Compound Miter Calculator

What a compound miter is

Butt two boards that are both angled in plan (they meet at a polygon corner) and tilted from the bench (the sides lean), and the joint plane between them is square to neither face. Reaching it takes two adjustments at once: swing the saw table to the miter and tilt the blade to the bevel. Tapered planters, shadow-box frames, waste baskets, hoppers — same geometry every time.

The convention (read this before trusting any table)

Published compound-miter tables disagree with each other constantly, and it’s almost never the trigonometry — it’s the convention. This calculator pins one: θ is the side slope measured from horizontal. θ = 0° is a flat frame lying on the bench; θ = 90° is a vertical-sided box. Many references measure from vertical instead — call that φ. Since φ = 90° − θ, the identities are exact complements (the sines and cosines swap):

miter = atan(cos θ · tan(180°/n)) = atan(sin φ · tan(180°/n))
bevel = asin(sin θ · sin(180°/n)) = asin(cos φ · sin(180°/n))

If a chart’s numbers look wrong, subtract its slope from 90° and recompute — nine times out of ten they now agree. Both outputs here are degrees from a square cut (0° = square), which is how miter-saw scales read; a table-saw miter gauge reads 90° at square, so it takes the complement, 90 − miter.

Where the formulas come from

Each corner of a regular n-sided assembly must turn 360°/n of plan-view rotation, split between two cut faces — so each face handles a half-angle of 180°/n. With the sides flat (θ = 0°) that’s the whole story: miter = 180°/n, bevel = 0. Tilt the sides up by θ and the joint plane rotates with them; projecting the half-angle onto the saw’s two axes contributes the cos θ factor to the miter (the plan-view swing shrinks as sides steepen) and the sin θ factor to the bevel (blade tilt grows from nothing to the full half-angle at vertical). The boundary cases fall straight out: a flat frame is all miter, a vertical box all bevel.

Worked example: 6-sided planter, 15° slope

Six sides, each leaning 15° from horizontal (a gently tapered planter). Half-angle = 180°/6 = 30°:

miter = atan(cos 15° · tan 30°) = 29.1°
bevel = asin(sin 15° · sin 30°) = 7.4°

Set the miter saw to swing 29.1° and tilt 7.4°, cut both ends of all six sides, and the 120° corners of the hexagon close up. On a table-saw miter gauge, the swing reads 90 − 29.1° = 60.9°. Cut a test set from scrap first — six corners means twelve cut faces, and a 0.2° error per face is a visible 2.4° gap at the last joint.

Crown molding is the same math, renamed

Crown molding sitting between wall and ceiling is a compound miter where the slope is called a spring angle — and it’s quoted off the wall, i.e. from vertical, which is exactly the complementary convention above. For crown-specific settings (spring-angle presets, inside/outside corners, left/right piece guidance), use the crown molding angle calculator — it speaks that trade’s language directly.