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 = 180° ÷ Number of Sides

Or equivalently, half the exterior angle: Miter Angle = (360° ÷ Number of Sides) ÷ 2

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

Common miter angles by polygon:

• Square or rectangle (4 sides): 45° miter each side
• Triangle (3 sides): 60° miter each side
• Pentagon (5 sides): 36° miter each side
• Hexagon (6 sides): 30° miter each side
• Octagon (8 sides): 22.5° miter each side
• Polygon (n sides): 180° ÷ n miter each side

A picture frame is the square case, so both boards at every corner get cut at 45°, and that is where the number everyone knows comes from.

Be careful about why, though, because the obvious explanation is wrong. It is tempting to say a 90° corner splits into two 45s, but a hexagon corner is 120° and its miter is 30°, not 60°. A miter saw reads its angle from square, not from the corner. So the setting is 90° minus half the interior angle:

For a hexagon: 90 − (120 ÷ 2) = 90 − 60 = 30° For a square: 90 − (90 ÷ 2) = 90 − 45 = 45°

Work that through for a general n-sided shape and it collapses neatly to 180 ÷ n, which is the formula above. The square is the one case where the shortcut and the real rule happen to agree, which is exactly why the shortcut survives.

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, measured from the wall, typically 38° or 45°). Set the spring angle in the calculator and it switches to the compound formulas: Miter = arctan(sin(spring angle) × tan(corner angle ÷ 2)) Bevel = arcsin(cos(spring angle) × sin(corner angle ÷ 2))

For standard 52/38 crown on a square corner, that gives 31.62° miter and 33.86° bevel, the two numbers printed on nearly every miter saw’s crown scale. If your saw settings come out at 35.26° and 30°, you have entered a 45° spring angle by mistake.

That pair, 31.6 and 33.9, is the single best sanity check on this whole page. Any crown calculator that does not produce those two numbers for a 38° spring on a square corner is doing something wrong, and so is any tutorial that tells you to just set both to 45.

Worked example, a picture frame: You want a rectangular picture frame, so 4 sides.

• Miter = 180 ÷ 4 = 45°, the same answer either way of getting there
• 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. A four-sided frame takes eight cuts, so half a degree of error on each one leaves a 4° gap by the time the last corner closes. No amount of clamping pressure pulls that shut, and glue will not fill it either.

Two habits fix most of it. Cut all the like pieces without touching the saw between them, and check the setting against a known-good test corner rather than trusting the detent, because a miter saw detent that has been knocked around a job site is off more often than not.