We apply the first-principles density functional theory + dynamical mean field theory framework to evaluate the crystal-field splitting on rare-earth sites in hard magnetic intermetallics. An atomic (Hubbard-I) approximation is employed for local correlations on the rare-earth 4f shell and selfconsistency in the charge density is implemented. We reduce the density functional theory selfinteraction contribution to the crystal-field splitting by properly averaging the 4f charge density before recalculating the one-electron Kohn-Sham potential. Our approach is shown to reproduce the experimental crystal-field splitting in the prototypical rare-earth hard magnet SmCo5. Applying it to RFe12 and RFe12X hard magnets (R =Nd, Sm and X =N, Li), we obtain in particular a large positive value of the crystal-field parameter A 0 2 r 2 in NdFe12N resulting in a strong out-of-plane anisotropy observed experimentally. The sign of A 0 2 r 2 is predicted to be reversed by substituting N with Li, leading to a strong out-of-plane anisotropy in SmFe12Li. We discuss the origin of this strong impact of N and Li interstitials on the crystal-field splitting on rare-earth sites.