Theoretical work on stochastic choice mainly focuses on the sources of choice randomness, and less on its economic consequences. We attempt to close this gap by developing a method of extracting information about the monetary costs of noise from structural estimates of preferences and choice randomness. Our method is based on allowing a degree of noise in choices in order to rationalize them by a given structural model. To illustrate the approach, 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 lower income.