Neural Radiance Fields (NeRFs) have shown promise in applications like view synthesis and depth estimation, butlearning from multiview images faces inherent uncertainties. Current methods to quantify them are either heuristicor computationally demanding. We introduce BayesRays, a post-hoc framework to evaluate uncertainty in any pretrained NeRF without modifying the training process. Our method establishes a volumetric uncertainty field using spatial perturbations and a Bayesian Laplace approximation. We derive our algorithm statistically and show its superior performance in key metrics and applications. Additional results available at: https://bayesrays.github.io/