Rule of thumb · MechanicalNº 46 / 149

Below 17 teeth, the cutter eats the tooth root

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°.

Why it works

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°.

When it fails

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.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

Open Gear Train Calculator →

More in Mechanical

← PreviousRing minus sun must be even, and the planets must divide Next →A 4-stroke camshaft turns at half crank speed

What is the minimum number of teeth on a gear?

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.

Browse all 149 rules of thumb →