Screws are defined by three measurements: diameter, pitch, and length. The diameter is the distance across the threads (how "fat" the screw is), length is how long the screw is, and pitch is the spacing between the threads. Screw length normally does not include the head, except for flat-head screws. For the pitch, you can either measure the distance between threads, or measure a fixed length of threads and count the number of threads in that length.

A good example is a 1/4"-20 x 1" screw. This screw would have a diameter of about 1/4", have 20 teeth per inch of threads, and be 1" long (plus the height of the head.) Since it has 20 threads per inch, and is 1 inch, we would expect there to be a total of 20 threads on the screw.

A metric example would be an M12x1.0 x 25mm. This screw would have a diameter of about 12mm, have a distance of 1.0mm between each thread, and be 25mm long. Since there is 1.0mm between each thread, and it's 25mm long, we would expect there to be a total of 25 threads on the screw.

However, this naming convention gets a little trickier for small imperial screws. Below 1/8" imperial screws use a number system (ranging from #12 to #0000, super tiny). Smaller numbers here mean a smaller diameter, so a #4 is smaller than #8. As screws got even smaller, they just started added zeroes, so a #00 is smaller than #0, and #0000 is even smaller still.

A common small imperial screw is the #6-32x1/2” which 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; we also have a lead angle calculator for screws and threads.

Starrett Thread Gage - Inch

Starrett Thread Gage - Metric

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: the second number is the length between threads, not the threads per inch. 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. 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.

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 = 25.4 / Module
Module = 25.4 / Diametral Pitch