Our goal in this paper is to use an evolutionary approach to explain the existence and design features of human moral cognition. Our premise is that humans are under selection to be good cooperative investments. Hence, they face a trade-off between maximizing the immediate gains of each social interaction and maximizing its long-term reputational effects. In a 2-player game, we show, under simplifying assumptions, that this trade-off leads individuals to maximize the generalized Nash product in evolutionary equilibrium, ie, to behave according to the generalized Nash bargaining solution. From this result we derive the theoretical proposition that morality is a calculator of this bargaining solution. We then describe the general consequences of this approach:(i) everyone in a social interaction deserves to receive a net benefit,(ii) people should act in a way that would maximize social welfare if everyone acted in the same way,(iii) all domains of social behavior can be moralized,(iv) moral duties can appear both principled and non-contractual, and (v) morality should depend on context. We then apply the approach to some of the most important areas of social life, and show that it allows us to explain with a single logic the entire set of what are generally considered to be distinct moral domains. Finally, we discuss the relationship between this account of morality and other evolutionary accounts of morality and cooperation.