For metric gears the gear proportions are based on the module. Modules is the ratio of the “Pitch Diameter” to the “Number of Teeth”.
m (module)= d (pitch diameter (mm)) / N (number of teeth)
When module (m) number for metric gears is getting bigger- size of the teeth is getting bigger too.
In the USA the module is not used and instead the “Diametric Pitch” or “Pitch” (p) is used.
p= N (number of teeth) / d (pitch diameter (Inch))
When pitch (p) number for inch gear is getting bigger- size of the teeth is getting smaller.
Calculation example: Having two dimensions for each gear we will try to find number of teeth (N) using above equations:
Metric gear:
Ф (pressure angle)= 10°
m (module)= 0.8
N (number of teeth)= ?
d (pitch diameter)= 16 [mm]

Inch gear:
Ф (pressure angle)= 10°
p (pitch)= 31
N (number of teeth)= ?
d (pitch diameter)= 0.615”
p= N/d ↔ N= p*d ↔ N= 31*0.615= 10
Conclusion: for both spur gears we calculated same number of teeth. Converting inch dimensions to metric (1”= 15.4mm) we can see how close these two gears are:
Knowing pitch (p) for inch gears we can simply calculate inch module:
m= (1”/31)= 0.03115
Or knowing pitch diameter (d) and number of teeth (N):
m= d/N= 0.615/10= 0.03115
Lets convert Inch module m= 0.03115 to metric using (1”= 15.4mm) converter from Inch to Metric dimensions.
0.03115 * 15.4= 0.794
Conclusion: We can see that the metric and inch spur gears are dimensionally very similar but we should not mesh them together duo to small differences developed during design and manufacturing stage.