Metal nanoparticles are known to be essential catalysts for various industrial-relevant chemical reactions. Their catalytic properties are strongly dependent upon their surface roughness, which is difficult to be measured and compared quantitatively. Fractal dimension is a measure that allows the roughness of irregular surfaces to be quantified. However, the calculation process often requires high computational cost, and there is a lack of research on the computing of fractal dimension of atomistic surfaces obtained from computational studies. In this work, we first showcase two approaches of estimating the fractal dimension of atomistic surfaces, by representing them as either voxelised point clouds or mathematically precise objects, and computing their box-counting dimensions. The methodology is published as an open-sourced Python package Sphractal, and its utility is demonstrated on a set of simulated palladium nanoparticles data. We subsequently attempted to reduce the cost of using box-counting dimension as a label for studies on atomistic objects such as metal nanoparticles. This is achieved by implementing supervised regression models that take the atomic coordinates of any given metal nanoparticle as input, and predict its box-counting dimension. Among the implemented models (including linear regressor with various regularisation techniques, neighbour-based regressor, support vector regressor, and tree-based regressors with boosting and bagging techniques), random forest regressor stood out as the model with the best predicting capability. However, further effort is required to mitigate the overfitting of the model. It was found that the most important features for the prediction of the box-counting dimensions by the random forest model are the percentage of atoms lying on surfaces with 1 to 10 degrees of curvature, and the percentage of atoms forming {100} surfaces.