Nanoparticles on surfaces are ubiquitous in nanotechnologies, especially in catalysis, where metal nanoparticles anchored to oxide supports are widely used to produce and use fuels and chemicals, and in pollution abatement. We show that for hemispherical metal particles of the same diameter, D, the chemical potentials of the metal atoms in the particles (μ) differ between two supports by approximately -2(E - E)V/D, where E is the adhesion energy between the metal and support i, and V is the molar volume of the bulk metal. This is consistent with calorimetric measurements of metal vapor adsorption energies onto clean oxide surfaces where the metal grows as 3D particles, which proved that μ increases with decreasing particle size below 6 nm and, for a given size, decreases with E. Since catalytic activity and sintering rates correlate with metal chemical potential, it is thus crucial to understand what properties of catalyst materials control metal/oxide adhesion energies. Trends in how E varies with the metal and the support oxide are presented. For a given oxide, E increases linearly from metal to metal with increasing heat of formation of the most stable oxide of the metal (per mole metal), or metal oxophilicity, suggesting that metal-oxygen bonds dominate interfacial bonding. For the two different stoichiometric oxide surfaces that have been studied on multiple metals (MgO(100) and CeO(111), the slopes of these lines are the same, but their offset is large (∼2 J/m). Adhesion energies increase as MgO(100) ≈ TiO(110) < α-AlO(0001) < CeO(111) ≈ FeO(111).