How this instrument works
Pitch diameter is the diameter of an imaginary cylinder that passes through a thread at the point where the thread groove and the thread ridge are exactly equal in width — not the outermost point you'd measure with calipers across the crest of the threads (that's the major diameter), and not the bottom of the groove either (the minor diameter), but the theoretical midline in between. It's the single dimension that actually determines whether two mating threaded parts — a bolt and a nut, a screw and a tapped hole — will fit together correctly.
For Unified inch screw threads (the UNC and UNF threads standard on US hardware), ASME B1.1 defines a basic pitch diameter formula: major diameter minus 0.6495 divided by the threads-per-inch count. That constant, 0.6495, comes from the geometry of the standard 60° thread form itself — it's not an arbitrary rounding, but a fixed relationship between a thread's pitch (the distance between adjacent threads) and how far that midline sits below the major diameter for that thread angle.
This 'basic' pitch diameter is a nominal reference value, not a manufacturing tolerance — actual thread gauges, go/no-go checks and manufactured parts allow a small permitted range around this number depending on the thread's tolerance class. But the basic figure is where every one of those tolerance ranges starts, which is why it's the number printed in ASME B1.1 and Machinery's Handbook thread tables for every standard UNC and UNF size.
- Enter the screw's outer thread size into Major diameter (in) — the nominal diameter across the thread crests, such as 0.25 for a 1/4-inch screw.
- Enter the thread density into Threads per inch (TPI) — the second number in a thread callout like 1/4-20, where 20 is the TPI.
- Read Basic pitch diameter for the reference diameter used to check the thread with a pitch-diameter micrometer, thread gauge or go/no-go gauge.
- Confirm both numbers match a real standard thread designation — 1/4-20, 3/8-16, 1/2-13 and similar UNC/UNF callouts — before trusting the result against a published thread table.
Worked example — a 1/4-20 UNC thread
Enter 0.25 into Major diameter (in) and 20 into Threads per inch (TPI) — the standard 1/4-20 UNC thread found on countless machine screws and bolts. Basic pitch diameter reads 0.217525 in.
By hand: 0.6495 divided by 20 is 0.032475, and 0.25 minus 0.032475 is 0.217525 in — matching the roughly 0.2175-inch pitch diameter published in ASME B1.1 and Machinery's Handbook UNC thread tables for this exact size.
Questions
What's the difference between major diameter, pitch diameter and minor diameter?
Major diameter is the largest of the three, measured across the outer crests of the thread — what you'd read off a caliper spanning the thread's high points. Minor diameter is the smallest, measured at the bottom of the thread groove. Pitch diameter sits in between, at the imaginary cylinder where the groove width and the ridge width are exactly equal — and it's that middle figure, not the largest one, that actually governs whether a bolt and nut fit together.
Where does the 0.6495 constant in the formula come from?
It comes from the fixed geometry of the Unified thread form's standard 60° included angle — the angle between the two sloped flanks of every UNC and UNF thread. Given that fixed angle, the vertical distance from the major diameter down to the pitch diameter turns out to be a constant multiple of the thread pitch, and 0.6495 is that multiple as published in ASME B1.1, the governing standard for Unified inch screw threads.
Is this the exact pitch diameter I should machine to, or just a reference figure?
It's the basic (nominal) pitch diameter — a reference starting point, not a manufacturing target on its own. Real thread tolerance classes (like 2A for external or 2B for internal threads) define a permitted range above or below this basic figure, and a specific manufactured part is machined to land within that range, not to this exact number. Check the applicable tolerance class before setting machine offsets from this figure.
Does this formula work for metric threads?
No — this is the ASME B1.1 formula specific to Unified inch threads (UNC and UNF), which use a threads-per-inch count and a constant derived from the inch-based 60° Unified thread form. Metric ISO threads use a millimetre pitch rather than TPI and a related but differently structured pitch-diameter formula defined in ISO 68-1, so plugging metric numbers into this formula will not give a correct result.
How do I read TPI off a real thread callout like 3/8-16?
In a standard UNC/UNF callout, the first number is the major diameter in inches (as a fraction or decimal) and the second number, after the dash, is the threads per inch. In '3/8-16', the major diameter is 0.375 in and the TPI is 16 — enter those two numbers directly into Major diameter (in) and Threads per inch (TPI) to get that thread's basic pitch diameter.