We present results of ab initio calculations of several L10 FeNi characteristics, such as the summary of the magnetocrystalline anisotropy energies (MAEs), the full potential calculations of the anisotropy constant K3, and the combined analysis of the Fermi surface and 3D -resolved MAE. Other calculated parameters are the spin and orbital magnetic moments, the magnetostrictive coefficient , the bulk modulus B0, and the lattice parameters. The MAEs summary shows rather big discrepancies among the experimental MAEs from the literature and also among the calculated MAE’s. The MAEs calculated in this work with the full potential and generalized gradient approximation (GGA) are equal to 0.47 MJ from WIEN2k, 0.34 MJ from FPLO, and 0.23 MJ from FP-SPR-KKR code. These results suggest that the MAE in GGA is below 0.5 MJ . It is expected that due to the limitations of the GGA, this value is underestimated. The L10 FeNi has further potential to improve its MAE by modifications, like e.g. tetragonal strain or alloying. The presented 3D -resolved map of the MAE combined with the Fermi surface gives a complete picture of the MAE contributions in the Brillouin zone. The obtained, from the full potential FP-SPR-KKR method, magnetocrystalline anisotropy constants K2 and K3 are several orders of magnitude smaller than the MAE/K1 and equal to kJ and 110 J , respectively. The calculated spin and orbital magnetic moments of the L10 FeNi are equal to 2.72 and 0.054 for Fe and 0.53 and 0.039 for Ni atoms, respectively. The calculations of geometry optimization lead to a c/a ratio equal to 1.0036, B0 equal to 194 GPa, and equal to 9.4 × 10−6.