Compound Miter Solver
Solve miter table angle and blade bevel for crown moulding, hip rafters and polygon frames. Enter corner angle + spring/tilt — get precise saw settings.
Why this calculation matters
Compound angles are unforgiving: a half-degree error compounds around every corner of a run and shows as a gap at the last joint.
Compound Miter — Solver
Solve miter table angle and blade bevel for crown moulding, hip rafters and polygon frames. Enter corner angle + spring/tilt — get precise saw settings.
📐 Compound Miter Solver
Calculates the two simultaneous saw settings needed when cutting wood angled in two planes at once. Crown moulding is the classic example — it leans from the wall at a spring angle while running along the wall-ceiling junction. Both miter table angle AND blade bevel must be set together for a perfect fit.
Where Used?
Formulas
Miter = arctan( sin(S) x tan(C/2) ) [S = spring, C = corner angle]Bevel = arcsin( cos(S) x sin(C/2) )Dihedral = arccos( cos2(S) x cos(C) + sin2(S) )Polygon corner = 180 - (360 / N_sides)About the Compound Miter Solver
A compound miter is a cut that's angled in two planes at once — needed wherever sloping pieces meet at a corner, like crown moulding, hopper bins, or angled boxes. Getting it right by trial and error wastes a lot of timber, because a small error in either angle shows up as an ugly gap at the joint. This solver takes the slope (spring angle) and the corner angle and gives you the exact blade tilt and miter setting to dial into your saw, so the first cut closes up tight. It replaces the crown molding angles chart taped to most saws, giving exact miter and bevel angles for any spring angle or corner.
Where Is This Used?
- Canonical crown values (31.62°/33.86°, 35.26°/30.00°)
- Flat polygon geometry
Formula checked against the sources above by an automated regression test (tests/test-calculators.js) that derives each expected value independently of this page. Last reviewed .
FAQ
Wood species data
Density, hardness and movement for 60 timbers
How the calculation works
A piece tilted away from vertical needs two cuts at once, and neither equals the corner angle. The saw setting depends on both how sharp the corner is and how far the piece leans, which is why crown moulding at a plain 90 degree corner is cut at neither 45 nor 90.
Show the formula
With S the spring angle and C the corner angle, half-angle H = (180 - C)/2. Miter = arctan(sin S x tan H). Bevel = arcsin(cos S x sin H). Dihedral = arccos(cos^2 S x cos C + sin^2 S).Verified against published crown-moulding values: 38 degree spring at a 90 degree corner gives 31.6 miter and 33.9 bevel. Walls are rarely square, so treat the result as a starting point and test on scrap.
References
No external standard governs this calculation — it is arithmetic from your inputs. Take product-dependent figures from the manufacturer data sheet, not from here.
Limitations of this calculation
Solves the angles for the geometry entered. It does not account for saw calibration error, stock thickness variation, wall or corner out-of-square, or cumulative error around a run.
Do not use this for Production cutting without a test piece in scrap of the same thickness.
Figures are engineering estimates from the inputs and assumptions shown. Verify against the actual material and, where the result affects structure or safety, against a qualified professional.
How to use this tool
- Enter your stock sizes below, then press Calculate.
- Pick your application type from the dropdown.
- Fill in polygon sides, corner / wall angle, spring / tilt angle.
- Press Calculate.
Worked example
Common mistakes to avoid
- Setting the mitre angle where the bevel should go, and the bevel where the mitre should go. Label your saw settings.
- Measuring the crown spring angle wrong. 38° and 45° crown need different settings — check yours before cutting.
- Cutting all pieces before test-fitting one corner. One wrong setting ruins the whole set.