Turning pass-through network architectures into iterative ones that take their own output as an input is a well-known approach to boosting their performance. In this paper we argue that such architectures deliver an additional benefit: The convergence rate of their successive outputs is highly correlated to the accuracy of the value they converge to. Thus, we can use the convergence rate as a useful proxy for uncertainty. This yields an approach to uncertainty estimation that delivers state-of-the-art estimates, at a much lower computational cost than techniques such as Ensembles and without requiring any modifications to the original iterative model.We demonstrate its practical value by embedding it into two application domains, road detection in aerial images and the estimation of aerodynamic properties of 2D and 3D shapes.