22.5°.
With a 12-inch outside width across flats and 3/4-inch stock, each upright stave is 4.971 inches wide on the outside and 4.349 inches on the inside. The inside width across flats is 10.5 inches. These are finished sizes; allow for the saw kerf when cutting parts from stock.
Setting a table saw or miter saw
For a flat frame, use the miter saw’s turntable or the table saw’s miter gauge to set the miter angle. Keep the blade square to the board’s face. For upright staves, tilt the table saw blade to the bevel angle and rip the edges.
For tapered sides cut flat, set both the blade bevel and the miter angle. Check which scale your gauge uses. Follow your saw’s instructions for supporting and holding the work, and cut a test set before the final pieces. The cutting-to-a-line guide and measuring and marking guide cover the layout steps.
Common polygon angles
| Polygon | Cut off square | Interior angle | Glue-up angle |
|---|---|---|---|
| Triangle 3 sides | 60° | 60° | 30° |
| Square 4 sides | 45° | 90° | 45° |
| Pentagon 5 sides | 36° | 108° | 54° |
| Hexagon 6 sides | 30° | 120° | 60° |
| Octagon 8 sides | 22.5° | 135° | 67.5° |
| Decagon 10 sides | 18° | 144° | 72° |
| Dodecagon 12 sides | 15° | 150° | 75° |
Use the angles in a project
Try the picture frame project to practise matching miters. The simple box project starts with square butt joints; use this calculator when you move to a box with beveled corners.
Geometry, privacy and corrections
This tool assumes a regular polygon with equal sides, equal corner angles and matching cuts. Sizes describe the finished shape, without kerf or waste. Tapered sizes are base measurements; enter thickness measured across the base in the top view. For odd-sided shapes, the reported widths are circle diameters rather than distances between opposite faces or corners.
Entries are saved on this device; the calculator sends no entries to a server. Report a problem through the contact page.
Planning your first build?
The free First 5 Projects Roadmap gives you the sequence, tool list and a printable worksheet.