Angle Calculator — Mitres, Bevels & Polygon Joints

A hexagon (6 sides) has interior angles of 120 degrees. The mitre saw setting is 180 divided by the number of sides: 180 / 6 = 30 degrees. Set the saw to 30 degrees (measured from a square crosscut, which most saws read as 0 degrees). Each joint is made from two pieces, each cut at the 30 degree setting, and the two cuts together close the 120 degree corner.

The interior angle is (n-2) x 180 / n, where n is the number of sides. The mitre saw setting is 180 / n (this equals 90 minus half the interior angle, measured from a square crosscut). For example: pentagon (5 sides) = 108 degrees interior, 36 degree saw setting; octagon (8 sides) = 135 degrees interior, 22.5 degree saw setting; square = 45 degrees; hexagon = 30 degrees.

A mitre angle is a cut across the face of the board (the saw head rotates left or right). A bevel angle is a cut through the thickness of the board (the saw blade tilts). Compound angles require both mitre and bevel adjustments simultaneously.

Use the law of cosines: cos(A) = (b² + c² - a²) / (2bc). This calculator handles this automatically. Enter all three side lengths and it will compute all three angles. This is useful for fitting pieces into irregular spaces.

Complementary angles sum to 90 degrees (useful for right-angle joints). Supplementary angles sum to 180 degrees (useful for straight-line joints). If you know one angle of a right-angle joint, the complementary angle is what your mitre saw needs to be set to.