What the spring angle is and how to measure it
Crown molding does not lie flat against either surface. Its back has two bearing edges, one touching the wall and one touching the ceiling, and the flat between them stands at an angle to both. That angle is the spring angle, and it determines every saw setting you will use on the job.
You can measure it without a protractor. Hold the molding in its installed position against a framing square: the leg down the wall is the height, and the leg across the ceiling is the projection. The spring angle at the ceiling is arctan(height ÷ projection). A molding that projects as far as it drops - equal legs - is a 45/45 crown. A molding that drops further than it projects sits at more than 45 degrees to the ceiling; a nominal 52/38 profile measures about 2-15/16 in down the wall and 2-5/16 in across the ceiling, giving arctan(2.9375 ÷ 2.3125) = 51.8 degrees.
The trade name lists the two angles the back makes with the two surfaces: 52 at the ceiling and 38 at the wall, which necessarily sum to 90. Both numbers describe the same profile, so it does not matter which you quote as long as you are consistent about which surface it refers to. This calculator uses the ceiling angle throughout and shows the wall angle alongside it, so you can check against whichever convention your supplier uses.
Measure rather than assume whenever the molding is old, reclaimed or custom milled. Profiles drift between manufacturers, and a two-degree error in the spring angle moves the bevel by more than a degree - visible on a painted inside corner.
Two ways to cut it, two sets of numbers
There are two established ways to cut crown, and they need different settings.
Nested - the traditional method. You hold the molding against the fence at its spring angle, upside down, with the ceiling edge on the saw table and the wall edge against the fence. The saw then only has to turn the corner in plan, so the blade stays square and the miter setting is simply A = 90 − C/2 - forty-five degrees at a square corner, whatever the spring angle. It is fast, it needs no arithmetic, and its weakness is that the molding must be held at exactly the same angle for every cut. Crown stops or a shop-made fence jig make it repeatable.
Flat - the compound method. The molding lies flat on the table, face up, and the saw provides both angles. Now the spring angle enters the calculation:
miter = arctan(cos S × tan A), bevel = arcsin(sin S × cos A).
For 52/38 crown at a square corner that gives 31.62 degrees of miter and 33.86 degrees of bevel - the numbers printed on the detent plate of most compound saws. For 45/45 crown it gives 35.26 and 30.00. Flat cutting suits wide crown that will not fit nested inside the saw's capacity, and it is more repeatable because the workpiece is fully supported.
Both methods depend on the same A, half the change of direction at the corner. At a square corner A is 45. At a 135 degree corner - a bay window's 45 degree turn - A is 22.5. The distinction matters because writing the formula with C/2 instead gives 67.5 for that corner, which is not a cut anyone can make.
Worked example: 52/38 crown into a 92 degree corner
You are running nominal 52/38 crown, and the angle finder reads 92 degrees at this inside corner rather than a true 90.
- Spring angle. Nominal 52/38 gives S = 52 degrees at the ceiling, so the wall angle is 90 − 52 = 38 degrees.
- Half the change of direction. A = 90 − 92/2 = 90 − 46 = 44 degrees.
- Flat-cut miter. cos 52° = 0.6156615 and tan 44° = 0.9656888, so the product is 0.5945374 and the miter is arctan(0.5945374) = 30.733 degrees.
- Flat-cut bevel. sin 52° = 0.7880108 and cos 44° = 0.7193398, so the product is 0.5668475 and the bevel is arcsin(0.5668475) = 34.531 degrees.
- Nested alternative. If you cut this molding standing against the fence instead, the blade stays square and the miter is simply A = 44 degrees.
Compare that with the square-corner settings for the same molding: 31.619 miter and 33.863 bevel. Two degrees of error in the corner moved the miter by 0.886 degrees and the bevel by 0.668 degrees. Neither is large, and both are more than enough to show as a hairline gap on a painted inside corner, which is why the corner is worth measuring rather than assuming.
Cut the mating piece at the same two settings on the opposite side of the blade, mark the ceiling edge of each, and test-fit the pair in the corner before you cut the full length.
Reading the settings and cutting the corner
The miter number is a scale reading from a square crosscut and the bevel is a blade tilt from vertical, so both go straight onto the saw. Both halves of a corner use the same two numbers; what changes is which piece is cut on which side of the blade and which end you keep. Cut both halves before you leave the saw, and mark the ceiling edge of every piece - a flat-cut crown offcut is almost impossible to orient afterwards.
