Background & Tutorial
This calculatorĀ is for determining the width-of-cut of a “V” shaped cutting tool.
Here is a quick tutorial on how the formula works.
http://woodworkerb.com/wp-content/uploads/2014/11/Tool1.png
Exaggerated example of a "V" shaped cutting tool. A 30 degree tool is very 'pointy' whereas a 60 degree tool is 'flatter'.
Notice also, that these tools do not come to a perfect point.
http://woodworkerb.com/wp-content/uploads/2014/11/Tool22.png
This shows that the width of the cut is related to the depth of the cut. The deeper the tool cuts into the material, the wider the final cut will be.
http://woodworkerb.com/wp-content/uploads/2014/11/Tool31.png
Two identical right triangles are added. Each triangle has a known angle (half of the tool angle) and a known length of one side (the depth of cut).
http://woodworkerb.com/wp-content/uploads/2014/11/Tool4.png
A little trig is used to calculate the side 'a'. Add two a's to the tip diameter, and you've got the width of cut.
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Tool width calculator
References
Inspired by the work of Jeff_Brit on the PCB-GCODE Phorum:
V-bit etching width calculator