The magnetic anisotropy of the ferromagnetic semiconductor (Ga, Mn) (As, P) is studied in a material-specific microscopic k . p approach. We calculate the electronic energy band structure of (Ga, Mn) (As, P) quaternary ferromagnetic alloys using a 40-band k . p model and taking into account the s, p-d exchange interaction and the strain of the (Ga, Mn) (As, P) layer on a GaAs substrate. We determine the variations of the carrier effective masses in the strained (Ga, Mn) (As, P)/GaAs system. The magnetic anisotropy constants obtained from our simulations using a mean-field model are compared with the experimental ones determined by ferromagnetic resonance spectroscopy on a set of samples with constant manganese concentration and varying phosphorus concentration. An excellent quantitative agreement between experiment and theory is found for the uniaxial out-of-plane and cubic in-plane anisotropy parameters.