# Equation to calculate angle for double bevel inlay or marquetry

 Blog entry by Jeff Vicenzi posted 01-25-2021 05:21 PM 615 reads 3 times favorited 2 comments

The “double-bevel” inlay method is a scroll saw technique where two equally thick pieces of wood are stacked on top of one another, and cut simultaneously at an angle, with the idea that the piece cut out of the lower piece ofwood, will slide into the hole created in the upper piece of wood, thereby creating an inlay. This is often done in marquetry, using two thin veneers of wood, but it can also be done with quite thick wood (I’ve done it with 3/4” wood). If the angle is chosen correctly, the lower piece will fit perfectly into the upper piece, like a cork in a bottle, with no gap between the pieces. The angle required is a function of the thickness of the wood being cut and the thickness of the saw blade (the blade kerf size).

I have not been able to find an equation for calculating the required angle anywhere on-line, so I thought I would share it here. The equation is :

Desired angle = arcsine ( Saw blade kerf in inches / wood thickness in inches)

Don’t let “arcsine” scare you, it is just a button on most calculators (it’s even on the calculator on my phone). So you simply take the saw blade kerf, divide that by the wood thickness, and then press the “arcsine” button and it will give you the angle. This button will often be labeled “asin” or sometimes “sin-1” on the calculator. As an example, with 1/4” thick wood, and a #5 scroll saw blade ( 0.016” kerf), the required angle is 3.7 degrees. As another example, with 1/40” thick veneers and a #3/0 blade (0.008” kerf), the required angle is 18.7 degrees.

Sometimes the calculated angle will give you a perfect fit, other times you might have to tweak the angle just a bit, so also do a test cut. It will always get you very close to the desired angle.

If you don’t like using equations, I’ve attached a chart I created using this equation, which allows you to look up the required angle for a range of common wood thicknesses and blade sizes. In case you wondering about the source of this equation, I’ve got a bit of a math background, so I derived it myself.

I hope this helps somebody sometime somewhere!