Spin-polarized density functional theory calculations have been performed to investigate the carbon pathways and hydrogenation mechanism for CH4 formation on Fe2C(011), Fe5C2(010), Fe3C(011), and Fe4C(100) We find that the surface C atom occupied sites are more active toward CH4 formation In Fischer-Tropsch synthesis (FTS), CO direct dissociation is very difficult on perfect FexCy surfaces, while surface C atom hydrogenation could occur easily. With the formation of vacancy sites by C atoms escaping from the FexCy surface, the CO dissociation barrier decreases largely As a consequence, the active carburized surface is maintained Based on the calculated reaction energies and effective barriers, CH4 formation is more favorable on Fe5C2(010) and Fe2C(011), while Fe4C(100) and Fe3C(001) are inactive toward CH4 formation. More importantly, it is revealed that the reaction energy and effective barrier of CH4 formation have a linear relationship with the charge of the surface C atom and the cl-band center of the surface, respectively On the basis of these correlations, one can predict the reactivity of all active surfaces by analyzing their surface properties and further give guides for catalyst design in FTS