© 2020 The Authors The displacements-per-atom (dpa) is widely used as an exposure unit to predict the operating lifetime of materials in radiation environments. Because the athermal-recombination-corrected dpa (arc-dpa) model is a more realistic model than the standard Norgett–Robinson–Torrens (NRT) model, new evaluation of radiation damage for various applications at nuclear fission, fusion, and accelerator facilities will be performed using the arc-dpa model as a standard. Determination of the rescaling factor from the NRT-dpa to arc-dpa model for various applications is also important. In this work, the recent arc-dpa model of various materials including C, Al, Si, Fe, Cu, and W are incorporated in the Particle and Heavy Ion Transport code System (PHITS), and the rescaling factors (NRT-dpa/arc-dpa) over a wide energy range are reported. For neutron incidences with the energy spectrum determined in selected nuclear facilities and proton incidences with energies of 600 MeV–50 GeV, the rescaling factor for each material is independent of these irradiation conditions with almost the same value for each material. This value is mainly determined by the saturation in the damage production efficiency in the damage energy region over approximately 1 keV. Our findings will be beneficial for rescaling the NRT-dpa used for radiation damage applications over a wide energy region at various facilities.