Scientific Methodology & Sources
Detailed mathematical formulas, scientific references, and technical limitations used across HealthToRun calculators.
🔬 Our Commitment to Scientific Transparency
At HealthToRun, we firmly believe that health and athletic tools are truly valuable only when users fully understand how results are produced. All our calculators implement mathematical models and protocols validated by international scientific literature. Please remember: our tools provide theoretical estimates based on population averages and do not replace personalized clinical evaluations.
1. Body Mass Index (BMI)
BMI = Weight (kg) / [Height (m)]²
Variáveis de Entrada:
Weight in kilograms (kg) and height in meters (m).
Interpretação e Faixas:
We adopt official World Health Organization (WHO) cutoffs for adults aged 20+: Underweight (< 18.5), Normal weight (18.5 to 24.9), Overweight (25.0 to 29.9), Obesity Class I (30.0 to 34.9), Obesity Class II (35.0 to 39.9), and Obesity Class III (≥ 40.0).
⚠️ Limitações Técnicas e Considerações Clínicas:
BMI is a simplified population screening tool. It does not differentiate lean muscle mass from adipose tissue, nor does it identify anatomical fat distribution (visceral vs subcutaneous). Muscular athletes frequently present elevated BMI classifications despite very low body fat.
Fontes e Referências:
- • World Health Organization (WHO). Physical status: the use and interpretation of anthropometry. Geneva: WHO, 1995.
- • National Institutes of Health (NIH). Clinical Guidelines on the Identification, Evaluation, and Treatment of Overweight and Obesity in Adults, 1998.
2. Basal Metabolic Rate (BMR) & Total Energy Expenditure (TDEE)
Mifflin-St Jeor Equation: • Men: BMR = (10 × weight in kg) + (6.25 × height in cm) - (5 × age in years) + 5 • Women: BMR = (10 × weight in kg) + (6.25 × height in cm) - (5 × age in years) - 161
Variáveis de Entrada:
Weight (kg), height (cm), chronological age (years), biological sex, and physical activity level (PAL factor 1.2 to 1.9).
Interpretação e Faixas:
BMR represents the baseline energy expenditure required to sustain vital physiological functions at complete rest. Multiplying BMR by the Physical Activity Level (PAL) provides the Total Daily Energy Expenditure (TDEE).
⚠️ Limitações Técnicas e Considerações Clínicas:
This is a statistical mathematical estimate. Individuals with higher muscle mass burn more calories at rest than predicted by total-weight equations. Endocrine factors, dieting history, and ambient temperature also influence actual metabolic rates.
Fontes e Referências:
- • Mifflin MD, St Jeor ST, Hill LA, Scott BJ, Daugherty SA, Koh YO. A new predictive equation for resting energy expenditure in healthy individuals. Am J Clin Nutr. 1990;51(2):241-247.
- • Food and Agriculture Organization / World Health Organization. Human energy requirements. Rome: FAO/WHO/UNU, 2004.
3. Running Pace and Average Speed
• Pace (min/km) = Total Time (decimal minutes) / Distance (km) • Average Speed (km/h) = 60 / Pace in decimal minutes
Variáveis de Entrada:
Distance covered in kilometers or meters and elapsed time in hours, minutes, and seconds.
Interpretação e Faixas:
Pace expresses the exact time needed to run one kilometer. It is the gold standard metric in road running because it enables precise split time management during training and races.
⚠️ Limitações Técnicas e Considerações Clínicas:
Calculations assume flat, neutral running conditions. In real outdoor environments, pace is affected by course elevation changes, ambient heat, relative humidity, and headwind.
Fontes e Referências:
- • Daniels J. Daniels' Running Formula. 4th ed. Human Kinetics, 2021.
- • American College of Sports Medicine (ACSM). ACSM's Guidelines for Exercise Testing and Prescription. 11th ed. Wolters Kluwer, 2021.
4. Body Fat Percentage Estimation (US Navy Method)
• Men: % Body Fat = 495 / [1.0324 - 0.19077 × log10(waist - neck) + 0.15456 × log10(height)] - 450 • Women: % Body Fat = 495 / [1.29579 - 0.35004 × log10(waist + hip - neck) + 0.22100 × log10(height)] - 450
Variáveis de Entrada:
Body circumference measurements in centimeters (neck, abdominal waist, and female hips) and height in centimeters.
Interpretação e Faixas:
Results are categorized according to American Council on Exercise (ACE) standards: Essential Fat (2-5% M / 10-13% F), Athletes (6-13% M / 14-20% F), Fitness (14-17% M / 21-24% F), Average (18-24% M / 25-31% F), and Obesity (≥25% M / ≥32% F).
⚠️ Limitações Técnicas e Considerações Clínicas:
The US Navy formula is an indirect anthropometric estimation. While highly practical (standard error of ~3% to 4%), variations in measuring tape tension or atypical body fat storage patterns can produce slight discrepancies compared to gold standard laboratory scans (DEXA or hydrostatic weighing).
Fontes e Referências:
- • Hodgdon JA, Beckett MB. Prediction of percent body fat for U.S. Navy men and women from body circumferences. Report No. 84-29 / 84-11. Naval Health Research Center, 1984.
- • American Council on Exercise (ACE). Body Fat Percentage Standards. ACE Fitness, 2020.
5. Cooper 12-Minute Run Test & VO₂ Max
Estimated VO₂ Max (ml/kg/min) = (Distance covered in 12 minutes in meters - 504.9) / 44.73
Variáveis de Entrada:
Maximum continuous distance completed in exactly 12 minutes on a flat surface.
Interpretação e Faixas:
Maximal oxygen uptake (VO₂ Max) measures the integrated capacity of the cardiovascular, respiratory, and muscular systems to transport and utilize oxygen during maximal exertion.
⚠️ Limitações Técnicas e Considerações Clínicas:
As a self-paced field benchmark, results depend heavily on pacing strategy. Inexperienced runners who start at sprint speeds build rapid acidosis, reducing overall distance. This test provides an estimate and does not replace cardiopulmonary exercise testing with metabolic cart analysis.
Fontes e Referências:
- • Cooper KH. A means of assessing maximal oxygen intake: Correlation between field and treadmill testing. JAMA. 1968;203(3):201-204.
- • The Cooper Institute. Physical Fitness Specialist Manual. Dallas: The Cooper Institute, 2017.
6. 1km and 3km Benchmarks & Race Predictions (Riegel Formula)
Riegel Formula: T2 = T1 × (D2 / D1)^1.06 Where T1 is reference time, D1 is reference distance, D2 is target race distance, and T2 is predicted time.
Variáveis de Entrada:
Accurate times completed in 1,000m and 3,000m track or flat road time trials.
Interpretação e Faixas:
The 1km time trial measures anaerobic lactic power and top-end speed, while the 3km trial assesses maximal aerobic power and VO₂ Max sustainability. Riegel's formula projects equivalent performance times for 5k, 10k, half marathon, and marathon.
⚠️ Limitações Técnicas e Considerações Clínicas:
Peter Riegel's formula assumes that the athlete has developed the aerobic endurance and weekly mileage necessary for the target distance. Predicting a marathon time (42.2 km) based on a 3km trial without proper long run volume will produce overly optimistic race predictions.
Fontes e Referências:
- • Riegel PS. Athletic records and human endurance. Am Sci. 1981;69(3):285-290.
- • Billat LV, Koralsztein JP. Significance of the velocity at VO2max and time to exhaustion at this velocity. Sports Med. 1996;22(2):90-108.