Methodology & Formulas
FitFuel Tools implements published formulas and public-health guidance. This page documents the equations, their origins, known limitations, and margin of error for each tool category.
Energy Expenditure (BMR & TDEE)
Mifflin-St Jeor (1990) — Primary
Males: BMR = 10W + 6.25H − 5A + 5 Females: BMR = 10W + 6.25H − 5A − 161
W = weight (kg), H = height (cm), A = age (years). Validated in 2005 by Frankenfield et al. as the most accurate predictive equation for resting energy expenditure in non-obese adults (±10% in 82% of individuals).
Source: Mifflin MD et al. A new predictive equation for resting energy expenditure in healthy individuals. Am J Clin Nutr. 1990;51(2):241-7.
Harris-Benedict (Original 1919)
Males: BMR = 66.5 + 13.75W + 5.003H − 6.775A Females: BMR = 655.1 + 9.563W + 1.850H − 4.676A
Published by James Arthur Harris and Francis Gano Benedict. Historically significant; tends to overestimate BMR by 5% vs modern equations.
Source: Harris JA, Benedict FG. A Biometric Study of Human Basal Metabolism. PNAS. 1918;4(12):370-373.
Harris-Benedict Revised (Roza & Shizgal 1984)
Males: BMR = 88.362 + 13.397W + 4.799H − 5.677A Females: BMR = 447.593 + 9.247W + 3.098H − 4.330A
Revision of the original formula using a larger sample. More accurate than the 1919 formula but slightly less accurate than Mifflin-St Jeor.
Source: Roza AM, Shizgal HM. The Harris-Benedict equation reevaluated. Am J Clin Nutr. 1984;40(1):168-82.
Activity Multipliers (Harris/McArdle)
Sedentary: ×1.2 | Light: ×1.375 | Moderate: ×1.55 | Active: ×1.725 | Very Active: ×1.9
Derived from the original Harris-Benedict work and validated by McArdle, Katch & Katch (Exercise Physiology). Most representative when honest activity level is selected.
Source: McArdle WD, Katch FI, Katch VL. Exercise Physiology: Nutrition, Energy, and Human Performance. 8th ed. LWW; 2014.
Body Composition
US Navy Circumference Method
Males: %BF = 86.010×log10(abdomen−neck) − 70.041×log10(height) + 36.76 Females: %BF = 163.205×log10(waist+hip−neck) − 97.684×log10(height) − 78.387
Developed for the US Navy by Hodgdon and Beckett (1984). Validated against hydrostatic weighing. Margin of error: ±3–4% vs DEXA scan.
Source: Hodgdon JA, Beckett MB. Prediction of percent body fat for US Navy men from body circumferences and height. 1984. NHRC Report 84-11.
BMI (World Health Organisation)
BMI = weight(kg) / height(m)²
WHO classification: <18.5 Underweight, 18.5–24.9 Normal, 25–29.9 Overweight, ≥30 Obese. Limitations: does not differentiate fat from muscle mass. Ethnic-specific thresholds: Asian populations ≥23 overweight, ≥27.5 obese (WHO 2004).
Source: WHO Expert Consultation. Appropriate body-mass index for Asian populations. Lancet. 2004;363(9403):157-63.
Lean Body Mass (Boer 1984) — Primary
Males: LBM = 0.407W + 0.267H − 19.2 Females: LBM = 0.252W + 0.473H − 48.3
Most widely validated formula. W = weight (kg), H = height (cm). Compared alongside James (1976) and Hume (1966) formulas.
Source: Boer P. Estimated lean body mass as an index for normalization of body fluid volumes in humans. Am J Physiol. 1984;247(4):F632-6.
FFMI (Fat-Free Mass Index)
FFMI = FFM(kg) / height²(m) Normalised FFMI = FFMI + 6.1 × (1.80 − height_m)
Natural ceiling established by Kouri et al. (1995) at FFMI 25 in a study of 157 athletes tested for anabolic steroids. Above 25 is considered highly unlikely without performance-enhancing drugs.
Source: Kouri EM et al. Fat-Free Mass Index in Users and Nonusers of Anabolic-Androgenic Steroids. Clin J Sport Med. 1995;5(4):223-228.
Protein & Nutrition
Protein Requirements
Sedentary: 0.8g/kg (RDA) | Active maintenance: 1.2–1.6g/kg | Muscle gain: 1.6–2.2g/kg | Athlete/deficit: 2.2–2.4g/kg
The 0.8g/kg RDA reflects minimum to prevent deficiency, not optimal for active individuals. Meta-analyses confirm 1.62g/kg maximises muscle protein synthesis (Morton et al. 2018). Upper bound of 2.4g/kg supported by Phillips et al. for athletes in caloric restriction.
