Background. The body mass index (BMI) is the standard parameter for predicting body fat fraction and for classifying degrees of obesity. Currently available regression equations between BMI and fat are based on 2 or 3 parameter empirical fits and have not been validated for highly obese subjects. We attempt to develop regression relations that are based on realistic models of body composition changes in obesity. These models, if valid, can then be extrapolated to the high fat fraction of the morbidly obese. Methods. The analysis was applied to 3 compartment (density and total body water) measurements of body fat. The data was collected at the New York Obesity Research Center, Body Composition Unit, as part of ongoing studies. A total of 1356 subjects were included, with a BMI range of 17 to 50 for males and 17 to 65 for females. The body composition model assumes that obese subjects can be represented by the sum of a standard lean reference subject plus an extra weight that has a constant adipose, bone and muscle fraction. Results. There is marked age and sex dependence in the relationship between BMI and fat fraction. There was no significant difference among Caucasians, Blacks and Hispanics while Asians had significantly greater fat fraction for the same BMI. A linear relationship between BMI and fat fraction provides a good description for men but overestimates the fat fraction in morbidly obese women for whom a non-linear regression should be used. New regression relations for predicting body fat just from experimental measurements of body density are described that are more accurate then those currently used. From the fits to the experimental BMI and density data, a quantitative description of the bone, adipose and muscle body composition of lean and obese subjects is derived. Conclusion. Physiologically realistic models of body composition provide both accurate regression relations and new insights about changes in body composition in obesity.