Methodology & Formulas
Every FitFuel Tools calculator uses peer-reviewed formulas and validated scientific sources. This page documents the exact 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.
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