Miter Angle Calculator

Miter angles are the precise angled cuts needed at the ends of boards so that two pieces join cleanly at a corner. The correct angle depends on the number of sides in the shape being built and whether you are cutting a flat miter, a bevel, or a compound cut.

Basic miter angle formula: Miter Angle = 90° ÷ Number of Sides

Or equivalently: Miter Angle = 180° ÷ (2 × Number of Sides)

This gives the angle each board end must be cut to, measured from the perpendicular (square cut = 0°).

Common miter angles by joint type:

• 90° corner (2 sides meeting): 45° miter each side
• Hexagon (6 sides): 30° miter each side
• Octagon (8 sides): 22.5° miter each side
• Pentagon (5 sides): 36° miter each side
• Triangle (3 sides): 60° miter each side
• Polygon (n sides): 90° ÷ n miter each side

Bevel vs. miter:

• Miter — angled cut across the face (flat board, angled ends, e.g. picture frames)
• Bevel — angled cut through the thickness (slanted cross-section, e.g. crown molding)
• Compound miter — both miter AND bevel applied simultaneously (e.g. angled crown molding on sloped ceiling)

Spring angle and compound miter (crown molding): Crown molding sits at an angle (spring angle, typically 38° or 45°). The compound cut formula: Miter = arctan(cos(spring angle) × tan(corner angle ÷ 2)) Bevel = arcsin(sin(spring angle) × sin(corner angle ÷ 2))

Worked example — picture frame: You want a rectangular picture frame (4 right-angle corners).

• Each corner = 90° total, split between two boards
• Each board miter = 90° ÷ 2 = 45°
• Cut each of your 4 frame pieces at 45° on both ends, mirrored (one left-hand, one right-hand cut per end)
• If your frame outer dimension is 12″ × 16″, long pieces are 16″ outside edge to outside edge; short pieces 12″ outside to outside

Tip: Always test with scrap wood before cutting finished material. Even 0.5° of error in four corners compounds to a 2° total gap — enough to ruin a frame join.