Probing the charge density distributions in materials at atomic scale remains an extremely demanding task, particularly in real space. However, recent advances in differential phase contrast-scanning transmission electron microscopy (DPC-STEM) bring this possibility closer by directly visualizing the atomic electric field. DPC-STEM at atomic resolutions measures how a sub-angstrom electron probe passing through a material is affected by the atomic electric field, the field between the nucleus and the surrounding electrons. Here, we perform a fully quantitative analysis which allows us to probe the charge density distributions inside atoms, including both the positive nuclear and the screening electronic charges, with subatomic resolution and in real space. By combining state-of-the-art DPC-STEM experiments with advanced electron scattering simulations we are able to map the spatial distribution of the electron cloud within individual atomic columns. This work constitutes a crucial step toward the direct atomic scale determination of the local charge redistributions and modulations taking place in materials systems.