Body fat and fat-free mass inter-relationships: Forbes's theory revisited
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A theoretical equation was developed by Forbes that quantifies the fat-free proportion of a weight change as a function of the initial body fat. However, Forbes's equation was strictly valid only for infinitesimal weight changes. Here, I extended Forbes's equation to account for the magnitude and direction of macroscopic body weight changes. The new equation was also re-expressed in terms of an alternative representation of body composition change defined by an energy partitioning parameter called the P-ratio. The predictions of the resulting equations compared favourably with data from human underfeeding and overfeeding experiments and accounted for previously unexplained trends in the data. The magnitude of the body weight change had a relatively weak effect on the predicted body composition changes and the results were very similar to Forbes's original equation for modest weight changes. However, for large weight changes, such as the massive weight losses found in patients following bariatric surgery, Forbes's original equation consistently underestimated the fat-free mass loss, as expected. The new equation that accounts for the magnitude of the weight loss provides better predictions of body composition changes in such patients.
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The percentage of weight reduction accounted for by lean mass loss is not constant and is expected to trend higher in people rapidly experiencing large weight reductions, as observed after bariatric surgery.
“However, this percentage is not a constant and is expected to trend higher in people rapidly experiencing large weight reductions, as observed after bariatric surgery.”
From Strategies for minimizing muscle loss during use of incretin‐mimetic drugs for treatment of obesity (2025) · cites this paper as [40]
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BackgroundJin, Z., Li, J., Thackray, A. E., Shen, T., Deighton, K., King, J. A., & Stensel, D. J. (2025) · International Journal of Obesity · doi:10.1038/s41366-025-01726-4 · Cited by 20 · see citing works
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Strain, G. W., Gagner, M., Pomp, A., Dakin, G. F., Inabnet, W. B., & Saif, T. (2011) · Surgery for Obesity and Related Diseases · doi:10.1016/j.soard.2011.09.028 · Cited by 17 · see citing works
Effect of Over- and Underfeeding on Body Composition and Related Metabolic Functions in Humans
Müller, M. J., & Bosy‐Westphal, A. (2019) · Current Diabetes Reports · doi:10.1007/s11892-019-1221-7 · Cited by 16 · see citing works
Serious analytical inconsistencies challenge the validity of the energy balance theory
Arencibia‐Albite, F. (2020) · Heliyon · doi:10.1016/j.heliyon.2020.e04204 · Cited by 16 · see citing works
“Alterations in body composition as a result of food intake restriction appear to depend primarily on the initial fat mass (FM) and on the magnitude of weight loss [23, 24, 25].”
BackgroundMethodInfluentialIndividual differences in the forced swimming test and neurochemical kinetics in the rat brain
Sequeira‐Cordero, A., Mora-Gallegos, A., Cuenca-Berger, P., & Trías, J. F. (2014) · Physiology & Behavior · doi:10.1016/j.physbeh.2014.01.037 · Cited by 16 · see citing works
Hackett, D. A., & Hagstrom, A. D. (2017) · Journal of Functional Morphology and Kinesiology · doi:10.3390/jfmk2040043 · Cited by 16 · see citing works
“Based on the first law of thermodynamics, an imbalance between energy intake and energy expenditure as a result of diet and/or exercise is accounted for by a gain or loss of body mass [2,3].”
BackgroundStubbs, R. J., Duarte, C., O’Driscoll, R., Turicchi, J., & Michałowska, J. M. (2019) · Proceedings of The Nutrition Society · doi:10.1017/s0029665119001083 · Cited by 16 · see citing works
“phase 2 of WL) most weight that is lost is in the form of reduced FM but FFM also decreases with WL, depending on initial body composition and the rate of WL((25)).”
BackgroundExploring obesity phenotypes: a longitudinal perspective
Rosero, R., Tamayo, M., Correa, R. R., Pantalone, K. M., Creel, D. B., Burguera, B. G., & Griebeler, M. L. (2025) · Reviews in Endocrine and Metabolic Disorders · doi:10.1007/s11154-025-09976-3 · Cited by 15 · see citing works
Martins, C., Nymo, S., Coutinho, S. R., Rehfeld, J. F., Hunter, G. R., & Gower, B. A. (2023) · Journal of Nutrition · doi:10.1016/j.tjnut.2023.03.026 · Cited by 13 · see citing works
Casanova, N., Beaulieu, K., Oustric, P., O’Connor, D., Gibbons, C., Duarte, C., Blundell, J. E., Stubbs, R. J., Finlayson, G., & Hopkins, M. (2020) · Obesity · doi:10.1002/oby.23034 · Cited by 13 · see citing works
“As body weight increases, FM is disproportionately increased relative to FFM (28), thus making the relationship between RMR and body weight curvilinear (29).”
BackgroundMcGrath, T., Murphy, K. G., & Jones, N. S. (2018) · Journal of The Royal Society Interface · doi:10.1098/rsif.2017.0736 · Cited by 10 · see citing works
“The law governing the partitioning of energy between the two compartments is Forbes’ law [71,72] (electronic supplementary material, S3.”
