First-principles (Density Functional Theory and SQS) calculations and the Calphad method are combined to obtain a thermodynamic description of the Cr-Mn-Si system. Especially the mixing enthalpies and the magnetic moments in solid solutions with substitutions of Cr by Mn are calculated at 0 K using the DFT for different structures. Such data are then used together with the available literature data to obtain a general description of the ternary system.