Pitch and Its Relation to Screws and Gears
Screws are defined by three measurements: diameter, pitch, and length.
Diameter and length are fairly straight-forward and call out the overall dimensions for the physical size of the screw while the last measurement, the pitch, defines the threads and ensures the screw can actually screw into the nut or threaded hole.
For example, a common imperial screw is the #6-32x1/2” and we can see the each of the measurements is clearly specified, although in a slightly cryptic manner. #6-32x1/2” means a #6 screw (which has major diameter of 0.138”), with 32 Threads Per Inch (TPI), that is 1/2” long. There are multiple methods of measuring pitch, and sometimes a thread pitch gage is the quickest method.
Calculating Threads Per Inch (TPI)
The Threads Per Inch (TPI) is the number of threads along one inch of the length of the screw, just as the name suggests. By simply counting the number of threads and dividing by the length you can easily calculate the TPI of a screw.
Metric screws convey the same information, but with slightly different terminology. For instance, an M6x1x20 screw has a diameter of 6mm (M6 means Metric, not a #6 imperial), a pitch of 1mm and length of 20mm.The pitch of 1 doesn’t mean that the screw has only 1 thread per inch, but rather that each thread is spaced apart by 1 mm (remember, this is a metric screw). Since there are 25.4 millimeters in 1 inch, the M6x1.00 screw has an equivalent TPI of 25.4.
As the TPI increases for screws it means there are more and more threads in the same one inch, so the threads are getting smaller and smaller: a 6-32 screw has bigger threads than a 6-40 screw. By contrast, in metric screws as the pitch increases the individual threads take up more space and are increasing in size, so an M6x1.00 has smaller threads than an M6x1.50 screw - TPI and pitch are inversely proportional.
For good or for bad, there hasn't been a Whitworth-esque standardization movement for gears.
Gears and Pitch
This same relationship holds for gears, the imperial dimension is Diametral Pitch and the metric dimension is called Module. The Diametral Pitch is the number of teeth of a gear per inch of its pitch diameter (effectively the same as a screw’s TPI), while Module is more directly the pitch of the gear. Just like in screws, a gear with a Module of 1 has an equivalent Diametral Pitch of 25.4. As the Module increases, gear teeth increase in size, but as Diametral Pitch increases those gear teeth decrease in size in order to fit more teeth into the same inch of pitch diameter. If you ever need to convert, just use the following equations:
Diametral Pitch = Module * 25.4
Module = Diametral Pitch / 25.4
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