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Segregation and precipitation of second phases in metals and metallic alloys is an important phenomenon that has a strong influence on the mechanical properties of the material. Models exist that describe the growth of coherent, semi-coherent and incoherent precipitates. One important parameter of these models is the energy of the interface between matrix and precipitate. In this work we apply ab initio density functional theory calculations to obtain this parameter and to understand how it depends on chemical composition and mechanical strain at the interface. Our example is a metastable Mo–C phase, the body-centred tetragonal structure, which exists as a semi-coherent precipitate in body-centred cubic molybdenum. The interface of this precipitate is supposed to change from coherent to semi-coherent during the growth of the precipitate. We predict the critical thickness of the precipitate by calculating the different contributions to a semi-coherent interface energy by means of ab initio density functional theory calculations. The parameters in our model include the elastic strain energy stored in the precipitate, as well as a misfit dislocation energy that depends on the dislocation core width and the dislocation spacing. Our predicted critical thickness agrees well with experimental observations.