Hydrogen has been considered as an important candidate of light elements in the Earth's core. Because iron hydrides are unquenchable, hydrogen content is usually estimated from in situ X-ray diffraction measurements that assume the following linear relation: x = (VFeHx – VFe)/ΔVH, where x is the hydrogen content, ΔVH is the volume expansion caused by unit concentration of hydrogen, and VFeHx and VFe are volumes of FeHx and pure iron, respectively. To verify the linear relationship, we computed the equation of states of hexagonal iron with interstitial hydrogen by using the Korringa-Kohn-Rostoker method with the coherent potential approximation (KKR-CPA). The results indicate a discontinuous volume change at the magnetic transition and almost no compositional (x) dependence in the ferromagnetic phase at 20 GPa, whereas the linearity is confirmed in the non-magnetic phase. In addition to their effect on the density-composition relationship in the Fe-FeHx system, which is important for estimating the hydrogen incorporation in planetary cores, the magnetism and interstitial hydrogen also affect the electrical resistivity of FeHx. The thermal conductivity can be calculated from the electrical resistivity by using the Wiedemann-Franz law, which is a critical parameter for modeling the thermal evolution of the Earth. Assuming an Fe1–ySiyHx ternary outer core model (0.0 ≤ x ≤ 0.7), we calculated the thermal conductivity and the age of the inner core. The resultant thermal conductivity is ∼100 W/m/K and the maximum inner core age ranges from 0.49 to 0.86 Gyr.