Miter Angle Calculator
When building picture frames, cabinet face frames, polygon tabletops, or any assembly where pieces meet at corners, you need to cut each piece at half the interior corner angle. For a regular polygon with n sides, the interior angle is (n-2) * 180 / n degrees, and the miter angle (the saw setting from 90 degrees square) is half that. This calculator accepts the number of sides and returns the interior corner angle and the miter saw angle setting. It also shows the exterior angle, which is useful when marking out the assembly.
Miter angle formula
Interior angle = (sides - 2) × 180 / sides
Miter angle = Interior angle / 2
Exterior angle = 360 / sides
For a square frame (4 sides): interior angle = (4-2)*180/4 = 90 degrees, miter angle = 45 degrees. For a hexagon (6 sides): interior angle = 120 degrees, miter angle = 60 degrees. The exterior angle (360/sides) equals the amount you turn from one side to the next when walking around the outside of the shape.
Using the miter angle
- Set your miter saw to the miter angle shown. Most saws show the angle from 90 degrees perpendicular, which matches this output directly.
- Cut both ends of every piece at the same miter angle, one cut mirrored from the other.
- For frames, measure the inside dimension first: the short point of the miter is at the inside corner.
- Test fit with scrap before cutting finished material. Even small errors in angle compound across multiple joints.
- For polygons with many sides (8 or more), a miter saw with a positive stop at the required angle simplifies accurate cutting.
Miter angle calculator: frequently asked questions
What miter angle do I need for a square frame?
A square frame has 4 sides, so the corner angle is 90 degrees. The miter cut on each piece is 90/2 = 45 degrees. Set your miter saw to 45 degrees.
What miter angle is needed for a hexagonal frame?
A regular hexagon has 6 sides. Interior angle = (6-2) * 180 / 6 = 120 degrees. Miter angle = 120/2 = 60 degrees. Equivalently, 90 - 180/6 = 90 - 30 = 60 degrees.
How is the miter angle different from the bevel angle?
A miter cut is made horizontally across the face of a board (swinging the saw table left or right). A bevel cut is made through the thickness of the board (tilting the saw blade). For flat frames such as picture frames, you need a miter cut. For compound miters such as crown moulding, you need both.
How do I calculate the miter angle for an irregular polygon?
This calculator is for regular polygons where all sides and angles are equal. For an irregular frame, you need to know the actual interior angle at each corner, then bisect it. The miter angle at any corner is half the interior angle.
What is the miter angle for an octagonal frame?
An octagon has 8 sides. Interior angle = (8-2) * 180 / 8 = 135 degrees. Miter angle = 135/2 = 67.5 degrees. This is the saw setting for each cut.
Official sources
- USDA Forest Products Laboratory: Wood Handbook, FPL-GTR-190 (general woodworking geometry).
- NIST: Weights and Measures.
Reviewed by the CalculatorHub team, edited by James Graham, 15 June 2026. See our methodology.