Association between insulin sensitivity and lean mass loss during weight loss
Bartholomew, C. L., Martins, C., & Gower, B. A. (2024) · Obesity · doi:10.1002/oby.24022 · Cited by 10 · see citing works
“Baseline LM was included in the models, given that baseline body composition has been shown to influence changes in body composition following weight loss [ 17].”
MethodConsistency of fat mass–fat-free mass relationship across ethnicity and sex groups
Broyles, S. T., Bouchard, C., Bray, G. A., Greenway, F. L., Johnson, W. D., Newton, R. L., Ravussin, É., Ryan, D. H., Smith, S. R., & Katzmarzyk, P. T. (2010) · British Journal Of Nutrition · doi:10.1017/s0007114510004794 · Cited by 10 · see citing works
“FM was log-transformed, based on Forbes’ empirical observations((1,4)) and on other evidence((7)) suggesting that FFM appears to be a logarithmic function of FM over the range of possible FM values.”
MethodState-of-the-art measurements in human body composition: A moving frontier of clinical importance.
Gallagher, D., Shaheen, I., & Zafar, K. (2008) · PubMed · Cited by 10 · see citing works
Real-Time Model Predictive Control of Human Bodyweight Based on Energy Intake
Fernández, A. P., Youssef, A., Heeren, C., Matthys, C., & Aerts, J. (2019) · Applied Sciences · doi:10.3390/app9132609 · Cited by 9 · see citing works
“Average Young information criterion (YIC) and coefficient of determination, R(2)T, together with their standard deviation, obtained during the system identification process for each of the 32 sub-datasets created from the Minnesota starvation excel spreadsheet used in the work of [31].”
BackgroundMethodChigutsa, E., Her, L., Ma, X., Urva, S., & Schneck, K. B. (2025) · Clinical Pharmacology & Therapeutics · doi:10.1002/cpt.3750 · Cited by 8 · see citing works
Costello, N. B., Deighton, K., Dalton‐Barron, N., Whitehead, S., Preston, T., & Jones, B. L. (2019) · European Journal of Sport Science · doi:10.1080/17461391.2019.1697373 · Cited by 8 · see citing works
“ΔE ΔBW = Pf + (Pl – Pf) ΔL ΔBW (Hall, 2007) (4)”
MethodSerra, M., Alceste, D., Hauser, F., Hulshof, P. J. M., Meijer, H. A. J., Thalheimer, A., Steinert, R. E., Gerber, P. A., Spector, A. C., Gerö, D., et al. (2023) · Frontiers in Nutrition · doi:10.3389/fnut.2023.1255499 · Cited by 7 · see citing works
Influence of previous body mass index and sex on regional fat changes in a weight loss intervention
Benito, P. J., Cupeiro, R., Peinado, A. B., Rojo, M. Á., Maffulli, N., & on behalf of the PRONAF Study Group (2017) · The Physician and Sportsmedicine · doi:10.1080/00913847.2017.1380500 · Cited by 8 · see citing works
Falkenhain, K., Redman, L. M., Chen, W. Y., Martin, C. K., Ravussin, É., & Shen, W. (2025) · Scientific Reports · doi:10.1038/s41598-024-83762-0 · Cited by 6 · see citing works
Kwan, A. T. H., Lakhani, M., & McIntyre, R. S. (2026) · Clinical Nutrition · doi:10.1016/j.clnu.2026.106620 · Cited by 6 · see citing works
González-Cano, H., Martín-Olmedo, J. J., Baz-Valle, E., Contreras, C., Schoenfeld, B. J., García‐Ramos, A., Jiménez‐Martínez, P., & Alix‐Fages, C. (2024) · The Journal of Strength and Conditioning Research · doi:10.1519/jsc.0000000000004697 · Cited by 6 · see citing works
“…AMA and PRO natural physique athletes in our study exhibited FFMI values # 25 kg · m 2 2 , it is well-known that male drug-free physique athletes may experience reductions in FFM and LBM during the competitive period, possibly because of reaching body fat levels close to essential levels (10,23).”
BackgroundHeymsfield, S. B., Ramirez, S., Yang, S., Thomas, D. M., Brown, J. C., Compton, S. L. E., Schuna, J. M., Smith, S. R., Ludwig, D. S., & Ebbeling, C. B. (2025) · Obesity · doi:10.1002/oby.24255 · Cited by 6 · see citing works
“…series of evaluations, we examined whether Δ FFM/ Δ BW with calorie restriction among the female individuals is comparable to that predicted by Forbes classic “ companionship ” rule relating Δ FFM/ Δ BW to baseline total body fat, i.e., Δ FFM/ Δ BW = 10.4/(10.4 + baseline total body fat) [23 – 26].”
