Background: Attempts to model cumulative intake curves with quadratic functions have not simultaneously taken gustatory stimulation, satiation, and maximal food intake into account. Objective: Our aim was to develop a dynamic model for cumulative intake curves that captures gustatory stimulation, satiation, and maximal food intake. Design: We developed a first-principles model describing cumulative intake that universally describes gustatory stimulation, satiation, and maximal food intake using 3 key parameters: 1) the initial eating rate, 2) the effective duration of eating, and 3) the maximal food intake. These model parameters were estimated in a study (n = 49) where eating rates were deliberately changed. Baseline data was used to determine the quality of model's fit to data compared with the quadratic model. The 3 parameters were also calculated in a second study consisting of restrained and unrestrained eaters. Finally, we calculated when the gustatory stimulation phase is short or absent. Results: The mean sum squared error for the first-principles model was 337.1 6 240.4 compared with 581.6 6 563.5 for the quadratic model, or a 43% improvement in fit. Individual comparison demonstrated lower errors for 94% of the subjects. Both sex (P = 0.002) and eating duration (P = 0.002) were associated with the initial eating rate (adjusted R2 = 0.23). Sex was also associated (P = 0.03 and P = 0.012) with the effective eating duration and maximum food intake (adjusted R2 = 0.06 and 0.11). In participants directed to eat as much as they could compared with as much as they felt comfortable with, the maximal intake parameter was approximately double the amount. The model found that certain parameter regions resulted in both stimulation and satiation phases, whereas others only produced a satiation phase. Conclusions: The first-principles model better quantifies interindividual differences in food intake, shows how aspects of food intake differ across subpopulations, and can be applied to determine how eating behavior factors influence total food intake.