George,
The confusion comes about because there is no commonly used term for TPI except possibly 'thread count', so people commonly use 'pitch' for it, which it isn't.
If I may quote: "Lead (pronounced /ˈliːd/) and pitch are closely related concepts. The difference between them can cause confusion, because they are equivalent for most screws. Lead is the distance along the screw's axis that is covered by one complete rotation of the screw (360°). Pitch is the distance from the crest of one thread to the next. Because the vast majority of screw threadforms are single-start threadforms, their lead and pitch are the same. Single-start means that there is only one "ridge" wrapped around the cylinder of the screw's body. Each time that the screw's body rotates one turn (360°), it has advanced axially by the width of one ridge. "Double-start" means that there are two "ridges" wrapped around the cylinder of the screw's body.[4] Each time that the screw's body rotates one turn (360°), it has advanced axially by the width of two ridges. Another way to say the same idea is that lead and pitch are parametrically related, and the parameter that relates them, the number of starts, often has a value of 1, in which case their relationship becomes equivalence.
While specifying the pitch of a metric thread form is common, inch-based standards usually use threads per inch (TPI), which is how many threads occur per inch of axial screw length. Pitch and TPI describe the same underlying physical property—merely in different terms. When units of measurement are constant TPI is the reciprocal of pitch and vice versa. For example, a 1⁄4-20 thread has 20 TPI, which means that its pitch is 1⁄20 inch (0.050")."
Screw thread - Wikipedia, the free encyclopedia
So for 24 TPI you subtract 1/24" from the diameter. For example, take the 3/8-24 UNF thread:
Tapping drill diam. = 3/8"-1/24"
converting from fractions to decimals = 0.365"-0.0417" = 0.333"
Look up the next larger drill size: Q = 0.339". Check against the nearest non-metric tapping drill chart.
QED, as we were taught to say in school.
Using the same mathematics, tapping diameter for 1/2-13 is 1/2"-1/13"
= 0.5"- 0.7629 = 0.4231". I'll leave you to look up the tapping drill gauge, but I believe you will find that it is correct.
One advantage of this approach is that it works for non-standard threads such as those found on lathe mandrels. I have no idea how well it works for thread profiles other than 60*, such as Whitworth.
George