Works Cited

BMRTDEE

Mifflin-St Jeor Equation (Basal Metabolic Rate)

Used to estimate resting daily energy expenditure based on weight, height, age, and sex.

Men: BMR = (10 × weight_kg) + (6.25 × height_cm) − (5 × age) + 5 Women: BMR = (10 × weight_kg) + (6.25 × height_cm) − (5 × age) − 161

Source: Mifflin MD, St Jeor ST, Hill LA, Scott BJ, Daugherty SA, Koh YO. "A new predictive equation for resting energy expenditure in healthy individuals." American Journal of Clinical Nutrition, 1990;51(2):241-247. Widely considered more accurate than the older Harris-Benedict equation and is the formula recommended by the Academy of Nutrition and Dietetics.

Total Daily Energy Expenditure (TDEE)

BMR is multiplied by an activity factor to estimate total daily calories burned including movement and exercise.

TDEE = BMR × Activity Multiplier Sedentary (little/no exercise): × 1.2 Lightly active (1–3 days/week): × 1.375 Moderately active (3–5 days/week): × 1.55 Very active (6–7 days/week): × 1.725 Extra active (athlete/physical job): × 1.9

Source: Activity multipliers are a standard adaptation of the original Harris-Benedict activity factor scale, used widely in clinical and fitness nutrition contexts (e.g. NIH Body Weight Planner methodology, American Council on Exercise guidelines).

Goal-Adjusted Calorie Target

Lose weight: Calorie Goal = TDEE − 500 kcal/day Maintain weight: Calorie Goal = TDEE Gain weight: Calorie Goal = TDEE + 300 kcal/day

A 500 kcal/day deficit is the standard clinical recommendation for a sustainable ~1 lb (0.45 kg) per week rate of weight loss, since 1 lb of body fat is approximately 3,500 kcal (500 × 7 days). A +300 kcal/day surplus reflects a conservative "lean bulk" approach to minimize fat gain while supporting muscle growth. Source: Centers for Disease Control and Prevention (CDC), "Losing Weight" guidance; Wishnofsky M. "Caloric equivalents of gained or lost weight." American Journal of Clinical Nutrition, 1958;6(5):542-546.

Clinical Mode — DEXA/BIA-Based Calculations

Katch-McArdleLean Body Mass

Katch-McArdle BMR (Lean Mass Method)

Used in Clinical Mode instead of Mifflin-St Jeor when DEXA scan or BIA body composition results are available, since it accounts for individual muscle mass rather than estimating it from height/weight/age alone.

BMR = 370 + (21.6 × Lean Body Mass in kg)

The Katch-McArdle equation uses lean body mass as its sole predictor of resting metabolic rate, rather than total body weight, height, age, and sex. Because muscle tissue is more metabolically active than fat tissue, two people of identical total weight but different body composition will have different energy needs — this formula captures that difference, whereas weight-based formulas cannot. It is considered more accurate than Mifflin-St Jeor for athletes, individuals with low body fat, or anyone with a known, measured body fat percentage from a DEXA scan or bioelectrical impedance analysis (BIA). Source: Katch FI, McArdle WD. Nutrition, Weight Control, and Exercise. 1973. Mathematically equivalent to the 1991 revised Cunningham equation.

Protein Target (Lean Mass Method)

Lose weight: Protein (g) = 1.2 × lean body mass (lbs) Maintain/Gain weight: Protein (g) = 1.0 × lean body mass (lbs)

Setting protein targets per pound of lean body mass (rather than total weight) is the approach used by sports nutritionists and dietitians once a person's actual lean mass is known, since fat tissue requires negligible protein to maintain. A range of roughly 0.8–1.2g/lb of lean mass is considered adequate for active individuals, with the higher end (1.2–1.4g/lb LBM) recommended during a calorie deficit to protect muscle from breakdown. This dashboard uses 1.2g/lb LBM when losing weight and 1.0g/lb LBM when maintaining or gaining. Source: Transparent Labs, "How Much Protein Should You Eat Each Day?"; International Society of Sports Nutrition Position Stand on protein and exercise.

Carbohydrate and fat targets in Clinical Mode use the same formulas as Standard Mode (see Macronutrient Targets below), based on total body weight and the calorie goal.

Macronutrient Targets

Protein

Protein (g) = 1 × body weight (lbs)

A widely cited general guideline for active individuals is approximately 0.7–1.0g of protein per pound of body weight to support muscle retention during a calorie deficit or muscle growth during a surplus. Source: Jäger R, et al. "International Society of Sports Nutrition Position Stand: protein and exercise." Journal of the International Society of Sports Nutrition, 2017;14:20.

