Calculate miter angles for frames, polygons, and corner joints in woodworking and construction. Quickly determine the complementary angle for two-piece miters.
2026-04-09T00:00:00Z
Enter number of sides for polygon (minimum 3)
An angle cut (or miter cut) is a diagonal cut made across the face of material to create angled joints. These cuts are essential in carpentry, framing, and decorative applications where materials need to meet at precise angles.
There are two primary types: a miter cut is an angled cut made across the face of a board (creating a 45° angle for 90° corners), while a bevel cut is an angled cut through the edge or thickness. When both cuts are applied simultaneously, the result is a compound cut, commonly used for crown molding and complex joinery. This calculator computes miter angles; bevel and compound angles require specialized references or software.
This calculator determines the exact miter angle needed for polygon shapes (hexagonal frames, octagonal windows, etc.) and custom corner angles that may not be perfectly square (common in older buildings or irregular spaces).
Each interior angle of a regular polygon is (n-2) × 180° / n, where n is the number of sides. To create a closed polygon with mitered corners, each cut angle is half this interior angle, which simplifies to 180° divided by the number of sides.
Example: A hexagon (6 sides) requires 30° cuts on each end (180° ÷ 6 = 30°).
For any corner angle (whether 90°, 120°, or irregular), divide by 2 to get the individual miter angle for each piece. This ensures both pieces meet perfectly at the desired corner angle.
Example: A 90° corner requires two 45° miter cuts (90° ÷ 2 = 45°).
Scenario: Building a hexagonal picture frame
A miter cut is made across the face of the board at an angle, while a bevel cut is made along the thickness or edge. A compound cut combines both for complex joinery like crown molding.
When two pieces meet at a corner, each receives half of the total corner angle. This symmetry ensures both pieces fit perfectly together at the desired angle.
Measure the actual corner angle with a protractor or angle finder. Enter that angle in Corner Mode, and the calculator will give you the correct cut angle for that specific corner.
Basic miter calculations work, but crown molding requires compound cuts considering the spring angle. Consult a crown molding angle chart or specialized calculator for precise compound angles.
The complementary angle (90° - miter angle) represents the angle between the cut and the edge perpendicular to the cut direction. It's useful for reference and verification.
For frames and visible joinery, maintain accuracy to at least 0.5°. Even 1° errors can cause joints to not close properly on larger pieces, creating visible gaps.
Square (4 sides): 45°, Pentagon (5 sides): 36°, Hexagon (6 sides): 30°, Octagon (8 sides): 22.5°. These are standard cuts for picture frames and decorative work.
Yes! The formula works for any number of sides 3 or greater. Triangle frames need 60° cuts, while a 12-sided dodecagon needs 15° cuts.
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