The critical quantity in understanding imaging using an atomic force microscope is the force the sample exerts on the tip. We put forward a simple one-to-one force to water density relationship, explain exactly how it occurs, and in which circumstances it holds. We argue that two wide classes of atomic force microscope (AFM) tip should lead to at least qualitative agreement with our model and represent a significant fraction of AFM tips as currently prepared. This connection between the short-range force and the unperturbed equilibrium water density removes the need to perform simulations for each tip location, conservatively speeding up simulations by around three orders of magnitude compared to current methods that explicitly calculate the force on a tip model at each point in space.