The characteristic scores and scales (CSS), introduced by Glanzel and Schubert (J Inform Sci 14:123–127, 1988) and further studied in subsequent papers of Glanzel, can be calculated exactly in a Lotkaian framework. We prove that these CSS are simple exponents of the average number of items per source in general IPPs. The proofs are given using size-frequency functions as well as using rank-frequency functions. We note that CSS do not necessarily have to be defined as averages but that medians can be used as well. Also for these CSS we present exact formulae in the Lotkaian framework and both types of CSS are compared. We also link these formulae with the h-index.