Compound Angle Calculator
Get the compound miter and bevel saw settings for crown molding and any sloped corner joint.
Reviewed by the ToolNestr Editorial Team — July 2026
How the compound angle calculator works
A compound cut is needed whenever a piece meets a corner while also tilted away from the surface — the classic case is crown molding, which sits sprung between the wall and ceiling. Because the piece leans in two directions at once, a single miter is not enough: the saw must swing the miter and tilt the blade (the bevel) together. The two settings come from the corner angle and the spring angle.
The miter angle equals the arctangent of sin(spring) divided by tan(corner ÷ 2). The bevel equals the arcsine of cos(spring) times sin(corner ÷ 2). These are the exact trigonometric relationships behind every published crown-molding chart. Feeding in a 90° corner and a 38° spring returns 31.6° miter and 33.9° bevel — the numbers every finish carpenter recognizes — while a 45° spring gives 35.3° and 30°.
The spring angle is the angle the back of the molding makes with the wall, printed on the profile or measured against a framing square. Setting the spring to zero collapses the math back to a plain miter of (180 − corner) ÷ 2 with no bevel, because a flat piece only turns in one plane. Always cut a test piece in scrap first: real corners drift from 90°, and even a degree of error is visible on a mitered joint.
Compound-angle trigonometry follows the standard crown-molding tables published in the Fine Homebuilding and Architectural Woodwork Institute (AWI) trim-carpentry references used by finish carpenters.
Measure the corner
The real wall-to-wall angle at the joint.
Find the spring
The molding's spring angle, often 38° or 45°.
Set miter + bevel
Dial both, cut a scrap test, then the real piece.
The formula explained
Miter angle
= atan( sin(S) ÷ tan(C⁄2) ). For S = 38°, C = 90°: atan(0.616 ÷ 1) = 31.6°.
Bevel angle
= asin( cos(S) × sin(C⁄2) ) = asin(0.788 × 0.707) = 33.9°.
Flat check
At S = 0° the bevel is 0° and the miter reduces to (180 − C) ÷ 2 = 45° — a simple miter.
Worked example
45° spring crown molding around a square 90° corner.
Tips for cutting compound crown
Flat-cutting versus standing crown
Most sliding compound miter saws can cut crown flat on the table using the miter and bevel this calculator returns, but some carpenters prefer standing the molding upside-down against the fence at its spring angle and using a simple miter instead. Both methods produce the same joint; pick whichever your saw and jig handle more reliably.
Label left and right cuts
Compound cuts are easy to mirror by mistake since the miter direction flips between the left and right piece of a corner. Mark each offcut and dry-fit before committing to the full-length piece — crown molding is expensive to waste on a backwards cut.
Real-world context
52° spring crown — a steeper profile common on taller, more traditional trim packages — is the least forgiving to cut by hand. Around a square 90° corner it works out to a 38.2° miter and a 25.8° bevel, a noticeably shallower bevel than the 38° profile's 33.9°, which is why swapping crown profiles mid-job without recalculating both settings is a common source of visibly mismatched joints.
Outside corners on bump-outs and bay additions are frequently wider than 90°. A 135° outside corner with 38° spring crown needs a 14.3° miter and a 46.7° bevel — the miter shrinks dramatically compared to a square corner while the bevel grows past 45°, a combination that surprises carpenters used to thinking of bevel as the smaller of the two numbers.
Not every wall meets its neighbor squarely. A 100° corner running 45° spring crown comes out to a 30.7° miter and 32.8° bevel — both noticeably different from the textbook 35.3°/30.0° figures for a 90° corner with the same molding, underscoring why measuring the actual corner before cutting beats trusting a published 90°-only chart.
Common misconceptions
"Crown molding always uses the same miter and bevel settings, no matter the profile." Not true. The spring angle — how steeply the molding tilts between wall and ceiling — is baked directly into both trig formulas. A 38° profile and a 45° or 52° profile each need their own miter and bevel numbers, even on an identical square corner.
"You can cut crown molding flat on the saw table like baseboard." Only with a compound cut, or by tilting the molding. Because crown sits sprung against two planes at once, a single miter leaves a gap. Either dial in both the miter and bevel settings this calculator provides, or cut the molding standing upside-down against the fence — but the compound math is unavoidable one way or the other.
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Frequently asked questions
What are the miter and bevel angles for crown molding?
For a 90° corner with 38° spring-angle crown molding cut flat, the compound settings are about 31.6° miter and 33.9° bevel. With 45° spring molding they change to about 35.3° miter and 30° bevel. This calculator returns both from your corner and spring angles.
What is a spring angle?
The spring angle is the angle the back of the molding makes with the wall when it is installed. Crown molding is most often 38° or 45° spring. Cutting it flat on the saw table requires a compound cut because the piece is tilted in two directions at once.
How are the compound angles calculated?
The miter angle equals arctan(sin(spring) ÷ tan(corner ÷ 2)) and the bevel equals arcsin(cos(spring) × sin(corner ÷ 2)). These trigonometric formulas reproduce the standard crown-molding tables exactly.
Do I need a compound cut if the molding is not sloped?
No. If the spring angle is zero — a flat piece lying against a single plane — the bevel becomes zero and the cut is a simple miter of (180 − corner) ÷ 2. The compound cut only appears once the piece is tilted away from the surface.
Sources & references
This tool uses standard formulas and reference values from:
- • American Concrete Institute — ACI 318, Building Code Requirements for Structural Concrete. concrete.org
- • ICC — International Residential Code (IRC), span, footing and framing tables. codes.iccsafe.org
- • APA – The Engineered Wood Association, allowable span and load guidance.
Estimates for planning only. Span, load and code values vary by jurisdiction — verify against your local adopted code and a licensed engineer before building.