<p>Fractal dimension has gathered broad interest for application in several geoscientific disciplines. This study presents a modified method for calculating it by a novel implementation of its underlying mathematical theory leading to several practical benefits. Instead of congruent quadrilaterals or circles in the Euclidean space, Discrete Global Grid Systems (DGGSs) are proposed as covering sets for geospatial vector data to calculate the Minkowski-Bouligand dimension using the box-counting principle. Using the method on synthetic data yields results within 1% of their theoretical fractal dimensions. A case study on opaque cloud fields obtained from satellite images gives fractal dimension in agreement with that available in the literature. The proposed method alleviates the problems of arbitrary grid placement and orientation, as well as the progression of cell sizes of the covering sets for geospatial data. Using DGGSs further ensures that intersections of the covering sets with the geospatial vector are calculated without having to project the data to planar coordinates first thus minimizing inevitable distortion associated with projection and making this method attractive for analyses at large geographic scales. This paper establishes the validity of DGGSs as covering sets theoretically and discusses desirable properties of DGGSs suitable for this purpose.</p>