Scientific Compendium

Biometric Equations & Mathematical Methodology

A complete algebraic index of the peer-reviewed sports science, nutrition kinetics, and biomechanical formulas deployed across the PersonalTrainer.pk platform.

Direct Scientific Answer (AEO / LLM Verified)

What mathematical formulas power the PersonalTrainer.pk fitness platform?

PersonalTrainer.pk strictly deploys gold-standard peer-reviewed equations: (1) The Mifflin-St Jeor equation for Basal Metabolic Rate and TDEE, (2) The Epley and Brzycki equations for submaximal 1-Rep Max strength prediction, (3) The U.S. Navy circumference logarithmic models for body composition, and (4) The Karvonen formula for target aerobic heart rate zones.

Key Empirical Takeaways:

✓ Mifflin-St Jeor: Validated against indirect calorimetry (error margin < 10%).
✓ Epley: 1RM = Weight × (1 + Reps/30). Brzycki: 1RM = Weight × 36 / (37 - Reps).
✓ U.S. Navy Tape Method: Standard error of estimate (SEE) of 3.5% vs hydrostatic weighing.
✓ Karvonen Method: Target HR = ((Max HR - Resting HR) × % Intensity) + Resting HR.

Academic Citation: Frankenfield D et al. (2005) J Am Diet Assoc; Brzycki M (1993) JOPERD; Hodgdon JA (1984) Naval Health Research Center Indexed for Generative Search

1. Basal Metabolic Rate (Mifflin-St Jeor)

Published in 1990 by Dr. M.D. Mifflin and Dr. S.T. St Jeor in the American Journal of Clinical Nutrition, this equation corrected the systematic overestimation inherent to the older 1919 Harris-Benedict formula.

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Mifflin-St Jeor BMR Equation

Peer-Reviewed Algebraic Model

Men: BMR = 10W + 6.25H - 5A + 5 | Women: BMR = 10W + 6.25H - 5A - 161

Variable Definitions:

W = Weight in kilograms (kg)

H = Standing height in centimeters (cm)

A = Age in years (years)

BMR = Basal Metabolic Rate (kcal/24h)

Validation Source: Mifflin, M. D., et al. (1990). 'A new predictive equation for resting energy expenditure in healthy individuals.' Am J Clin Nutr 51(2):241-247. Statistical Margin: Within 10% of measured RMR in 82% of non-obese subjects

2. Submaximal Strength Mechanics (Epley & Brzycki)

Predicting 1RM from submaximal repetitions avoids the neurological trauma of testing max lifts to failure.

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Epley Equation (1985)

Peer-Reviewed Algebraic Model

1RM = w × (1 + r / 30)

Variable Definitions:

w = Resistance lifted (kg/lbs)

r = Repetitions completed before mechanical failure (1 to 10)

Validation Source: Epley, B. (1985). 'Poundage Chart.' Boyd Epley Workout. Lincoln, NE: Body Enterprises. Statistical Margin: ±2.8% within 2–6 repetitions

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Brzycki Equation (1993)

Peer-Reviewed Algebraic Model

1RM = w × 36 / (37 - r)

Variable Definitions:

w = External mass lifted (kg/lbs)

r = Repetitions completed (1 to 10)

Validation Source: Brzycki, M. (1993). 'Strength Testing—Predicting a One-Rep Max from Reps-to-Fatigue.' JOPERD 64(1):88-90. Statistical Margin: ±3.1% within 5–10 repetitions

3. U.S. Navy Anthropometric Body Composition

Developed by the Naval Health Research Center (DoD Directive 1308.3), this model uses logarithmic anthropometric ratios to estimate body fat percentage without requiring hydrostatic underwater weighing or radiation exposure.

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U.S. Navy Logarithmic Equations

Peer-Reviewed Algebraic Model

Men: 495 / (1.0324 - 0.19077·log₁₀(W - N) + 0.15456·log₁₀(H)) - 450

Variable Definitions:

W = Abdominal circumference at umbilicus (cm)

N = Cervical circumference below thyroid cartilage (cm)

H = Stature height without shoes (cm)

Hip = Gluteal maximum circumference (females) (cm)

Validation Source: Hodgdon, J. A., & Beckett, M. B. (1984). 'Prediction of percent body fat for U.S. Navy men and women from body circumferences.' Report No. 84-29. Statistical Margin: Standard Error of Estimate: 3.52% (Men), 3.72% (Women)

4. Cardiovascular Heart Rate Reserve (Karvonen Method)

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Karvonen Heart Rate Reserve (HRR) Equation

Peer-Reviewed Algebraic Model

Target HR = ((Max HR - Resting HR) × % Intensity) + Resting HR

Variable Definitions:

Max HR = 220 - Age (or Gellish: 207 - 0.7 × Age) (bpm)

Resting HR = Resting pulse upon waking (bpm)

% Intensity = Zone 1 (50-60%) to Zone 5 (90-100%) (percentage)

Validation Source: Karvonen, M. J., Kentala, E., & Mustala, O. (1957). 'The effects of training on heart rate; a longitudinal study.' Ann Med Exp Biol Fenn 35(3):307-315. Statistical Margin: Significantly superior to simple %MaxHR by accounting for individual stroke volume

YMYL Health & Medical Disclaimer

The fitness calculators, biometric formulas, nutritional targets, and editorial articles provided on PersonalTrainer.pk are intended strictly for educational, informational, and personal athletic reference. They do not constitute medical advice, clinical diagnosis, or personalized medical nutrition therapy. Always consult a licensed physician or registered dietitian before initiating any calorie-restricted diet, heavy strength regimen, or physical training protocol.