The excitation of the low-energy intermolecular modes of ammonia clusters by helium atom scattering has been calculated using classical trajectories. The energy transfer is investigated as a function of scattering angle (from 10degrees to 90degrees), collision energy (94.8 and 50.5 meV), cluster size (n=18, 100, 1000), and cluster temperature (T-c=1 K, 30-50 K, and 105 K). It is observed that predominantly the mode at 7 meV and to a lesser extent also the one at 12 meV are excited. These are surface modes that mainly originate from the angular motion of three adjacent N atoms. The excitation is nearly independent of the cluster size and the probability for multiphonon excitation steadily increases with increasing deflection angle. This trend is even strengthened by increasing the collision energy. The role of the cluster temperature is to broaden the energy transfer distribution with increasing values. The calculations are compared with previous and new measurements presented here of the double-differential cross sections (dsigma/domega)(DeltaE) of ammonia clusters of average size [n]=92 at two collision energies and [n]=1040 at one energy. While the general trends in the angular and energy dependence could be well reproduced, the correct cluster temperature was crucial in getting good agreement at the lower collision energy for n=100. At the higher collision energy, the large energy transfer is not reproduced, probably a shortcoming of the potential models to account correctly for the anharmonicity of the strong multiquantum excitations.