Gear Module, Pitch & Tooth Dimensions Calculator

How it works

Pitch diameter d = m z; outside da = m(z + 2); root df = m(z − 2.5); base db = d cos α; circular pitch p = π m; centre distance a = m(z₁ + z₂)/2; DP = 25.4 ÷ m; z_min = 2 ÷ sin²α

The module is the size of a gear tooth — the pitch diameter divided by the number of teeth — and two gears only mesh if their modules (and pressure angles) match. Everything else follows from it: the pitch diameter is module times teeth, the addendum equals one module, the dedendum 1.25 modules, and the outside diameter is the module times the tooth count plus two, which is the key to identifying an unknown gear with a caliper. Imperial gears use diametral pitch, the number of teeth per inch of pitch diameter, which is simply 25.4 divided by the module. The centre distance of a pair is the sum of their pitch radii, and pinions with too few teeth for their pressure angle suffer undercut at the root, which is why 20° gears usually have at least 17 or 18 teeth.

Worked example

Module 2, 30-tooth pinion: pitch diameter 60 mm, outside 64 mm, root 55 mm, tooth depth 4.5 mm. With a 75-tooth gear (150 mm) the centre distance is 105 mm and the ratio 2.5:1.

Frequently asked questions