Ligand binding plays a fundamental role in stimulating the downstream signaling of membrane receptors. Here, ligand-binding kinetics of the full-length human adenosine receptor A2A (A2AR) reconstituted in detergent micelles were measured using a fluorescently labeled ligand via fluorescence anisotropy. Importantly, to optimize the signal to noise ratio, these experiments were conducted in the ligand depletion regime. In the ligand depletion regime, the assumptions used to determine analytical solutions for one-site binding models for either one or two ligands in competition are no longer valid. We therefore implemented a numerical solution approach in order to analyze kinetic binding data as experimental conditions approach the ligand depletion regime. By comparing the results from the numerical and the analytical solutions, we highlight the ligand-receptor ratios at which the analytical solution begins to lose predictive accuracy. Using the numerical solution approach, we determined the kinetic rate constants of the fluorescent ligand, FITC-APEC, and those for three unlabeled ligands using competitive association experiments. The association and dissociation rate constants of the unlabeled ligands determined from the competitive association experiments were then independently validated using competitive dissociation data. Based on this study, a numerical solution is recommended to determine kinetic ligand-binding parameters for experiments conducted in the ligand-depletion regime.