Miter from square
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Shop estimate. Measure your stock and cut a test on scrap.
How to use it
- Choose a flat frame, a splayed side, or crown cut flat.
- For a frame, count the sides. The miter from a square cut is 180° divided by the number of sides.
- For a planter, measure the slope from the bench, not from the wall. Zero is flat on the bench. Ninety is a vertical side. If your drawing measures from vertical, subtract it from 90 first.
- For crown, enter the wall corner and the spring angle printed for that profile. 38° at a square corner is the common chart.
- Cut the whole joint from scrap. A small error at each corner closes up, or opens up, on the last piece.
The formula
Flat miter = 180° ÷ sides. Splay: miter = atan(cos θ · tan(180° ÷ n)), bevel = asin(sin θ · sin(180° ÷ n)), with θ from horizontal.
- θ. Slope of the side from horizontal. Complement it if your sketch measures from vertical.
- Spring. The crown angle. Miter = atan(sin S ÷ tan(C ÷ 2)). Bevel = asin(cos S · cos(C ÷ 2)).
- Gauge. Table-saw miter gauges read 90° at square, so the gauge is 90° minus the miter.
Worked example
A flat six-sided frame is a 30° miter from square, and the bevel stays at 0. A square picture frame is 45°. An octagon is 22.5°.
Tip the same six sides up so they rise 15° from the bench (75° from vertical). The saw then wants about 29.15° of miter and 7.44° of bevel. A miter saw’s 0 is a square cut. A table-saw miter gauge’s 90 is a square cut, so that gauge reads 90 minus the miter shown here.
Crown molding at a 38° spring angle, cut flat, meeting a 90° corner, is the chart pair: about 31.62° miter and 33.86° bevel. Nested crown, stood against the fence at its installed angle, is a plain miter and no bevel. Cut a test pair.
What it will not decide
- Inside and outside corners use the same angles and opposite orientations. The page does not tell you which end of the stick is which.
- Walls are rarely the angle you hoped. Measure the corner.
- Compound charts disagree when one of them measures slope from the other direction. This page states its direction.
Questions
What do I set for a hexagonal frame?
30° from square, no bevel, on every end of every piece. Dry-fit the ring before glue. Six corners hide a small error until the last one.
Why do two crown charts disagree by a degree?
Usually because one of them swapped spring and the complement, or measured the wall from the other side. For 38° spring at 90°, this page gives about 31.62° and 33.86°, which is the pair printed on most saw charts. If your corner is 92°, do not keep the chart.
Does nested crown use the compound numbers?
No. Crown stood upside down against the fence, at the angle it will sit on the wall, takes a plain miter of half the corner and a bevel of zero. The compound numbers are for molding lying flat.