The adsorption of ammonia on the two low index (111) and (100) surfaces of rhodium has been studied by periodic calculations with density functional theory and compared to experimental results. The geometries of the adsorbates and the surfaces are completely optimized. For both surfaces the top site is found to be the most stable while the adsorption energy of ammonia is 8-10 kJ . mol(-1) larger on the (100) surface. The presence of steps on the (100) surface has a minor effect on the heat of adsorption. The theoretical predictions of the adsorption energies and the changes in work function by NH3 are in good agreement with experimental data. Moreover the prediction of the ontop adsorption as well as the weak interactions between the adsorbates is confirmed. The broadening of the temperature programmed desorption spectra and the two desorption peaks for the first adlayer are mainly due to an entropy effect which affects the preexponential factor of the desorption rate constant.