Why V-bit width matters for V-carving and sign work
A V-bit does not cut a fixed-width groove the way a straight end mill does. The width of the cut changes continuously with how deep the bit plunges, since a V-shaped tool gets wider the further it goes into the material. Getting the relationship between depth and width right is the entire basis of V-carving lettering, decorative grooves, and chamfered edges.
How the number is calculated
Cut width equals two times the plunge depth, multiplied by the tangent of half the V-bit's included angle. A 90 degree V-bit plunged half an inch deep, for example, cuts a groove exactly as wide as it is deep, since the tangent of 45 degrees is one.
Practical tips
This same relationship runs in reverse: if a design calls for a specific stroke width, solve this formula for depth instead of width to find exactly how deep the V-bit needs to plunge to achieve it. Different included angles produce very different width-to-depth ratios, so a 60 degree V-bit will cut noticeably narrower at the same depth than a 90 degree one, which matters when choosing a bit for fine detail versus bold lettering.