Harish-Chandra's volume formula shows that the volume of a flag manifold G/T, where the measure is induced by an invariant inner product on the Lie algebra of G, is determined up to a scalar by the algebraic properties of G. This article explains how to deduce Harish-Chandra's formula from Weyl's law by utilizing the Euler–Maclaurin formula. This approach suggests that there may be an elementary explanation available for the appearance of the power series x/(1−e−x) in the Atiyah–Singer index theorem.