[en] Quantum close-coupling and coupled-states approximation scattering calculations for rotational energy transfer of rotationally excited NH₃ and ND₃ due to collisions with He are presented. Calculations were performed for collision energies between 10^-5 and 10000 cm^-1 using the NH₃-He potential of Hodges and Wheatley. State-to-state and total quenching cross-sections from some selected initial states are presented. Rate coefficients for ortho-NH₃ for the quenching 10+ -> 00+ transition were obtained on potentials scaled to reproduce measurements of second Virial coefficients with the results showing strong sensitivity to the potential, especially at low temperatures. Significant isotope effects are found in quenching cross-sections in the cold to ultra-cold regime particularly in the region dominated by quasi-bound resonances, ∼0.1 to 10 cm^-1. As ammonia has been translational cooled via Stark deceleration methods, it is a good candidate for experimental study of such effects at cold temperatures. Comparison of rate coefficients with available theoretical results are also presented. (authors)