Pitch in mm = 25.4 / TPI, and TPI = 25.4 / pitch. 20 TPI is a 1.27 mm pitch, closest to a 1.25 mm metric thread; a 1.5 mm pitch is 16.93 TPI, close to but not interchangeable with 16 TPI.
Near misses matter: 1.25 mm and 20 TPI differ by 1.6% per thread, which is enough to bind after a few turns. A thread pitch gauge settles it in seconds.
Tools for this job
The tooling this calculation is usually for, spread across the price range.
How does the thread pitch converter work?
Threads per inch counts crests in one inch of length; metric pitch is the distance from one crest to the next. They are reciprocals with a unit conversion, so the arithmetic is simple. The trap is that several inch and metric pitches are close enough to start but not close enough to tighten.
Frequently asked questions
Is 1.5 mm pitch the same as 16 TPI?
No. 1.5 mm is 16.93 TPI. A 16 TPI nut will start on a 1.5 mm thread and then bind within a few turns, because the error accumulates by about 0.09 mm per thread. Treat any pair that is not an exact match as incompatible for anything longer than a couple of threads.
How do I identify an unknown thread?
Measure the major diameter with a caliper, then try leaves of a thread pitch gauge until one sits in the thread with no light showing. If the diameter is a round metric number and no inch leaf fits, it is metric. The converter here then shows which standard threads are closest.
Keep going
Formulas are standard shop math; starting speeds are conservative conventions for hobby machines. Not professional engineering advice. Wear eye protection and keep hands, gloves and sleeves clear of rotating work.