The saw angle for picture frames and any-sided polygons, and the compound miter and bevel for splayed boxes — planters, hoppers and staved columns. Enter the number of sides, or set a custom corner angle.
Project type
A regular shape with this many equal sides. Four sides is an ordinary rectangular frame.
The angle of the joint between two pieces. A square frame corner is 90°. Miter = (180° − this) ÷ 2.
How far the sides lean outward from plumb. 0° is a straight-walled box. If the top overhangs the base by d over a side height h, slope = arctan(d ÷ h).
A saw is only as accurate as its calibration. Always cut scrap test pieces and dry-fit a corner before cutting your finished stock.
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Cutting crown molding against a wall and ceiling?
The Crown Molding Angle Calculator handles sprung molding at any spring angle, with the flat-on-table and nested methods and a saw-orientation diagram for inside and outside corners.
The one rule for flat frames
For any regular flat frame — the kind where every piece lies in a single plane — the saw miter angle is simply:
miter = 180° ÷ number of sides
Four sides give 45° (a normal picture frame), six give 30°, eight give 22.5°. You set that angle on the saw and cut both ends of every piece, swinging the saw to opposite sides for the two ends so each piece is a little trapezoid. The bevel stays at zero, because nothing is tilting out of the plane.
If the shape isn’t regular — one odd corner, or pieces meeting at an angle you measured directly — tick the custom box and work from the corner angle the two pieces form. The miter is half of what’s left after that corner: (180° − corner) ÷ 2. A 90° corner gives 45°; a 120° corner gives 30°.
Splayed boxes need a second angle
Once the sides lean outward — a planter, a hopper, a tapered tray, a staved column — each joint stops being flat and becomes a compound cut. Now you set both a miter and a bevel. With N sides and a slope T measured from vertical:
miter = arctan( cos T × tan(180° ÷ N) ) bevel = arcsin( sin T × sin(180° ÷ N) )
As the slope grows, the miter drifts a little smaller and the bevel opens up. At a slope of 0° the bevel vanishes and the miter falls back to 180° ÷ N — the flat-frame number — which is a handy check that you’ve entered things correctly.
Common frame chart
Shape
Sides
Miter (saw)
Triangle
3
60.0°
Square / rectangle
4
45.0°
Pentagon
5
36.0°
Hexagon
6
30.0°
Octagon
8
22.5°
Dodecagon
12
15.0°
Splayed 4-sided box, by slope
Slope
Miter
Bevel
5°
44.9°
3.5°
10°
44.6°
7.1°
15°
44.0°
10.5°
22.5°
42.7°
15.7°
30°
40.9°
20.7°
Getting tight corners
Calibrate the saw against a known square before trusting the scale; a fraction of a degree multiplies across every corner.
Cut opposite sides to identical lengths — a stop block beats a pencil mark for repeat cuts.
Hold the work firmly to the fence; a piece that creeps mid-cut changes the angle.
Dry-fit with a band clamp or tape before any glue touches the joint.
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Frequently asked questions
What miter angle do I cut for a picture frame?
A four-sided frame has 90° corners, so each end is cut at 45° — set the saw to 45° and cut both ends of every piece. The general rule is miter = 180° ÷ number of sides: a triangle is 60°, a pentagon 36°, a hexagon 30°, an octagon 22.5°. Both mating ends use the same setting, swung to opposite sides.
How do I find the miter for a polygon with any number of sides?
For a flat regular polygon, the saw miter is 180 divided by the number of sides. Five sides give 36°, seven about 25.7°, ten give 18°. If the shape isn’t regular, work from the corner angle the pieces form: miter = (180° − corner) ÷ 2, so a 120° corner needs a 30° miter.
What’s the difference between a flat frame and a splayed box?
In a flat frame every piece lies in one plane, so you set only a miter and leave the bevel at zero. A splayed box has sides that lean outward — a planter, hopper or staved column — so each joint is a compound cut with both a miter and a bevel. As the slope rises the miter shrinks a little and the bevel grows; at zero slope it reverts to a flat frame.
Why don’t my frame corners close up tight?
Usually a saw set a hair off, pieces cut to slightly different lengths, or the workpiece shifting against the fence. With four corners, a half-degree error at each becomes two degrees of gap. Cut test pieces in scrap, dry-fit, and nudge the saw a little at a time before cutting good stock.
How do I measure the slope angle for a splayed box?
Slope is how far the sides lean from vertical: a straight box is 0°, a side flaring 15° from plumb has a 15° slope. If the top edge overhangs the base by d over a side height h, the slope is arctan(d ÷ h). Enter that and the calculator returns the compound miter and bevel for each joint.