A standard full-depth gear needs about 2/sin²α teeth before the cutter starts undercutting the root — 17 at a 20° pressure angle, but 32 at 14.5° and only 12 at 25°.
The tooth flank is generated by a rack rolling past the blank. On a small enough gear the tip of the rack sweeps inside the base circle and scoops material out of the root, thinning exactly the section that carries the bending load. The limit depends only on pressure angle, which is why the number moves so much between standards — and why old 14.5° imperial gearing looks coarse next to modern 20°.
Profile shift beats it: move the cutter out and a 12-tooth pinion at 20° is perfectly sound, at the cost of a changed centre distance and a thinner tip. The rule is a limit on the plain full-depth cutter, not on what a gear can be.
Estimate with the rule, then check it against the calculator that models it properly.
Open Gear Train Calculator →A standard full-depth gear needs about 2/sin²α teeth before the cutter starts undercutting the root — 17 at a 20° pressure angle, but 32 at 14.5° and only 12 at 25°. The tooth flank is generated by a rack rolling past the blank.