Gardner A (2020) Price’s equation made clear. Philosophical Transactions of the Royal Society of London Series B — Biological Sciences 375, 20190361.Price’s equation provides a very simple—and very general—encapsulation of evolutionary change. It forms the mathematical foundations of several topics in evolutionary biology, and has also been applied outwith evolutionary biology to a wide range of other scientific disciplines. However, the equation’s combination of simplicity and generality has led to a number of misapprehensions as to what it is saying and how it is supposed to be used. Here, I give a simple account of what Price’s equation is, how it is derived, what it is saying and why this is useful. In particular, I suggest that Price’s equation is useful not primarily as a predictor of evolutionary change but because it provides a general theory of selection. As an illustration, I discuss some of the insights Price’s equation has brought to the study of social evolution.