How seismic magnitudes are distributed is important for estimating stress levels in seismic hazard studies, and two methods of characterizing the magnitude distribution are through the Gutenberg-Richter b-value, or equivalently through , and through the information entropy. A closed relationship between the b-value and the entropy (applicable to any exponential distribution and its entropy) is presented and is checked through numerical evaluation of the entropy using exact probabilities derived directly from the magnitude exponential distribution. Since the numerical evaluation of the entropy is done over a finite magnitude range, it is possible to assess the possible contribution to the entropy of real or hypothetical very large magnitudes, and these contributions are found to be quite small. The relationship is also compared with entropies calculated from synthetic data, and Monte Carlo simulations are used to explore the behavior of entropy determinations as a function of sample size. Finally, it is considered how, for the usual case of having data from a single realization, in spite of the relation between them, because entropy and Aki-Utsu b-value are measured in different ways, both measures are not redundant and may be complementary and useful in determining when a sample is large enough to give reliable results.