Calcite-water interactions are important not only in carbon sequestration and the global carbon cycle, but also in contaminant behaviour in calcite-bearing host rock and in many industrial applications. Here we quantify the effect of variations in surface structure on calcite surface reactivity. Firstly, we employ classical Molecular Dynamics simulations of calcite surfaces containing an etch pit and a growth terrace, to show that the local environment in water around structurally different surface sites is distinct. In addition to observing the expected formation of more calcium-water interactions and hydrogen-bonds at lower-coordinated sites, we also observed subtle differences in hydrogen bonding around acute versus obtuse edges and corners. We subsequently used this information to refine the protonation constants for the calcite surface sites, according to the Charge Distribution MUltiSite Ion Complexation (CD-MUSIC) approach. The subtle differences in hydrogen bonding translate into markedly different charging behaviour versus pH, in particular for acute versus obtuse corner sites. The results show quantitatively that calcite surface reactivity is directly related to surface topography. The information obtained in this study is not only crucial for the improvement of existing macroscopic surface models of the reactivity of calcite towards contaminants, but also improves our atomic-level understanding of mineral-water interactions.