Calculating Pitch Diameter of Symmetrical Threads

The general formula for determining the pitch diameter of any thread whose sides are symmetrical with respect to a line drawn through the vertex and perpendicular to the axis of the thread, in which the slight effect of lead angle is taken into account, is:

Formula 1
E=M_w+\frac{\cot \alpha}{2_n}-\omega [1+(\csc ^2\alpha +\cot^2\alpha\tan ^2\lambda' )^\frac{1}{2}]

IN WHICH
Pitch Diameter
Measurement Over Wires
Half Angle of Thread
n Number of Threads per Inch =
Mean Diameter of Wires
Angle Between Axis or Wire and Plane Perpendicular to Axis of Thread

This formula is a very close approximation, being based on certain assumptions regarding the positions of the points of contact between the wire and the thread.

Formula 1 can be converted to the following simplified form, which is particularly useful when measuring threads of large lead angle:

Formula 2

IN WHICH
The Angle Whose Tangent =

When Formula 1 is used, the usual practice is to expand the square root term as a series, retaining only the first and second terms, which gives the following:

Formula 3

For large lead angles it is necessary to measure the wire angle, , but for lead angles of 5 degrees or less, if the “best size” wire is used, this angle may be assumed to be equal to the lead angle of the thread at the pitch line, . The value of tan , the tangent of the lead angle, is given by the formula:

\tan \lambda = \frac{\iota }{3.1417E} = \frac{1}{3.1416NE}

IN WHICH
Lead
Number of Turns per Inch
Nominal Pitch Diameter, or an Approximation of the Measured Pitch Diameter
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