 Gear circular pitch

Gear circular pitch is the arc distance between corresponding points on successive gear teeth, measured on the gear reference circle. If that circle has diameter $d$ and tooth count $N$, its circumference contains $N$ repetitions, givingwhere $m$ is gear module. The length is measured along the reference arc, rather than as a straight chord between tooth positions.^[ref]

For a spur gear with $m=2\mathrm{mm}$ and $N=30$, reference diameter is $60\mathrm{mm}$, gear circular pitch is $2\pi \mathrm{mm}\approx 6.283\mathrm{mm}$, and angular tooth spacing is $2\pi /30$. The corresponding chord on the reference circle isThe small numerical difference matters when a dimensional inspection is intended to measure reference arc spacing. Increasing the tooth count while holding gear module fixed enlarges the gear reference circle but preserves gear circular pitch.

For an involute tooth profile, the gear base circle provides another spacing, the gear base pitch. Since $d_b=d\cos \alpha$, with reference gear pressure angle $\alpha$,At $\alpha =20{}^{\circ }$, the preceding example gives $p_b\approx 5.904\mathrm{mm}$. Compatible contact must preserve the spacing of successive tooth flanks along their gear line of action; this explains why equal gear circular pitch with incompatible gear pressure angles is not enough to specify a mating pair. Tooth thickness and backlash are additional quantities: gear circular pitch includes an entire tooth-and-space repetition.