Machinery's Handbook 26th ed:
The tensile- stress area for Unified thread is based on a diameter equivalent to the mean of the pitch and minor diameters. The pitch and the minor diameters for Unified screw threads can be found from the major (nominal) diameter, d, and the screw pitch, P=1/n, where n is the number of threads per inch, by use of the following formulas: the pitch diameter dp=d-0.649519*P; the minor diameter dm=d-1.299038*P. The tensile stress area As, for Unified threads can be then found as follows:
As=(pi/4)*((dm+dp)/2)^2
