Theoretical work on stochastic choice mainly focuses on the sources of choice randomness, and less on its economic consequences. We close this gap by developing a method of extracting information about the costs of noise from structural estimates of preferences and choice randomness. Our method is based on interpreting the degree of noise in choices as a way to rationalize them by a given structural model. We consider risky binary choices made by a sample of the general Danish population in an artefactual field experiment. The estimated welfare costs are small in terms of everyday economic activity, but they are considerable in terms of the actual stakes of the choice environment. Higher welfare costs are associated with higher age, lower education, and certain employment status.