Here, we present a methodology for the generalized quantification of the carbon (C)-formation risk in hydrocarbon mixtures based on the normalized chemical activity. An open-source computational thermodynamics tool is coupled to a solid oxide fuel cell (SOFC) stack model to apply and validate this approach with literature data based on methane-fueled SOFC systems with anode off-gas recirculation. Two- and three-dimensional C-formation risk maps valid for all C-H-O mixtures are proposed for a practical, accurate, and meaningful assessment of the trade-off between C-deposition risk and SOFC performance. Compared to conventional risk evaluation methods such as steam-to-carbon ratio (SCR), oxygen-to-carbon ratio (OCR), or C-H-O ternary-phase diagrams, this approach allows a system-agnostic evaluation of different designs operated at varying conditions at a constant C-formation risk margin. The generalized formulation allows integration into process optimization workflows to obtain high-performance system designs with extended stack operating windows.