Miter Angle Calculator
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Calculate miter saw angles for any corner and learn how to calculate miter angles step by step: simple 90° corners, polygon and picture-frame miters (hexagon miter, octagon miter, any N-sided frame), compound miter and bevel for crown molding with any spring angle, and a segmented-turning mode for woodturners (segment angle, segment length, ring stack). Every result includes the saw setting, degrees-minutes-seconds, and a live diagram.
Simple miter angle
Two pieces meet at a corner. Each piece is cut at half the corner angle — this is the answer to "what angle to miter corners" of any shape. Use it as a miter angle finder: enter a measured corner (also works for splayed miter / non-90° corners) and get the exact saw setting.
Set your miter saw dial to the miter angle (0° on the saw = square cut). For an outside corner, flip the workpiece; the angle is the same.
Miter joint vs butt joint
| Miter joint | Butt joint | |
|---|---|---|
| Cut on each piece | — | 90° (square) on one piece; other runs full length |
| End grain visible | Hidden on both faces | Visible on one face |
| Glue surface | Angled — mostly end grain; add splines/biscuits for strength | End grain to long grain — simple, decent with screws |
| Best for | Picture frames, trim, visible corners | Carcasses, shop furniture, hidden joints |
Polygon / picture-frame miter
For a regular N-sided frame, cut each end of each piece at 180° ÷ N. Hexagon = 30°, octagon = 22.5°, pentagon = 36°.
Cut both ends of every piece at the miter angle. Dry-fit the full ring before glue-up; a 0.25° error per joint multiplies across N joints.
Compound miter + bevel (crown molding)
Crown molding corners need a miter (saw table swing) and a bevel (blade tilt) cut at the same time. Enter the wall corner angle and the molding's spring angle (angle between the molding's back and the wall).
Common check: 90° corner + 38° spring → miter 31.62°, bevel 33.86°. Cope inside corners when the profile allows; walls are rarely square, so measure each corner.
Segmented turning
Glue trapezoid segments into rings, stack the rings, turn the vessel. Each segment end is cut at 180° ÷ segments; the segment length is the chord of the ring plus your fudge factor.
Cut all segments a hair long, glue the ring slightly oversize, then true it on the lathe or sander. The arc-length shortcut runs ~1% long — free fudge.
Miter angle charts
How the math works
Simple miter
Each workpiece carries half the corner. A 90° corner needs two 45° cuts; a 135° splayed corner needs two 67.5° cuts.
Polygon / frame miter
Walking around a closed polygon turns 360° total; each joint turns 360°/N, and each of the two meeting cuts takes half: 180°/N.
Compound miter (crown molding)
bevel = arcsin( sin(C/2) × cos(S) )
where C = wall corner angle and S = spring angle. Verified against the textbook case (90° corner, 45° spring → miter 35.26°, bevel exactly 30°) and cross-checked with an independent Python implementation.
Segmented turning
segment outer length = outside diameter × sin(180° ÷ N)
shop shortcut = π × outside diameter ÷ N
The ring is a regular N-gon, so the cut angle is the polygon miter. The exact segment length is the polygon's side (chord); the arc-length shortcut is about 1% longer and works as built-in oversize.
Frequently asked questions
What is a miter angle?
A miter angle (also spelled mitre) is the angle cut on the end of each workpiece so that two pieces meet cleanly at a corner. For a standard 90-degree corner, each piece is cut at 45 degrees, so the two 45-degree faces close to form the 90-degree corner.
What angle do I set my miter saw to for a 90-degree corner?
Set the saw to 45 degrees. On almost every miter saw the scale reads 0 degrees for a square crosscut, so the saw setting equals the miter angle directly: 45 degrees on the saw cuts a 45-degree miter, which is what each piece of a 90-degree corner needs.
How do you calculate miter angles for a polygon?
For a regular polygon with N sides, cut each end of each piece at 180 divided by N degrees. A hexagon (6 sides) needs 30-degree miters, an octagon (8 sides) needs 22.5-degree miters, and a pentagon needs 36-degree miters.
What is the miter angle for a hexagon? For an octagon?
A hexagon uses a 30-degree miter on each end of each of its 6 pieces (180/6). An octagon uses a 22.5-degree miter on each end of each of its 8 pieces (180/8). See the polygon chart above for more.
What is the difference between a miter angle and a bevel angle?
The miter angle is cut across the width of the board (the miter saw table swings left/right to set it). The bevel angle is cut through the thickness of the board (the saw blade tilts to set it). A compound cut combines both at once, which is what crown molding corners require.
What is spring angle on crown molding?
The spring angle is the angle between the back of the crown molding and the wall when the molding is installed. The most common profiles are 38 degrees (a 38/52 profile), 45 degrees, and 52 degrees. The spring angle is the key input for compound miter calculations.
How do you calculate compound miter angles?
Given the corner angle C and the spring angle S: miter = arctan(sin(S) ÷ tan(C/2)) and bevel = arcsin(sin(C/2) × cos(S)). For example, a 90-degree corner with 38-degree spring angle gives a 31.62-degree miter and a 33.86-degree bevel.
Is an inside corner miter different from an outside corner miter?
The angles are identical; only the orientation of the workpiece flips. For an inside corner the long point of the miter faces the back of the piece, for an outside corner it faces the front. Always measure the actual wall angle first, since real walls are rarely exactly 90 degrees.
How do I miter a corner that is not 90 degrees (splayed corner)?
Measure the actual corner angle with an angle finder, then cut each piece at half that angle. A 135-degree splayed corner needs a 67.5-degree miter on each piece. Use the Simple miter mode of this calculator with your measured angle.
For segmented woodturning, what angle do I cut each segment?
Cut each end of every segment at 180 divided by the number of segments. A 12-segment ring needs 15-degree cuts, a 16-segment ring needs 11.25-degree cuts. This is the same polygon miter formula applied to a turning ring.
How do I calculate segment length for segmented turning?
The exact-fit outer length of each segment is the chord of the ring: outside diameter × sin(180 degrees / number of segments). Many turners use the shop shortcut arc length (π × diameter / segments), which runs about 1 percent long, then add a 1/4-inch fudge factor and trim after glue-up.
Miter joint vs butt joint — which is stronger?
A butt joint (one square-cut piece butted into the other) is simpler and the end grain is hidden on only one side, but it shows end grain on the outside face. A miter joint hides end grain on both faces and looks cleaner, though the angled glue surface is mostly end grain and benefits from splines, biscuits, or dowels for strength.
My miter saw scale only goes 0 to 45 — how do I set it?
Zero on the scale is a square 90-degree crosscut, so you set the dial directly to the miter angle: 45 for a picture frame corner, 30 for a hexagon, 22.5 for an octagon. The calculator shows the saw setting explicitly for every result.
Can I see the answer in degrees, minutes, and seconds?
Yes. Every result on this page shows the decimal degrees plus the degrees-minutes-seconds equivalent, for example 31.62 degrees = 31° 37' 8". Useful when your saw or angle finder reads in DMS.
Should I cut exactly to the calculated length or add extra?
Add a fudge factor. Wood moves, blades deflect, and glue-ups need trimming: most woodworkers add about 1/4 inch to segment lengths and sneak up on the final fit. Always make a test cut in scrap with your actual saw and blade before cutting good stock.
Is my data private when I use this calculator?
Yes. This calculator runs 100% in your browser with no server, no tracking of your inputs, and no network requests. Your dimensions never leave your device.