Hydrogen is a strong candidate for light alloying elements in the terrestrial cores.Previous first-principles studies on non-stoichiometric hexagonal close-packed (hcp) and double hexagonal close-packed (dhcp) FeH x predicted a discontinuous volume expansion across the magnetic phase transition from non-magnetic (NM) or antiferromagnetic (AFM) to ferromagnetic (FM) state with increasing the hydrogen content, x at 0 K. However, previous high pressure and temperature neutron diffraction experiments on face-centered cubic (fcc) FeH x did not show such nonlinearity. The discrepancy between theory and experiment may be due to differences in the crystal structure, magnetism, or temperature. In this study, we computed the equation of states for fcc FeH x by using the Korringa-Kohn-Rostoker method combined with the coherent potential approximation (KKR-CPA). In addition to the four types of ground-state magnetism (FM, AFM-I, AFM-II, and NM), we also calculated the local magnetic disorder (LMD) state, which approximates the paramagnetic (PM) state with local spin moment above the Curie temperature. The results show that even though FM, AFM-I, AFM-II, and NM calculations predict a discontinuity in the volume at 0 K, the volume becomes continuous above the Curie temperature, consistent with the previous high-temperature experiment. From the enthalpy comparison at 0 K, FM fcc FeH (x = 1) undergoes the NM state above ~48 GPa. The magnetic transition pressure decreases with decreasing hydrogen content. Therefore, below the magnetic transition pressure, local spin moments affect the density and elastic wave velocity of fcc FeH x , which may be important for small terrestrial bodies such as Mercury and Ganymede. On the other hand, at the Earth's core pressure above 135 GPa, fcc FeH x becomes NM. Thus, we calculated the density and bulk sound velocity as a function of pressure at 0 K for NM This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America.The published version is subject to change. Cite as Authors (Year) Title. American Mineralogist, in press.