Abstract : “Computing the pessimism” means bounding the overestimation produced by an inclusion function. There are two important distinctions with classical error analysis. First, we do not consider the image by an inclusion function but the distance between this image and the exact image (in the set-theoretical sense). Second, the bound is computed over a infinite set of intervals. To our knowledge, this issue is not covered in the literature and may have a potential of applications. We first motivate and define the concept of pessimism. An algorithm is then provided for computing the pessimism, in the univariate case. This algorithm is general-purpose and works with any inclusion function. Next, we prove that the algorithm converges to the optimal bound under mild assumptions. Finally, we derive a second algorithm for automatically controlling the pessimism, i.e., determining where an inclusion function is accurate.