The centromere, responsible for chromosome segregation during mitosis, is epigenetically defined by CENP-A containing chromatin. The amount of centromeric CENP-A has direct implications for both the architecture and epigenetic inheritance of centromeres. Using complementary strategies, we determined that typical human centromeres contain ∼400 molecules of CENP-A, which is controlled by a mass-action mechanism. This number, despite representing only ∼4% of all centromeric nucleosomes, forms a ∼50-fold enrichment to the overall genome. In addition, although pre-assembled CENP-A is randomly segregated during cell division, this amount of CENP-A is sufficient to prevent stochastic loss of centromere function and identity. Finally, we produced a statistical map of CENP-A occupancy at a human neocentromere and identified nucleosome positions that feature CENP-A in a majority of cells. In summary, we present a quantitative view of the centromere that provides a mechanistic framework for both robust epigenetic inheritance of centromeres and the paucity of neocentromere formation.DOI: http://dx.doi.org/10.7554/eLife.02137.001.