A compound miter calculator determines the exact miter and bevel angles for your table saw or miter saw when building polygon shapes with sloped sides. Enter the number of sides, the splay angle (how far the finished sides lean out of vertical) and how the board sits in the finished piece, and you get precise blade settings for picture frames, planters, crown molding, and hopper joints. Stock is cut lying flat on the saw table throughout.
Project Parameters
Saw Settings
Technical Blueprint
Precision Measurement Gear
Compound angles require absolute precision. If your table saw blade is off by even half a degree, the joints on your splayed planter or hopper box will have glaring gaps. We strongly recommend using a magnetic digital angle gauge to set your blade bevel perfectly to the decimal. For setting your miter gauge or chop saw rotation, throw away the cheap plastic protractor and use a high-quality machined aluminum miter protractor.
How to Calculate Compound Miter Angles
A four-sided box with straight vertical sides is easy, but it has two different easy answers and they are not the same cut. Build it from boards whose wide faces become the walls and every corner is a 45° bevel with the table square. Build the same square as a flat picture frame and it is a 45° miter with the blade plumb. One of the two settings is zero either way. The moment you lean the sides out of vertical, for a wooden planter, a dust collection hopper, or crown molding sprung off the wall, both settings come off zero at once and neither of them is 45° any more. That is the compound angle: the Miter Angle is the rotation of your saw table and the Bevel Angle is the tilt of your saw blade, and they have to be set together.
Because the two orientations are exactly one complement apart, a splay angle fed to the wrong one returns a pair of numbers that looks entirely reasonable and cuts a joint that will not close. So tell the calculator both things: how far the sides lean out of vertical, and whether the board's wide face becomes the sloping side or lies across the opening. Stock is cut lying flat on the saw table in both cases. As a sanity check you can run against any printed crown chart: a 38° spring crown at a 90° corner is four sides at 38° of splay with the wide face as the sloping side, and AngleForge returns 31.6° miter and 33.9° bevel.
Frequently Asked Questions
What is a compound miter cut?
A compound miter cut combines two angles simultaneously: a miter angle (the blade rotates left or right) and a bevel angle (the blade tilts). This is required when joining boards that meet at both a horizontal angle and a vertical slope, such as crown molding, picture frames with sloped sides, or polygon planters.
How do you calculate compound miter angles for a polygon box?
Splay is how far the finished sides lean out of vertical, and the stock is cut lying flat on the saw table. When the board's wide face becomes the sloping side, as in a planter, a hopper or crown molding, the miter angle is arctan(sin(splay) × tan(180°/N)) and the bevel angle is arcsin(cos(splay) × sin(180°/N)). When the wide face instead lies across the opening, as in a picture frame or a segmented ring, the two splay factors swap: arctan(cos(splay) × tan(180°/N)) and arcsin(sin(splay) × sin(180°/N)). The polygon factor inside the bevel is sin(180°/N) either way. A 38° spring crown at a 90° corner is N = 4 with 38° of splay, which gives 31.6° miter and 33.9° bevel.
Which orientation do I pick, sloping side or flat frame?
Look at the finished piece, not the saw. If the board's wide face ends up as one of the sloping sides, the way it does in a planter, a hopper, a tapered box or a run of crown molding, pick the sloping side. If the wide face ends up lying across the opening the way a picture frame or a segmented turning ring does, pick the flat frame. Both are cut lying flat on the saw table. The two answers are one complement apart, so choosing the wrong one hands you a plausible pair of numbers and a joint that will not close.
Why don't my compound miter joints close properly?
The most common causes are: (1) cutting the stock in the wrong orientation, because the same joint needs one pair of settings when the board's wide face becomes the sloping side and a different pair when that face lies across the opening, and the two are not interchangeable, (2) reading the complement off the saw scale, since some scales measure from the fence and some from the blade, (3) calibration drift on the miter or bevel scales, and (4) blade thickness eating into one side of the joint. Always make test cuts on scrap wood first.