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