In this work, several (unreported) structures of NO on Rh(111) are presented for coverages ranging from 0-0.78 ML. The formation of these structures as evidenced experimentally by scanning tunneling microscopy (STM) images is explained using density-functional theory derived values for the lateral interactions and adsorption energies of NO on Rh(111). Kinetic Monte Carlo simulations using the derived lateral interactions are performed to determine structures at finite temperatures. The resulting structures can be directly compared to the molecular arrangements observed in the STM experiment. The configuration of the first three structures that form for increasing coverage is the same both experimentally and theoretically. In all three structures, the molecules only occupy the fcc and hcp adsorption sites. Yet, at high coverage, at which the top adsorption sites become occupied, a discrepancy arises.