Compound Miter Angles For Sloped Work

A flat-frame box only needs one saw setting per corner. The moment the sides lean — a flared planter, a raked picture frame, crown moulding running along a raked ceiling line — the saw needs two settings working together: a miter (rotation in the horizontal plane) and a bevel (blade tilt). Get either one wrong and the panels won't meet flush, even if the other is perfect.

Why one angle stops being enough

On a flat frame, each panel's face points straight out, radially, from the centre of the polygon, and the miter formula (180° divided by the number of sides) is the whole story. Tilt that same panel by a slope angle and its face normal picks up a vertical component too — the panel isn't just rotated around the shape anymore, it's also leaning in or out. Solving for the two saw settings that still cut a flush joint against that tilted neighbour means working from the actual 3D geometry of the panel faces, not just halving an angle on paper. Cut a sloped box with only the flat-frame miter angle and no bevel, and every joint will show a visible wedge-shaped gap, because the panels no longer meet edge-to-edge along their full length.

The two numbers, and what each one does

• Miter angle — the saw table or gauge rotation, still broadly tracking the flat-frame formula but reduced by how much the slope has tilted the panel.
• Bevel angle — the blade's tilt from vertical, driven entirely by the slope; a flat (unsloped) frame needs zero bevel, and the bevel grows as the sides flare more aggressively.

Both are derived together from the panel's actual face-normal geometry for a given side count and slope — see the angle calculator for the live computation across any combination.

A few worked pairs, to show how the two numbers move independently

Sides	Slope	Miter	Bevel
4	30°	40.893°	20.705°
6	45°	22.208°	20.705°
8	15°	21.806°	5.684°

Read the first two rows together: a 4-sided frame at 30° slope and a 6-sided frame at 45° slope land on the identical bevel angle (20.705°) despite different side counts and different slopes — because bevel depends on the interaction of both numbers together, not on either one alone, and two different combinations can produce the same blade tilt while needing a completely different miter rotation to go with it. That's exactly why compound work can't be eyeballed by analogy to a flat-frame table: the two settings are coupled, and changing either the side count or the slope changes both outputs, not just the one you'd expect.

The convention that trips people up before the saw even gets set

This site's calculator measures slope from the horizontal — a slope of 0° is a completely flat, unflared frame, and the slope figure grows as the sides lean further from that flat starting position. Plenty of published compound-miter tables measure the same physical tilt from the vertical instead — the same real-world cut, described from the opposite reference axis, which makes the two tables' numbers look different for what is physically the identical joint. Before cutting a test piece from a published table you didn't generate here, confirm which axis it's measuring from; mixing the two conventions on the same project is the single most common way a compound-miter setup goes wrong before a single board is cut.

A practical workflow

Cut a test joint in scrap at the computed settings before committing real stock — compound joints are unforgiving of a saw that's a fraction of a degree off on either axis, and a scrap test costs nothing compared to a ruined panel. For crown moulding specifically, the "slope" here is the profile's spring angle measured off square, which converts directly into this same two-angle system — see the individual crown-moulding answer pages for that conversion applied to the two spring angles you'll actually encounter on commercial profiles.