A better understanding of the binding preference of amino acids for gold nanoparticles of different diameters could aid in the design of peptides that bind specifically to nanoparticles of a given diameter. Here we identify the binding preference of 19 natural amino acids for three gold nanoparticles with diameters of 1.0, 2.0, and 4.0 nm, and investigate the mechanisms that govern these preferences. We calculate potentials of mean force between 36 entities (19 amino acids and 17 side chains) and the three gold nanoparticles in explicit water using well-tempered metadynamics simulations. Comparing these potentials of mean force determines the amino acids' nanoparticle binding preferences and if these preferences are controlled by the backbone, the side chain, or both. Twelve amino acids prefer to bind to the 4.0 nm gold nanoparticle, and seven prefer to bind to the 2.0 nm one. We also use atomistic molecular dynamics simulations to investigate how water molecules near the nanoparticle influence the binding of the amino acids. The solvation shells of the larger nanoparticles have higher water densities than those of the smaller nanoparticles while the orientation distributions of the water molecules in the shells of all three nanoparticles are similar. The nanoparticle preferences of the amino acids depend on whether their binding free energy is determined mainly by their ability to replace or to reorient water molecules in the nanoparticle solvation shell. The amino acids whose binding free energy depends mainly on the replacement of water molecules are likely to prefer to bind to the largest nanoparticle and tend to have relatively simple side chain structures. Those whose binding free energy depends mainly on their ability to reorient water molecules prefer a smaller nanoparticle and tend to have more complex side chain structures.