In this Barrett Honors Thesis, I developed a model to quantify the complexity of Sankey diagrams, which are a type of visualization technique that shows flow between groups. To do this, I created a carefully controlled dataset of synthetic Sankey diagrams of varying sizes as study stimuli. Then, a pair of online crowdsourced user studies were conducted and analyzed. User performance for Sankey diagrams of varying size and features (number of groups, number of timesteps, and number of flow crossings) were algorithmically modeled as a formula to quantify the complexity of these diagrams. Model accuracy was measured based on the performance of users in the second crowdsourced study. The results of my experiment conclusively demonstrates that the algorithmic complexity formula I created closely models the visual complexity of the Sankey Diagrams in the dataset.