Body Mass Index is mathematically related to the square of height

Peterson CM, Su H, Thomas DM, Heo M, Golnabi AH, Pietrobelli A, Heymsfield SB. Tri-Ponderal Mass Index vs Body Mass Index in Estimating Body Fat During Adolescence.. 2017. https://doi.org/10.1001/jamapediatrics.2017.0460

Discusses how body mass index traditionally divides weight by height squared, though noting scaling limitations in children.

Karoline Hood, J. Ashcraft, Krista Watts, Sangmo Hong, W. Choi, S. Heymsfield, R. Gautam, Diana M. Thomas. Allometric scaling of weight to height and resulting body mass index thresholds in two Asian populations. 2019. https://doi.org/10.1038/s41387-018-0068-3

Confirms through allometric analysis that weight scales to height squared across general adult populations.

S. Heymsfield, John D. Sorkin, Diana M. Thomas, Shengping Yang, Moonseong Heo, C. McCarthy, Jasmin B Brown, Angelo Pietrobelli. Weight/height2: Mathematical overview of the world's most widely used adiposity index. 2024. https://doi.org/10.1111/obr.13842

Details Quetelet's historical mathematical derivation establishing that body weight is proportional to the square of height in adults.

H. Ogata, Sayaka Nose-Ogura, Narumi Nagai, Momoko Kayaba, Yosuke Isoyama, J. Kruse, V. Seleznov, Miki Kaneko, Taiki Shigematsu, Ken Kiyono. Allometric multi-scaling of weight-for-height relation in children and adolescents: Revisiting the theoretical basis of body mass index of thinness and obesity assessment. 2024. https://doi.org/10.1371/journal.pone.0307238

Notes that the standard body mass index formula uses weight divided by height squared, which converges to validity in adults.