|Compound Angle Calculators|
I recently had a woodworking project with compound angles. A quick search of the web for an online calculator quickly showed that, even though there are plenty of great miter calculators out there, I wasn't able to find to for calculate a butted joint at a compound angle. After a bit of research, I discovered the possible reason why – calculating a butted joint is much more complicated than calculating a mitered joint.
These two calculators were designed with a tablesaw in mind, although you could use it with any tool.
Just adjust angular orientation accordingly.
Notes on angles:
Included angle refers to the angle the two pieces meet in plan view. The angle is measured between the two pieces – 90° is a 4-sided box, 120° is 6-sides, etc.
Bevel is given in degrees from vertical, when the piece is laying flat on a horizontal plane (like on the top of a saw table). 0° a square edge (no bevel), 45° is a piece cut with a 1:1 bevel. Bevel is the angle you'd set your blade to.
Butted compound angles.
Butted compound angles are more complex than a simple mitered joint. Unlike a mitered joint where the two pieces to be joined are tipped at the same angle, in a butted joint, the two pieces to be joined can have different angles.
It doesn't actually matter which piece butts and which caps,
so in the calculator, they are simply referred to as A and B.
If you're interested in playing or checking my work (please!), here are the formulas I used:
For the miter:
For the butted joint:
If either of these values exceed 90°, I subtract from 180 to provide a negative angle that indicates the angle goes the other way.
Bevel angle: asin( cos(slopeA) * cos(slopeB) - sin(slopeA) * cos(slopeB) * cos(corner_angle))
A spreadsheet version is available as well.
This page is offered "as-is" -- use it at your own risk. If you find a mistake, I'd love to hear about it. If it doesn't do what you want, go ahead and make your own, like this excellent page: Bjorn Jansson's Compound Miter Saw Calculator (his does butted joint too!)