In this paper, we evaluate the effect of demand uncertainty on hospital costs. Since hospital managers want to minimize the probability of not having enough capacity to satisfy demand, and since demand is uncertain, hospitals have to build excess capacity and incur the associated costs. Using panel data comprising information for 43 Portuguese public hospitals for the period 2007-2009, we estimate a translog cost function that relates total variable costs to the usual variables (outputs, the price of inputs, some of the hospitals' organizational characteristics) and an additional term measuring the excess capacity related to the uncertainty of demand. Demand uncertainty is measured as the difference between actual and projected demand for emergency services. Our results indicate that the cost function term associated with the uncertainty of demand is significant, which means that cost functions that do not include this type of term may be misspecified. For most of our sample, hospitals that face higher demand uncertainty have higher excess capacity and higher costs. Furthermore, we identify economies of scale in hospital costs, at least for smaller hospitals, suggesting that a policy of merging smaller hospitals would contribute to reducing hospital costs.