The construction of Euclidean quantum gravity can be rephrased as the mathematical problem of constructing a random metric on the space manifold. In recent years toy models of Euclidean flat (or constant-curvature) quantum gravity, in which this manifold is the two-dimensional disk, have received much attention, because of their alleged holographic properties. This begs the mathematically rephrased question: what is a uniformly random flat metric on the disk? In this talk I will give a simple answer to this question, that should be understandable to someone with no background in gravity.