Mitre Angle Polygon
Calculator

The mitre angle equals 180 degrees divided by the number of sides, then divided by 2 (equivalently, 90 degrees minus 180/n divided by 2, depending on how the angle is referenced). For a standard 4-sided square frame this gives the familiar 45-degree mitre.

Each corner of a closed polygon must account for an equal share of the total 360-degree turn around the shape. A hexagon (6 sides) needs a smaller angle turn per corner than a square (4 sides), so the mitre cut angle at each joint is correspondingly different.

This depends on your saw's angle convention: a mitre saw scale usually reads the angle from square (90 degrees), while some references state the angle from the board's long edge. Always confirm which convention your tool uses before cutting, since the two conventions are complements of each other.

A slightly inaccurate saw calibration gets multiplied by the number of corners in a closed polygon, so small errors compound and leave a visible gap at the last joint. Cutting a test frame first and checking closure before committing to final stock is the standard way to catch this.

Yes, this calculator assumes a regular polygon with equal sides and equal angles. An irregular shape needs each corner's angle calculated individually from its own interior angle, since there's no single mitre angle that applies to every joint.