Compound miter calculator (with spring angle)
A 90° inside corner with standard 38°/52° crown moulding is the only case most online calculators cover. This one handles the actual jobs: walls that aren't square (5° off is normal in old houses), crown with non-standard spring angle, and saw calibration offsets you can dial in. Both miter and bevel come out with the right spring-angle compensation.
Calculator
Why spring angle exists
Crown moulding is shaped so that when it sits flat against the wall and ceiling, its back is at an angle. That's the spring angle. Standard US crown is 38° (so its back face sits 38° off the wall, with the ceiling contact at 52°). UK crown is usually 45°.
Most compound miter cuts are made with the crown lying flat on the saw bed — that gives the miter angle a "spring-angle-compensated" result. The math is:
Miter = arctan( sin(spring) / (cos(spring) + 1/tan(wall/2)) ) Bevel = arctan( cos(spring) * tan(wall/2) )
For standard 38° spring at a 90° wall, this gives miter 31.6°, bevel 33.9°. Your saw's manual probably has a "31.6 / 33.9" sticker for exactly this case. The calculator does the same calculation for any wall and any spring angle.
Outside vs inside corners
Inside corners (the corner of a room) need an outside miter on the back of the crown — the joint points toward the room. Outside corners (a wall sticking out into the room) need an inside miter on the back. The geometry inverts. The calculator flips the sign of the bevel for you; physically that means rotating the crown around to the other face.
Limitations
- Assumes the spring angle is constant. Built-up or curved crown is more complex.
- Doesn't model blade kerf — for tight-fitting joints, file the back of the cut.
- Doesn't account for walls that are twisted (out-of-plane). Measure both ends.
- Doesn't replace test cuts. Always cut a 12″ scrap first.
Frequently asked questions
My walls are 90° but my miters gap. Why?
Three likely reasons: (1) the spring angle of the crown is not what you think — many crown mouldings are 38°, not 45°, and they look similar in the rack. (2) your saw's miter or bevel stops are off by a degree. (3) the walls really aren't square; measure with a bevel gauge and re-enter.
Should I nest the crown or lay it flat?
Lay it flat (crown lying on the saw bed, bevel up against the fence) — it's the standard approach and gives the spring-angle-compensated values directly. Nesting (crown upside-down against the fence) gives the same physical cut but with the miter and bevel inverted, which is confusing. Most pros cut flat.
What's a typical wall corner variance in an old house?
±2° is normal. ±5° is common in 19th-century construction. Beyond that, the corners are not just out of square — they're twisted, which the calculator doesn't model; cope or scribed joints are the right answer there.