Cutting Miters and Compound Angles

The corner is always the same math

Any regular frame with n sides has corner angles of 360° / n. For a flat piece the miter cut is simply half that corner:

Miter (flat) = 360° / (2·n)

A square frame: 90°/2 = 45°. A hexagon: 60°/2 = 30°.

Compound angles (tilted pieces)

When the piece is tilted (crown molding, angled frames) with spring angle tilt:

Miter = atan( tan(corner/2) × cos(tilt) )
Bevel = asin( sin(corner/2) × sin(tilt) )

Worked example

Crown molding at 38° spring around a 90° corner:

corner/2 = 45°
miter = atan( tan45 × cos38 ) = atan(0.788) ≈ 38.2°
bevel = asin( sin45 × sin38 ) = asin(0.435) ≈ 25.8°

Practical tips

• Mark the outside face of every piece — miters meet on the same side.
• Test on offcuts first: saws read angles from different reference planes.
• A stop block makes identical cuts repeatable.

Let the miter angle calculator do the trig and print the table.