How do I calculate compound miter angles?

For an N-sided assembly whose sides slope by angle T from vertical: miter = arctan(cos(T) · tan(180/N)) and bevel = arcsin(sin(T) · cos(180/N)). This tool does it for you.

Compound Miter Calculator

Q: What is a compound miter?

A compound miter is a cut that combines a miter angle (across the face) with a bevel angle (blade tilt). You need it whenever the sides of a box or vessel lean inward or outward, like a planter, hopper, or staved column.

Building a planter, hopper, or any box with sloped sides? Get the exact miter and bevel angles for a clean, gap-free ring — the math people most often get wrong. Sign in to save your setups.

Number of sides

Side slope from vertical (degrees)

0° = a straight-walled box. Larger = more flare (planter, hopper, bowl).

Miter (saw)

44.01°

gauge from square

Bevel (tilt)

10.55°

blade from vertical

Set your miter gauge to 44.01° and tilt the blade to 10.55°. Always cut a test piece in scrap first — small slope errors compound around the ring.

For planning purposes only. Woodworking involves variation in materials, moisture, and technique, so results are estimates — always double-check the numbers against your own measurements and judgment, and test on scrap before committing to a real workpiece. Sawdust Journey is not liable for material loss, injury, financial damages, or errors resulting from use of this tool.

Compound miter angles, without the guesswork

A compound miter is any cut that combines two angles at once: a miter across the face of the board and a bevel through its thickness. You need one whenever the sides of a project lean in or out instead of standing straight up — canted planter boxes, hoppers and chutes, staved columns, flared bins, and multi-sided vessels. Get both angles right and the pieces close into a perfect ring; get them a little wrong and the gaps multiply around every joint. This compound miter calculator gives you both angles for any number of sides and any slope, so you set the saw once and cut with confidence.

Miter vs. bevel: what the two numbers mean

The miter angle is what you set on the miter gauge or the swing of a miter saw, measured from a square (90°) crosscut. The bevel angle is how far you tilt the saw blade away from vertical. For a shape with N sides whose faces lean out from vertical by an angle T, the exact relationships are:

miter = arctan( cos(T) × tan(180 / N) )
bevel = arcsin( sin(T) × cos(180 / N) )

When the sides stand straight up (T = 0) the bevel is zero and the miter is just the ordinary flat-frame angle — 45° for a four-sided box, 30° for a hexagon, 22.5° for an octagon. As the slope steepens, the bevel grows and the miter shrinks.

Common shapes and slopes

A four-sided box with sides sloped 45° from vertical — the classic hopper — works out to roughly a 35.3° miter and a 30° bevel. A six-sided planter with a gentle 10° flare needs only a small bevel and a miter close to 30°. Because both angles depend on the number of sides and the slope together, even a couple of degrees of extra flare changes the settings — which is exactly why guessing, or reusing a chart for the wrong slope, leads to gappy joints.

How to use the calculator

Pick the number of sides — 4 for a box, 6 or 8 for a planter or vessel, and so on.
Enter the slope from vertical in degrees. Zero is a straight-walled box; larger numbers flare the sides out more.
Read off the miter (miter-gauge setting) and bevel (blade tilt), set your saw, and cut a test ring in scrap first.

Tips for tight compound-miter joints

Always test in scrap. Cut all the pieces for one ring and dry-fit before touching good stock — small slope errors compound around the ring.
Cut every piece with the same setup. Consistency matters more than absolute perfection; if all the angles are equally “off,” the ring can still close.
Mind the blade-tilt direction. Flip or rotate pieces consistently so the bevel leans the right way on each joint.
Dry-fit with tape — a strip across each outside joint acts as a hinge and makes glue-up of a multi-sided ring far easier.

Frequently asked questions

What is a compound miter cut?

A cut with two angles at once — a miter across the face and a bevel through the thickness — used whenever the sides of a box or vessel are tilted rather than vertical.

What are the angles for a 4-sided box with 45° sloped sides?

Set the miter gauge to about 35.26° and tilt the blade to 30°.

Does this work for crown molding?

The same math underlies crown-molding cuts, though crown is usually described by its “spring angle” against the wall. For sloped boxes, planters, and vessels, enter the number of sides and the slope directly and you’ll get the saw settings straight away.