We propose a fast algorithm for the computation of local thickness in 2D and 3D. Compared to the conventional algorithm, our fast algorithm yields local thickness in just a fraction of the time. In our algorithm, we first compute the distance field of the object and then iteratively dilate the selected parts of the distance field. In every iteration, we employ small structuring elements, which makes our approach fast. Our algorithm is implemented in Python and is freely available as a pip-installable module. Besides giving a detailed description of our method, we test our implementation on 2D images and 3D volumes. In 2D, we compute the ground truth using the conventional local thickness methods, where the distance field is dilated with increasingly larger circular structuring elements. We use this as a reference to evaluate the quality of our results. In 3D, we have no ground truth since it would be too time-consuming to compute. Instead, we compare our results with the golden standard method provided by BoneJ. In both 2D and 3D, we compare with another Python-based approach from PoreSpy. Our algorithm performs equally well or better than other approaches, but significantly faster.