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100 lines
3.2 KiB
Markdown
100 lines
3.2 KiB
Markdown
# Formulas Reference
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Scientific references for all calculators used in the fitness-nutrition skill.
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## BMI (Body Mass Index)
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**Formula:** BMI = weight (kg) / height (m)²
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| Category | BMI Range |
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|-------------|------------|
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| Underweight | < 18.5 |
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| Normal | 18.5 – 24.9 |
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| Overweight | 25.0 – 29.9 |
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| Obese | 30.0+ |
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**Limitation:** BMI does not distinguish muscle from fat. A muscular person
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can have a high BMI while being lean. Use body fat % for a better picture.
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Reference: Quetelet, A. (1832). Keys et al., Int J Obes (1972).
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## TDEE (Total Daily Energy Expenditure)
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Uses the **Mifflin-St Jeor equation** — the most accurate BMR predictor for
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the general population according to the ADA (2005).
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**BMR formulas:**
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- Male: BMR = 10 × weight(kg) + 6.25 × height(cm) − 5 × age + 5
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- Female: BMR = 10 × weight(kg) + 6.25 × height(cm) − 5 × age − 161
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**Activity multipliers:**
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| Level | Description | Multiplier |
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|-------|--------------------------------|------------|
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| 1 | Sedentary (desk job) | 1.200 |
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| 2 | Lightly active (1-3 days/wk) | 1.375 |
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| 3 | Moderately active (3-5 days) | 1.550 |
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| 4 | Very active (6-7 days) | 1.725 |
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| 5 | Extremely active (2x/day) | 1.900 |
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Reference: Mifflin et al., Am J Clin Nutr 51, 241-247 (1990).
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## One-Rep Max (1RM)
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Three validated formulas. Average of all three is most reliable.
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- **Epley:** 1RM = w × (1 + r/30)
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- **Brzycki:** 1RM = w × 36 / (37 − r)
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- **Lombardi:** 1RM = w × r^0.1
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All formulas are most accurate for r ≤ 10. Above 10 reps, error increases.
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Reference: LeSuer et al., J Strength Cond Res 11(4), 211-213 (1997).
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## Macro Splits
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Recommended splits based on goal:
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| Goal | Protein | Fat | Carbs | Calorie Offset |
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|-------------|---------|------|-------|----------------|
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| Fat loss | 40% | 30% | 30% | −500 kcal |
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| Maintenance | 30% | 30% | 40% | 0 |
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| Lean bulk | 30% | 25% | 45% | +400 kcal |
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Protein targets for muscle growth: 1.6–2.2 g/kg body weight per day.
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Minimum fat intake: 0.5 g/kg to support hormone production.
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Conversion: Protein = 4 kcal/g, Fat = 9 kcal/g, Carbs = 4 kcal/g.
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Reference: Morton et al., Br J Sports Med 52, 376–384 (2018).
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## Body Fat % (US Navy Method)
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**Male:**
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BF% = 86.010 × log₁₀(waist − neck) − 70.041 × log₁₀(height) + 36.76
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**Female:**
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BF% = 163.205 × log₁₀(waist + hip − neck) − 97.684 × log₁₀(height) − 78.387
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All measurements in centimeters.
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| Category | Male | Female |
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|--------------|--------|--------|
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| Essential | 2-5% | 10-13% |
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| Athletic | 6-13% | 14-20% |
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| Fitness | 14-17% | 21-24% |
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| Average | 18-24% | 25-31% |
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| Obese | 25%+ | 32%+ |
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Accuracy: ±3-5% compared to DEXA. Measure at the navel (waist),
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at the Adam's apple (neck), and widest point (hip, females only).
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Reference: Hodgdon & Beckett, Naval Health Research Center (1984).
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## APIs
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- wger: https://wger.de/api/v2/ — AGPL-3.0, exercise data is CC-BY-SA 3.0
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- USDA FoodData Central: https://api.nal.usda.gov/fdc/v1/ — public domain (CC0 1.0) |