Objectives The positive influence of fat mass (FM) on fat‐free mass (FFM) has been quantified previously by various methods involving regression analysis of population data, but some are fundamentally flawed through neglect of the tendency of taller individuals to carry more fat. Differences in FFM due to differences in FM—and not directly related to differences in height—are expressed as ΔFFM/ΔFM, denoted KF. The main aims were to find a sounder regression‐based method of quantifying KF and simultaneously of estimating mean BMI0, the BMI of hypothetical fat‐free individuals. Other, related, objectives were to check the linearity of FFM‐FM relationships and to quantify the correlation between FM and height. Methods New statistical methods, explored and verified by Monte Carlo simulation, were applied to NHANES data. Regression of height2 on FFM and FM produced estimates of mean KF and indirectly of BMI0. Both were then adjusted to allow for variability in KF around its mean. Its standard deviation was estimated by a novel method. Results Relationships between FFM and FM were linear, not semilogarithmic as is sometimes assumed. Mean KF is similar in Mexican American men and women, but higher in men than women in non‐Hispanic European Americans and African Americans. Mean BMI0 is higher in men than in women. FM correlates more strongly with height than has been found previously. Conclusions A more accurate way of quantifying mean BMI0 and the dependence of FFM on FM is established that may be easily applied to new and existing population data.