Moral norms are fundamental for virtually all social interactions, including cooperation. Moral norms develop and change, but the mechanisms underlying when, and how, such changes occur are not well-described by theories of moral psychology. We tested, and confirmed, the hypothesis that the commonness of an observed behavior consistently influences its moral status, which we refer to as the “common is moral” (CIM) heuristic. In nine experiments, we used an experimental model of dynamic social interaction that manipulated the commonness of altruistic and selfish behaviors to examine the change of peoples' moral judgments. We found that both altruistic and selfish behaviors were judged as more moral, and less deserving of punishment, when common than when rare, which could be explained by a classical formal model (Social Impact Theory) of behavioral conformity. Furthermore, judgments of common versus rare behaviors were faster, indicating that they were computationally more efficient. Finally, we used agent-based computer simulations to investigate the endogenous population dynamics predicted to emerge if individuals use the CIM heuristic, and found that the CIM heuristic is sufficient for producing two hallmarks of real moral norms; stability and sudden changes. Our results demonstrate that commonness shapes our moral psychology through mechanisms similar to behavioral conformity with wide implications for understanding the stability and change of moral norms.