m = d - 1.732p + 3w
For a Whitworth standard thread:
m = d - 1.6008p + 3.1657w
In these formulas, d = standard outside diameter of screw; m = measurement over wires; w = diameter of wires; p = pitch of thread = 1 ÷ number of threads per inch.
To illustrate the use of the formula for the U. S. standard thread, let us assume that a screw having 6 threads per inch (1/6-inch pitch) is to be cut to a diameter of 11/2 inch, and that wires 0.140 inch diameter are to be used in conjunction with a micrometer for measurement. Then the micrometer reading m should be
11/2 - 1.5155 × 1/6 + 3 × 0.140 = 1.6674 inch
If the micrometer reading were 1.670 inch, it would indicate that the pitch diameter of the screw was too large, the error being equal to difference between 1.667 and the actual reading.
Fig. 27. Rivett-Dock Circular Threading Tool in Working Position