An important problem in knowledge-based systems is inconsistency handling. This problem has recently been attracting a lot of attention in AI community. In this paper, we tackle the problem of evaluating the amount of conflicts in knowledge bases, and provide a new fine grained inconsistency measure, denoted |MCC, based on maximal consistent sets (MCSes). The main idea consists in quantifying the inconsistency of a knowledge base by considering that all its consistent pieces of information are possible. Furthermore, we provide an epistemic interpretation of our inconsistency measure using the multimodal logic S5. Then, we show that |MCC satisfies several state-of-the-art postulates. Moreover, we provide an encoding in integer linear programming for computing our inconsistency measure, which is defined from the set of MCSes. We also propose a Partial Max-SAT encoding, which allows us to avoid the computation of the MCSes. Finally, we provide a comparison between |MCC and two related existing inconsistency measures