Miter & Compound Miter Angles
Miter angle for any corner, compound miter and bevel for crown moulding laid flat from the corner and spring angle, and the cut angle for n-sided frames.
Saw settings from square for each piece (miter, and bevel for crown) with which end to keep, the cut angle from the edge, and for polygons the interior angle and number of cuts.
Example: A 135° bay-window corner is a 22.5° miter; 38° crown on a square corner cuts flat at miter 31.6° and bevel 33.9°, 45° crown at 35.3° / 30°; an octagon frame is 22.5° per cut.
Half the corner —
or the crown formulas.
How the flat miter is found, what the compound formulas do, and how saws are set.
Flat miters
Two pieces meeting at a corner of C degrees each need a cut of C/2 from the edge, which on a saw is (180 − C)/2 from square: 45° for a square corner, 22.5° for a 135° bay window. An n-sided frame turns 360/n at each joint, so each cut is 180/n from square (22.5° for an octagon) and the interior angle is (n − 2)·180/n.
Crown moulding laid flat
Crown sits at a spring angle S between wall and ceiling; cut flat on the saw table it needs both a miter and a bevel: miter = atan(sin S ÷ tan(C/2)), bevel = asin(cos S · cos(C/2)). For a square corner these give the familiar detents — 31.6° / 33.9° for 38° crown, 35.3° / 30° for 45° crown. Which way to swing the miter and which end to keep differs for inside and outside corners and for the left and right pieces; the page spells it out. Nesting the crown upside-down against the fence needs only the plain miter.
Measure and test
Real corners are rarely 90°: measure with an angle finder and enter that. Saw scales, blade deflection and the moulding's actual spring angle each add a degree or so, so cut test pieces first. Settings are "from square" throughout (0° = square cut). Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.
SOURCES
- Flat miter = (180° − corner) ÷ 2; crown laid flat: miter = atan(sin S ÷ tan(C/2)), bevel = asin(cos S · cos(C/2)) with spring angle S and corner C; polygon miter = 180° ÷ n
Last reviewed 22 September 2026. How results are checked: How we verify.