A First-Principles Theory of the Human Body: The End of BMI's Reign

Body mass index (BMI) and many related anthropometric indices describe the human body through selected arithmetic relations among mass, height, circumferences, exponents, coefficients, and group-specific interpretation rules. These constructions retain anthropometric information but do not provide one physical coordinate that relates body mass to measured longitudinal and transverse body geometry. This paper compares BMI with the coordinate k = m/(w²h), where m is body mass, h is height, and w is waist circumference. The term w²h is used as a circumference-based body-volume proxy. Kernel density estimation and descriptive statistics were applied to unweighted NHANES 2017–2023 data. The matched full-sample comparison included 20,699 observations with valid body mass, height, and waist circumference measurements. The distributions were examined in the full working sample and across male and female groups, NHANES race and ethnicity categories, and broad age groups. The same definition of k was applied before stratification, without sex-specific, age-specific, or race/ethnicity-specific correction factors. In the matched full sample, the coefficient of variation decreased from 30.26% for BMI to 17.16% along the k axis, skewness decreased from 0.85 to 0.36, and excess kurtosis changed from 1.29 to −0.55. Male and female profiles along the k axis had 44–45% lower relative dispersion and approximately 62% lower skewness than the corresponding BMI profiles, while their mean and median positions were closely aligned. All listed NHANES race and ethnicity categories showed lower within-category relative dispersion and lower skewness along the k axis. Their central ordering differed from BMI, and the relative between-category span of the means was narrower along the k axis: 4.1% of the full-sample k mean, compared with 20.4% of the full-sample BMI mean on the BMI scale. Across broad age groups, BMI showed a non-monotonic increase–plateau–decline pattern, whereas the mean, median, and KDE-peak positions along the k axis decreased successively from younger to older groups. Childhood remained a distinct developmental region: relative dispersion along the k axis was higher than for BMI in children aged 0–11 but lower from adolescence onward. The coordinate k is therefore not a monotonic rescaling or empirical correction of BMI. It begins from a different physical relation in which body mass is interpreted relative to a three-dimensional geometric proxy that includes measured transverse body size. The resulting profiles provide a more statistically tractable basis for comparing heterogeneous population groups on one coordinate. The study does not establish clinical thresholds, individual diagnostic interpretation, or longitudinal trajectories of aging. This work is part of the research series A First-Principles Theory of the Human Body. Series repository: Open Science Framework, DOI: https://doi.org/10.17605/OSF.IO/ENAUQ.