InfluentialMethodological Challenges in Estimating the Lifetime Medical Care Cost Externality of Obesity
Schell, R. C., Just, D. R., & Levitsky, D. A. (2021) · Journal of Benefit-Cost Analysis · doi:10.1017/bca.2021.6 · Cited by 6 · see citing works
“We propose this 2PM both because of its reliance on more reasonable assumptions and history of use in the existing literature allowing for comparability (Thorpe et al., 2004; Wee et al., 2005; Yang & Hall, 2007; Bell et al., 2011; Cawley & Meyerhoefer, 2011; Trogdon et al., 2012).”
Müller, M. J., Braun, W., Enderle, J., & Bosy‐Westphal, A. (2022) · European Journal of Clinical Nutrition · doi:10.1038/s41430-022-01208-0 · Cited by 6 · see citing works
Dinparastisaleh, R., Khan, S. A., & Santhanam, P. (2023) · Springer eBooks · doi:10.1007/978-3-031-40116-9_33 · Cited by 7 · see citing works
Metabolic elasticity — a new trait associated with health?
Fernández‐Verdejo, R., & Galgani, J. E. (2023) · Nature Reviews Endocrinology · doi:10.1038/s41574-023-00914-4 · Cited by 5 · see citing works
Dinparastisaleh, R., Khan, S. A., & Santhanam, P. (2023) · Springer eBooks · doi:10.1007/978-3-319-12125-3_33-2 · Cited by 4 · see citing works
Energy balance, energy turnover, and risk of body fat gain
Thomas, D. M., & Westerterp, K. R. (2017) · American Journal of Clinical Nutrition · doi:10.3945/ajcn.116.141887 · Cited by 4 · see citing works
“is algebraically related to FR through the validated Forbes model (4),”
MethodChatterjee, A., Bajpai, R. C., & Gerdes, M. W. (2021) · Research Square · doi:10.21203/rs.3.rs-584141/v1 · Cited by 4 · see citing works
“Forbes [40] used crosssectional body composition data to explain the non-linear observational relationship between FFM and FM and concluded that the longitudinal change of body composition might be defined by the displacement along the cross-sectional curve theoretically.”
BackgroundMethodInfluentialBeyond Sarcopenia: A Systematic Review and Meta‐Analysis on Muscle Outcomes After Bariatric Surgery
Eksteen, G., Dubois, L., der Schueren, B. V., Vanuytsel, T., & Matthys, C. (2026) · Obesity Reviews · doi:10.1111/obr.70142 · Cited by 3 · see citing works
Glucagon‐Like Peptide‐1 Receptor Agonist‐Based Agents and Body Composition: Filling More Gaps
Dubin, R. L., Sanders, T. N., Schwab, H. M., Heymsfield, S. B., & Greenway, F. L. (2026) · Obesity · doi:10.1002/oby.70212 · Cited by 3 · see citing works
Chatterjee, A., Pahari, N., Gerdes, M. W., & Bajpai, R. C. (2022) · IEEE International Conference on e-Health Networking, Applications and Services (Healthcom) · doi:10.1109/healthcom54947.2022.9982785 · Cited by 3 · see citing works
“Forbes [17] used cross-sectional body composition data to explain the non-linear observational relationship between fat-mass (FM) and FFM.”
BackgroundMethodInfluentialModelling body weight, dieting and obesity traps
Barbieri, P. N. (2016) · Physica A Statistical Mechanics and its Applications · doi:10.1016/j.physa.2016.10.046 · Cited by 3 · see citing works
Ackland, T. R., & Stewart, A. D. (2013) · doi:10.1002/9781118692318.ch6 · Cited by 3 · see citing works
- Authors
- Hall, K. D.
- Affiliations
- National Institutes of Health (US)
- Corresponding author
- Hall, Kevin D.
- ORCID
- Hall, Kevin D.
- Venue
- British Journal of Nutrition
- Publisher
- Cambridge University Press (CUP)
- Published
- 2007-06
- Volume
- 97
- Issue
- 6
- Pages
- 1059-1063
- ISSN
- 0007-1145 (ISSN-L)
- 1475-2662
- PMC
- PMC2376748
- OpenAlex
- W2127115822
- Cited by
- 129
- References
- 23
- Citations by year
- 2026: 11 · 2025: 12 · 2024: 7 · 2023: 7 · 2022: 6 · 2021: 3 · 2020: 7 · 2019: 6 · 2018: 3 · 2017: 4 · 2016: 7 · 2015: 6 · 2014: 13 · 2013: 6 · 2012: 5
- FWCI
- 3.12
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- British Journal Of Nutrition (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institutes of Health
- National Institute of Diabetes and Digestive and Kidney Diseases (Z01DK013036)
- Topics
- Health Sciences › Medicine › Physiology › Body Composition Measurement Techniques
- Life Sciences › Neuroscience › Endocrine and Autonomic Systems › Regulation of Appetite and Obesity
- Health Sciences › Medicine › Physiology › Nutrition and Health in Aging
- Keywords
- fat mass, fat-free mass, body composition changes, weight change, energy allocation, underfeeding, overfeeding, bariatric surgery, weight loss
- MeSH terms
- Adipose Tissue, Body Composition, Female, Humans, Models, Biological, Weight Gain, Weight Loss
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