Cutting & joints
Regular polygon mitres
- where
- interior angle (°)
- number of sides
- saw setting from square (°)
Explain this equation
Gives the corner angle and mitre setting for a flat frame with any number of equal sides, such as a hexagonal or octagonal frame or planter.
n is the number of sides. θ is the interior angle at each corner, in degrees. β is the saw setting from square for each end of every piece.
Going round any closed shape turns through 360° in total, so each corner turns 360/n, and the interior angle is 180 minus that. Each joint is shared by two pieces, so each cut is half the turn: 180/n.
A square is 90° with 45° cuts. A hexagon is 120° with 30° cuts. An octagon is 135° with 22.5° cuts.
Watch out: this is for flat frames only. Boxes with sloping sides need compound angles.
Calculate equal mitres for a flat regular polygon frame.
Enter your values to see the result.
Good to know
Equal sides and coplanar members. This is not a compound bevel for sloping-sided boxes.
Sources
- Geometry / arithmetic
This is a calculation aid, not a structural design or compliance certificate. Every default is an example, not a specification for your project.