Miter & Bevel Angle Calculator
Calculate miter and bevel angles for flat frames, pyramid structures, and angled polygon assemblies given the number of sides and frame type. Ideal for picture frames, roof peaks, and decorative polygon boxes.
About this calculator
The required miter angle depends on both the number of sides in the polygon and the geometry of the frame. For a flat frame, the miter angle is: miterAngle = 90 − (360 / (2 × numberOfSides)). For a pyramid or 3D structure, the compound miter involves the bevel angle and the polygon geometry: miterAngle = arctan(cos(π / numberOfSides) × tan(bevelAngle)) × (180 / π). For other frame types, the formula uses: miterAngle = 45 − (360 / (4 × numberOfSides)). Each formula ensures that all corner joints close perfectly when identical pieces are assembled. A flat 4-sided frame gives the familiar 45° miter; a flat 6-sided frame gives 60°; an 8-sided flat frame gives 67.5°. Pyramid frames introduce a tilt (bevel angle) that requires trigonometric correction.
How to use
Example 1 — flat hexagon picture frame (6 sides): miterAngle = 90 − (360 / (2 × 6)) = 90 − 30 = 60°. Set the miter saw to 60° and cut both ends of each of the 6 pieces. Example 2 — pyramid frame with 4 sides and a 30° bevel angle: miterAngle = arctan(cos(π / 4) × tan(30°)) × (180 / π) = arctan(0.7071 × 0.5774) × 57.296 = arctan(0.4082) × 57.296 ≈ 22.2°. Set miter to 22.2° and bevel to 30° for a clean pyramidal assembly.
Frequently asked questions
What miter angle do I need to cut a regular octagon frame?
For a flat 8-sided (octagon) frame, the formula gives miterAngle = 90 − (360 / (2 × 8)) = 90 − 22.5 = 67.5°. Each of the eight pieces gets a 67.5° miter cut on both ends. Most miter saws only tilt to 60°, so you may need to set the saw to 67.5° on the miter scale (not the bevel). Always dry-fit all eight pieces before applying glue to confirm the joints close without gaps.
How do I calculate compound miter angles for a pyramid box or tapered frame?
A pyramid or tapered frame requires both a miter angle and a bevel angle because the sides lean inward at a tilt. The miter angle is calculated as arctan(cos(π / numberOfSides) × tan(bevelAngle)), where bevelAngle is the desired lean of the sides from vertical. Both angles must be set simultaneously on the saw — the miter adjusts the horizontal cut and the bevel adjusts the vertical tilt. This two-angle compound cut is more complex than a flat frame miter, so making test cuts in cheap material before using finish lumber is strongly recommended.
Why does a square frame need 45° miters but other polygons need different angles?
A square has four 90° corners, and to bisect a 90° corner evenly between two pieces, each piece gets a 45° cut. A pentagon has five 108° corners, requiring a 54° miter; a hexagon has six 120° corners, needing 60° miters. The general rule for a flat frame is that the miter angle equals half the interior angle of the polygon, which simplifies to 90 − (180 / numberOfSides). This calculator handles all regular polygons so you do not need to compute the interior angles manually.