Theoretical scanning tunneling microscopy (STM) images for all group-III and -V dopants on the GaAs (110) surface are calculated using density functional theory (DFT). In addition, a geometrical model based on the covalent radii of the dopants and substrate atoms is used to interpret the images. We find that the covalent radius of the dopant determines the geometry of the surface, which in turn determines the contrast seen in the STM images. Our model allows bond lengths to be predicted with an error of less than 4.2% and positions to be predicted with an average deviation of only 0.19 Å compared to positions from fully relaxed DFT. For nitrogen we demonstrate good qualitative agreement between simulated and experimental STM images for dopants located in the first three surface layers. We are able to explain differences in both the contrast and positions of bright and dark features in the STM image based on our geometrical model. We then provide a detailed quantitative analysis of the positions of the bright features for nitrogen dopants in the second layer. The agreement of the DFT calculation with experiment is excellent, with the positions of the peaks in simulated and experimental STM scans differing by less than 2% of the lattice constant. For dopants other than nitrogen, we compare the calculated STM image contrast with the available experimental data and again find good agreement.