Miter Angle Calculator
Splitting a Corner Evenly Between Two Pieces
Building a picture frame, planter box, or any regular polygon out of mitered pieces comes down to one piece of geometry: the full corner angle needs to be split evenly between the two pieces that meet there, and your miter saw is set to that half-angle rather than the corner angle itself. Get the saw setting wrong by even a degree or two on each of several joints and the errors compound into a frame that won't close.
The Formulas
Miter Cut Angle (saw setting) = 180 ÷ N
N is the number of sides in the regular polygon. Since two mitered pieces meet at each corner and together must account for the full corner angle, each piece's saw angle is exactly half of the corner angle — which simplifies to 180 divided by the number of sides.
Miter Angles for Common Shapes
| Sides (N) | Shape | Corner angle | Miter saw setting |
|---|---|---|---|
| 3 | Triangle | 120° | 60° |
| 4 | Square/rectangle | 90° | 45° |
| 5 | Pentagon | 72° | 36° |
| 6 | Hexagon | 60° | 30° |
| 8 | Octagon | 45° | 22.5° |
| 12 | Dodecagon | 30° | 15° |
The familiar 45° picture-frame setting is simply the N=4 case — every other regular polygon frame uses a different miter angle, which is easy to forget when a project moves away from standard rectangular frames.
Where This Matters
- Building picture frames and boxes — standard rectangular frames use the well-known 45° setting, but any non-rectangular frame shape needs its own calculated angle.
- Constructing octagonal or hexagonal projects — planters, tabletops, and gazebo-style structures built as regular polygons all rely on getting this angle exact, since small errors compound around the full perimeter.
- Custom picture mats and segmented turning — woodturners building segmented bowls from wedge-shaped pieces use this same angle logic to determine each segment's cut angle.
How to Use This Calculator
- Enter the Number of Sides (N) of the frame.
- Select Calculate to see the full corner angle and the miter saw setting for each piece.
Related Calculations
Work out table leg splay angles with the Table Leg Angle Calculator, or plan your cut list before starting the frame with the Wood Cutting Calculator.