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Pitch Diameter of Thread Formulae and Calculator

Pitch Diameter of Thread Calculator and Formula

Calculating the Pitch Diameter of Unified (UN) and Metric (M) Threads. It is often necessary to find the pitch diameter of the various unified (UN) and metric (M) thread sizes.This is necessary for threads that are not listed in the tables of thread sizes and when the thread is larger than that normally listed in handbooks.These include threads on large bolts and threads on jack screws and lead screws used on various machinery or machine tools. In order to calculate the pitch diameters, refer to Fig. 1.

Eq. 1
H = 0.5 · 30.5 · p = 0.866025 · p

Eq. 2
Pitch Dia.external thread
D2, (d2) = ( d / 2 - 5 H / 8 + H / 4 ) · 2

Eq. 3
Pitch Dia.internal thread


p = pitch of the thread. In the UN system, this is equal to the reciprocal of the number of threads per inch (i.e., for a 3⁄8-16 thread the pitch would be 1⁄16 = 0.0625 in). For the M system, the pitch is given in millimeters on the thread listing (i.e., on an M12 × 1.5 metric thread, the pitch would be 1.5 mm or 1.5 × 0.03937 in = 0.059055 in).
D, (d) = basic major diameter of internal (external) thread
D1, (d1) = basic minor diameter of internal (external) thread
D2, (d2) = basic pitch diameter of internal (external) thread
H = basic thread profile height

Basic thread profile for unified (UN) and metric (M) threads (ISO 68).
Figure 1 Basic thread profile for unified (UN) and metric (M) threads (ISO 68).
Click on image to enlarge

If you check the basic pitch diameter for this thread in a table of pitch diameters, you will find that this is the correct answer when the thread is class 3A and the pitch diameter is maximum. Thus, you may calculate any pitch diameter for the different classes of fits on any UN- or M-profile thread, since the thread geometry is shown in Fig. 1. Pitch diameters for other classes or types of thread systems may be calculated when you know the basic thread geometry, as in this case for the UN and M thread systems.


Handbook of Machining and Metalworking, 2001
Ron A. Walsh