 Gear module

The gear module specifies the size of metric gear teeth through the gear reference circle. For a spur gear with reference diameter $d$ and $N$ teeth,The tooth count is dimensionless, so gear module has units of length, conventionally millimetres. A larger gear module means a larger reference diameter at fixed tooth count. It does not mean a larger gear ratio, which depends on the tooth counts of the meshing pair.^[ref]

The gear circular pitch $p$ is the arc length between equivalent points on adjacent teeth, measured along the gear reference circle. Dividing the circumference by the tooth count givesFor example, a spur gear with $m=1.5\mathrm{mm}$ and $N=24$ has reference diameter $36\mathrm{mm}$ and gear circular pitch $1.5\pi \mathrm{mm}\approx 4.712\mathrm{mm}$. A 48-tooth gear of the same gear module has diameter $72\mathrm{mm}$ but the same tooth spacing. Their standard axis separation is $(36+72)/2=54\mathrm{mm}$, and their reduction gear ratio is $48/24=2$.

Conversely, two gears can have the same diameter without compatible tooth spacing: $d=36\mathrm{mm}$ can describe 24 teeth of gear module $1.5\mathrm{mm}$ or 18 teeth of gear module $2\mathrm{mm}$. Such teeth do not form the specified standard pair. For ordinary compatible spur gears, matching gear module is necessary but does not by itself specify the complete tooth geometry: the gear pressure angle and other tooth details must also agree. The definition uses reference diameter, not the diameter through the tooth tips or the operating pitch circle of a particular mounting.