This study presents a mathematical model of human metabolism to quantify the effect of energy imbalance on body weight. The model simulates energy expenditure adaptations during weight loss and predicts weight change dynamics. It shows that body weight response to energy intake changes is slow, with a half-life of about one year. Adults with higher adiposity experience greater weight loss for the same energy intake change and take longer to reach steady-state weight. A population-averaged model shows that a small persistent daily energy imbalance of about 30 kJ underlies the average weight gain in the US. However, energy intake must increase to match increased expenditure associated with weight gain. The average increase in energy intake needed to sustain weight is about 0.9 MJ per day, highlighting the public health challenge of reversing the obesity epidemic. The study also shows that the popular static weight-loss rule (3500 kcal per pound) is inaccurate because it ignores dynamic physiological adaptations. A dynamic model predicts that a 2 MJ/day energy intake reduction results in a slower weight loss than the static rule. The model also shows that weight loss time courses depend on initial body composition, with individuals with higher initial fat mass losing more weight from fat than lean tissue. Physical activity increases energy expenditure and can lead to weight loss, but the effect varies depending on body weight. The model also shows that changes in energy intake and physical activity can lead to compensatory effects, which can affect weight change. The study also addresses the issue of diet composition and its effect on weight loss. While the energy balance principle suggests that all reduced energy diets should lead to equivalent weight loss, some diets may lead to greater weight loss due to differences in macronutrient composition. The model shows that changes in diet composition can lead to small changes in energy expenditure, but these changes are often not significant enough to affect weight loss over long periods. However, diets that reduce hunger and improve satiety may lead to better adherence and weight loss. The study also discusses the implications of the obesity epidemic at the population level. The average adult bodyweight in the US has increased over the past 30 years, and the model shows that this is due to a small persistent daily energy imbalance. The model also shows that reversing the obesity epidemic would require substantial changes in energy intake, particularly for obese individuals. The study concludes that accurate mathematical models of human metabolism are needed to properly assess the quantitative effect of interventions at both the individual and population levels. The model provides a web-based simulation tool to help health-care and health-policy practitioners make better informed decisions.This study presents a mathematical model of human metabolism to quantify the effect of energy imbalance on body weight. The model simulates energy expenditure adaptations during weight loss and predicts weight change dynamics. It shows that body weight response to energy intake changes is slow, with a half-life of about one year. Adults with higher adiposity experience greater weight loss for the same energy intake change and take longer to reach steady-state weight. A population-averaged model shows that a small persistent daily energy imbalance of about 30 kJ underlies the average weight gain in the US. However, energy intake must increase to match increased expenditure associated with weight gain. The average increase in energy intake needed to sustain weight is about 0.9 MJ per day, highlighting the public health challenge of reversing the obesity epidemic. The study also shows that the popular static weight-loss rule (3500 kcal per pound) is inaccurate because it ignores dynamic physiological adaptations. A dynamic model predicts that a 2 MJ/day energy intake reduction results in a slower weight loss than the static rule. The model also shows that weight loss time courses depend on initial body composition, with individuals with higher initial fat mass losing more weight from fat than lean tissue. Physical activity increases energy expenditure and can lead to weight loss, but the effect varies depending on body weight. The model also shows that changes in energy intake and physical activity can lead to compensatory effects, which can affect weight change. The study also addresses the issue of diet composition and its effect on weight loss. While the energy balance principle suggests that all reduced energy diets should lead to equivalent weight loss, some diets may lead to greater weight loss due to differences in macronutrient composition. The model shows that changes in diet composition can lead to small changes in energy expenditure, but these changes are often not significant enough to affect weight loss over long periods. However, diets that reduce hunger and improve satiety may lead to better adherence and weight loss. The study also discusses the implications of the obesity epidemic at the population level. The average adult bodyweight in the US has increased over the past 30 years, and the model shows that this is due to a small persistent daily energy imbalance. The model also shows that reversing the obesity epidemic would require substantial changes in energy intake, particularly for obese individuals. The study concludes that accurate mathematical models of human metabolism are needed to properly assess the quantitative effect of interventions at both the individual and population levels. The model provides a web-based simulation tool to help health-care and health-policy practitioners make better informed decisions.