Coping beats mitring on inside corners, and it is worth the extra minute. Cut the first piece square into the corner, then cut the second at the flat miter setting to expose the profile and back-cut along that line with a coping saw. A coped joint slides over its partner, so it closes rather than opens when the framing moves in the heating season. Outside corners have to be mitred, and there the settings on this page are the whole answer.
Measure every corner separately. Rooms are not square, and even in new work a corner reading 88.5 or 91.5 is unremarkable. That is a change of three quarters of a degree in A, which moves the miter by half a degree - enough to open a joint you will see from across the room. If two adjacent corners disagree, each piece between them has a different setting at each end.
Watch the bevel limit. Shallow corners - large corner angles, small A - drive the bevel up sharply, and past about 48 degrees most compound saws run out of tilt. When that happens, cut nested instead: the nested miter is always the modest angle A, and the blade stays square.
Saw settings by corner angle and profile
| Corner (deg) | 52/38 miter | 52/38 bevel | 45/45 miter | 45/45 bevel | Nested miter |
|---|---|---|---|---|---|
| 60 | 46.84 | 23.20 | 50.77 | 20.70 | 60.00 |
| 70 | 41.32 | 26.87 | 45.28 | 23.93 | 55.00 |
| 80 | 36.27 | 30.43 | 40.12 | 27.03 | 50.00 |
| 90 | 31.62 | 33.86 | 35.26 | 30.00 | 45.00 |
| 100 | 27.32 | 37.13 | 30.68 | 32.80 | 40.00 |
| 110 | 23.32 | 40.20 | 26.34 | 35.40 | 35.00 |
| 120 | 19.57 | 43.03 | 22.21 | 37.76 | 30.00 |
| 135 | 14.31 | 46.72 | 16.32 | 40.79 | 22.50 |
| 150 | 9.37 | 49.57 | 10.73 | 43.08 | 15.00 |
Every cell is arctan(cos S × tan A) or arcsin(sin S × cos A) with A = 90 − C/2, evaluated with the same expressions the calculator uses. The 90 degree row reproduces the familiar 31.62 / 33.86 and 35.26 / 30.00 pairs.
Where crown corners go wrong
- Assuming the corner is square. The single most common cause of an open crown joint. Measure it.
- Mixing up the two spring-angle conventions. Ceiling angle and wall angle are complements; using 38 where the formula wants 52 gives a plausible-looking but wrong pair of settings.
- Losing the nested angle between cuts. If the molding shifts against the fence, the effective spring angle changes and the joint follows. Use crown stops.
- Cutting both halves the same way. The two pieces at a corner are mirror images, not copies.
- Mitring inside corners in solid wood. A mitre opens as the framing dries. Cope instead.
- Forgetting that ceiling and wall are rarely flat. A perfect joint on the bench can still show a gap on the ceiling; a bead of caulk is a finish, not a fix for a wrong angle.
Test in scrap, every time
Cut two short offcuts at the calculated settings and hold them into the actual corner before you cut a 12 ft length. The test tells you three things at once: whether the corner angle you measured is right, whether the spring angle you assumed matches the molding in your hands, and whether the saw's scale agrees with its own detents. Scrap is cheap and crown is not.
Crown among the other trim cuts
Crown is the hardest trim to fit because it is the only common molding that touches two planes at once. Baseboard and casing lie flat against a single surface, so their corners are plain miters and the only variable is whether the wall is square. That is why a carpenter comfortable with base can still be defeated by crown: the geometry genuinely is different, not merely harder.
The same trigonometry appears wherever a tilted piece turns a corner, which is why this page and the compound miter angle calculator share their formulas. The difference is only the convention: crown is described by its spring angle, and a splayed box by the tilt of its sides. Feed the crown spring angle into the compound calculator as the tilt and you get the same numbers.
For built-up crown - a crown molding stacked on a frieze board or bed molding - calculate each element separately, because each has its own spring angle. For a room where the ceiling is not level, run the crown to the ceiling and let the wall reveal vary; the eye reads the ceiling line and forgives the wall.
Once the profile and the corner counts are settled, the board foot calculator prices the stock, and if you are trimming a room out completely, the paint coverage calculator covers the finish. For the flat miters on base and casing at out-of-square walls, the polygon miter angle calculator is the quicker tool.