Molecular simulations can become computationally expensive when studying systems of increasing size taking a prohibitively long time to run. One strategy to cut down the time of these simulations is to make use of approximations to replace the lengthy calculations a computer would otherwise have to do. This study focused on the Derjaguin approximation, which is often used to simplify the calculation of the forces between two curved surfaces when the length scale of the interaction is much less than the curvature of the surface - λ ≪ R_C . The problem is that it is often invoked without consideration of when this approximation breaks down, and there is currently not a good quantitative understanding of where that happens. Using the molecular simulation software LAMMPS, two spherical colloids in a solution with simple bead-spring polymers were simulated and the colloids’ behavior was analyzed to determine the separation distances between them over time. Then the predictions using the Derjaguin approximation were compared to the approximation free results to obtain a quantitative understanding of how and when it breaks down. The sizes of the colloids were varied to help draw a relationship between their size, the range of the interaction (I.e. the polymer size) and the breakdown of the Derjaguin approximation. Thus we now have bounds on the Derjaguin approximation, and can now make informed decisions as to when to use the Derjaguin approximation when simulating colloids in solution.