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The solubility of carbon in α-Fe as a function of lattice strain and in the vicinity of the Σ5(310)[001] symmetrical tilt grain boundary is calculated with ab initio methods based on density-functional theory (DFT). The results are compared to four different empirical potentials: the embedded-atom method (EAM) potentials of Lau et al., Ruda et al., and Hepburn et al., and the modified embedded-atom method (MEAM) potential of Lee. The results confirm that the solubility of carbon in body-centered-cubic (bcc) Fe increases under local volume expansion and provide quantitative data for the excess enthalpy to be used in thermodynamic databases. According to our study the excess enthalpy obtained from DFT is more strain-sensitive than the ones obtained from the tested empirical potentials. The comparison of the applied methods furthermore reveals that among the empirical potentials the MEAM is most appropriate to describe the solubility of C in bcc Fe under strain. The differences between the four empirical potentials stem from different parameterizations of the EAM potentials and, in the case of the MEAM, from the altogether different formalism that also includes angular dependent terms in the binding energy.