The IEC 60153-2 and IEEE 1785.1 international
standards for rectangular metallic waveguides are currently
undergoing revision. Textbook derivations of the associated
equations for the metal-pipe rectangular waveguide attenuation
constant to be given in the revised standards are presented. These
derivations provide important mathematical traceability for
these equations, which has previously not been proven in the
open literature for these standards. Furthermore, the historical
approximations used in the original equations are identified and
now corrected here. Results using the newly derived equations
are demonstrated, with comparison to experimental results in the
WM-380 (500 GHz to 750 GHz) band.