Characterizing the breadth of the Planck function

The breadth of the Planck blackbody spectrum is quantified by computing the standard deviation of the distribution in frequency space when weighting by both frequency and number of photons. The calculations can be carried out analytically, and they reveal that the standard deviation captures about three-quarters of both the total energy emission and number of photons, independent of the temperature of the source. It is advocated that this approach be used to complement, if not entirely replace, common (and potentially misleading) textbook “peak value” discussions.