Source: Morton RW et al. A systematic review, meta-analysis and meta-regression of the effect of protein supplementation on gains in muscle mass and strength. Br J Sports Med. 2018;52(6):376-384.
Water Intake
Base: 35ml/kg bodyweight | +500ml per hour of moderate exercise | Adjusted for climate (+200-400ml hot/humid)
European Food Safety Authority reference values: 2.0L/day women, 2.5L/day men total fluid. US Institute of Medicine: 3.7L men, 2.7L women from all sources.
Source: EFSA Panel on Dietetic Products, Nutrition, and Allergies. Scientific Opinion on Dietary Reference Values for water. EFSA Journal. 2010;8(3):1459.
Dietary Fibre
14g fibre per 1,000 kcal of intake (minimum) Absolute minimum: 25g/day women, 38g/day men
Based on 2020-2025 US Dietary Guidelines for Americans. Adequate Intake values from National Academies of Sciences, Engineering, and Medicine.
Source: Dietary Guidelines for Americans, 2020-2025. US Department of Agriculture and US Department of Health and Human Services.
Heart Rate & Cardiovascular
Heart Rate Zones — Karvonen Method
Target HR = ((Max HR − Resting HR) × intensity%) + Resting HR Max HR = 208 − 0.7 × age (Tanaka formula)
Karvonen formula accounts for individual fitness level through resting heart rate. More accurate than simple % of max HR. Tanaka formula for max HR is more accurate than the classic '220 − age' for adults over 40.
Source: Tanaka H, Monahan KD, Seals DR. Age-predicted maximal heart rate revisited. J Am Coll Cardiol. 2001;37(1):153-6.
Zone 2 — Maffetone Method (Primary)
Zone 2 upper = 180 − age Adjustments: −10 if recovering from illness/injury, −5 if inconsistent training, +5 if >2 years consistent training, +10 if elite
Developed by Dr Phil Maffetone. Corresponds to the upper limit of fat oxidation and aerobic base development. Cross-validated against Karvonen Zone 2 (60–70% HRR). Zone 2 training improves mitochondrial density and fat oxidation (San Millan & Brooks, 2018).
Source: San Millan I, Brooks GA. Assessment of Metabolic Flexibility by Means of Measuring Blood Lactate, Fat, and Carbohydrate Oxidation During a Incremental Exercise Test. Front Physiol. 2018;9:141.
Longevity & Biological Age
Biological Age Estimation
Composite score from 10 lifestyle factors weighted by hazard ratios from longitudinal studies
Factors and weightings derived from: Levine et al. PhenoAge (2018), Harvard 75-year longitudinal study, Holt-Lunstad meta-analyses on social connection and mortality, and population health data from NHANES. Not a clinical diagnostic — estimates risk profile relative to chronological age.
Source: Levine ME et al. An epigenetic biomarker of aging for lifespan and healthspan. Aging (Albany NY). 2018;10(4):573-591.
Strength & Fitness Testing
One Rep Max — Multiple Formulas
Epley: 1RM = W × (1 + r/30) Brzycki: 1RM = W × 36/(37−r) Lander: 1RM = W × 100/(101.3−2.67123×r) Lombardi: 1RM = W × r^0.10 Mayhew: 1RM = W × 100/(52.2 + 41.9 × e^(−0.055r))
W = weight lifted, r = repetitions. All five formulas are averaged to reduce prediction error. Most accurate at 3–10 repetitions. Error increases above 10 reps.
Source: Epley B. Poundage chart. Boyd Epley workout. 1985. University of Nebraska-Lincoln.
Push-up Fitness Standards
Age/sex-stratified percentile norms
ACSM normative data from Health-Related Physical Fitness Assessment Manual. Categories: Below Average (<25th), Average (25–49th), Good (50–74th), Very Good (75–89th), Excellent (≥90th percentile).
Source: ACSM. ACSM's Health-Related Physical Fitness Assessment Manual. 5th ed. LWW; 2018.
Review status
This methodology is maintained by the FitFuel Tools Editorial Team. The team is not presented as a medical provider. The formulas are implemented from cited publications and public-health guidance, but the site has not yet completed an independent clinical review. See our editorial and corrections policy.
Medical Disclaimer
All calculators on FitFuel Tools are for informational and educational purposes only. Results are estimates based on population averages and validated predictive equations — they are not a substitute for individualised medical advice, clinical diagnosis, or treatment from a qualified healthcare professional. Margin of error varies by formula and individual factors including body composition, ethnicity, and health status. Always consult a doctor, registered dietitian, or certified fitness professional before making significant changes to your diet or exercise programme.
Use the calculators with these formulas applied