Neural Radiance Fields (NeRFs) have shown promise in applications like view synthesis and depth estimation, but their learning from multiview images faces inherent uncertainties. Current methods to quantify them are either heuristic or computationally demanding. We introduce BaysRays, a post-hoc framework to evaluate uncertainty in any pre-trained 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 highlight its superior performance in key metrics and NeRF-related applications.