Logical conflicts are likely to arise in logic-based intelligent systems. Managing these conflicts has been intensely studied in various parts of Artificial Intelligence (AI). So far, the AI research community has paid more attention to measuring the degree of inconsistency of knowledge bases. The key question we address in the present paper is how much a given formula contributes to the inconsistency of a knowledge base. Different such measures are studied and compared in a principle-based way against the backdrop of a list of desiderata. Two families of inconsistency measures are introduced and compared with measures from the literature: one is based on the notion of problematic formulas, while the other one is defined via the notion of free formulas in knowledge bases.