For a 60 degree thread, best wire size = 0.57735 x pitch and measurement over wires M = major diameter - 1.5155 x pitch + 3 x wire. A 1/2-13 with best wires (0.0444 inch) measures about 0.5167 inch over the wires at basic pitch diameter.
P is the pitch (1 / TPI, or mm). E is the basic pitch diameter. Real threads are cut slightly under basic by their class tolerance, so a good external thread measures a little below this M.
Tools for this job
The tooling this calculation is usually for, spread across the price range.
How does the three-wire thread measurement calculator work?
Three-wire measurement checks a thread at its pitch diameter, where the flanks actually bear, using a micrometer and three identical wires laid in the thread. It is how you know a thread cut on the lathe will fit a nut you do not have in hand.
Frequently asked questions
Why is it called the best wire size?
The best wire touches the thread flanks exactly at the pitch diameter, so small errors in the thread angle have almost no effect on the reading. For a 60 degree thread it is 0.57735 times the pitch. Wires a little larger or smaller still work with the formula, but angle errors creep in.
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.