We introduce range utility theory for decisions under risk. Two functions are implicated in the representation of preferences: a traditional utility function for wealth---or changes in wealth---and a range distortion function. The latter introduces a local deformation of the utility function on the range under consideration, possibly magnifying the sensitivity to intermediate outcomes. In a sense we make precise, range utility theory is an alternative way to extend the binary rank dependent model to more than two outcomes. It can account for the fourfold pattern, as well as for the preference reversal phenomenon. When the range is fixed, range utility is linear in probabilities. We illustrate this advantage in game theory applications.