For a UN thread, the v-height is (√3/2)÷TPI, the actual thread height is 5/8 of the v-height, and the nominal minor diameter is the major diameter - twice the thread height. That simplifies to:
Major diameter - 0.625×√3÷TPI
or
Major diameter - 1.0825÷TPI
which is just a tiny schooch smaller than the Md-1/TPI mentioned above. The factor of (√3/2) is just 1/2 of the tangent of 60°, which is the thread angle.
That gives you 100% of a UN thread form, which is pretty close to the "75%" thread you'll see referred to, which is 75% of the obsolete American National thread form. IIRC the American National thread form was replaced by the Unified National thread form during WWII.
The American National thread form had a thread height of 3/4 the v-height, and called for internal threads that were slightly sharper than UN threads. Compared to American National threads, UN threads have slightly blunter internal threads and UN external threads don't have to be as deep.
One other factor is the allowance for class 2A/B threads and tolerances for both class 2 & 3 A/B threads. That calculator from the Theoretical Machinist web site is the only one I'm aware of that provides a calculator for the tolerances and gives you actual minimum and maximum values for minor, pitch, and major diameters.
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