Carbohydrates

Carbs (g) = (Calorie Goal × 0.50) ÷ 4

Carbohydrates provide 4 kcal per gram. Allocating roughly 45–65% of total calories to carbohydrates falls within the Acceptable Macronutrient Distribution Range (AMDR) set by the U.S. Dietary Guidelines; this dashboard uses the midpoint of 50%. Source: U.S. Department of Agriculture & U.S. Department of Health and Human Services, Dietary Guidelines for Americans, 2020–2025.

Fat

Lose weight: Fat (g) = 0.8 × body weight (lbs) Gain weight: Fat (g) = 1.5 × body weight (lbs)

Fat intake recommendations vary by goal; higher fat intake during a surplus supports hormone production and caloric density, while a moderate fat intake during a deficit preserves essential fatty acid needs while prioritizing protein and training performance. General guidance derived from sports nutrition literature on body-weight-based macro planning (e.g. International Society of Sports Nutrition position stands; precision nutrition coaching standards).

Sugar & Salt Limits

Added Sugar

Added Sugar Limit

Men: ≤ 36g added sugar/day (≈150 kcal, 9 tsp) Women: ≤ 25g added sugar/day (≈100 kcal, 6 tsp)

This dashboard uses the American Heart Association's (AHA) stricter, gender-specific "ideal" limits rather than the more permissive U.S. Dietary Guidelines threshold (which allows up to 50g/day, or 10% of calories, for a 2,000 kcal diet). The AHA recommends no more than 100 calories (about 6 teaspoons, 25g) of added sugar per day for most women, and no more than 150 calories (about 9 teaspoons, 36g) per day for most men, based on a recommended upper limit of roughly 5–6% of total daily calories from added sugar. Source: American Heart Association, "Added Sugars" and "How Much Sugar Is Too Much?"; Johnson RK, et al. "Dietary Sugars Intake and Cardiovascular Health: A Scientific Statement From the American Heart Association." Circulation, 2009;120(11):1011-1020.

Sodium

Sodium Limit

Sodium ≤ 1,500 mg/day (ideal, all adults)

The U.S. Dietary Guidelines for Americans set a general upper limit of 2,300 mg/day of sodium (about 1 teaspoon of table salt) for the average adult. However, this dashboard uses the American Heart Association's stricter "ideal" target of no more than 1,500 mg/day, which the AHA recommends for optimal cardiovascular and blood pressure health for most adults, not only those with hypertension. Source: American Heart Association, "How Much Sodium Should I Eat Per Day?"; U.S. Food & Drug Administration, "Sodium in Your Diet"; Centers for Disease Control and Prevention, "About Sodium and Health."

Exercise Calorie Burn Estimator

MET-style estimation

Base Burn Formula

Base Calories = 9.8 × weight (kg) × duration (hours)

This is a simplified energy expenditure formula consistent with Metabolic Equivalent of Task (MET)-based estimation methods, where calories burned scale linearly with body mass and duration of activity. The constant (9.8) was calibrated against the reference data point of a 150 lb individual burning approximately 333 kcal in 30 minutes of moderate activity.

Reference calibration points: 120 lbs (54.43 kg), 30 min → 9.8 × 54.43 × 0.5 ≈ 267 kcal 150 lbs (68.04 kg), 30 min → 9.8 × 68.04 × 0.5 ≈ 333 kcal 180 lbs (81.65 kg), 30 min → 9.8 × 81.65 × 0.5 ≈ 400 kcal

Exercise Intensity Multipliers

Each activity is assigned a low/high multiplier derived from typical calorie ranges burned by a 150 lb (68 kg) person in 30 minutes, then scaled proportionally to the user's body weight using the base formula above.

Running (10 min/mile pace): ~300 kcal / 30 min
HIIT: ~200–400 kcal / 30 min
General weight training: ~110–220 kcal / 30 min
Stationary biking: ~130–230 kcal / 30 min
Brisk walking (~3.5 mph): ~110–150 kcal / 30 min
Yoga: ~85–120 kcal / 30 min

Source: TODAY.com (NBC Universal), "How many calories do popular workouts actually burn?"; Byrdie, "How Many Calories Should You Burn in a Workout?"; Medical News Today, "How many calories do common exercises burn?"; The Training Room, "How Many Calories Does Your Workout Burn?". Additional sport and activity calorie ranges (basketball, swimming, cycling, martial arts, etc.) were estimated using standard MET value tables published by the Compendium of Physical Activities (Ainsworth BE, et al., 2011 update), applying the same body-weight scaling formula.

Body Fat — Height & Weight Method

BMI-based estimate

Body Mass Index

BMI = (weight_lbs ÷ height_inches²) × 703

Deurenberg Body Fat Formula

Body Fat % = (1.20 × BMI) + (0.23 × Age) − (10.8 × sex) − 5.4 (sex: male = 1, female = 0)

Source: Deurenberg P, Weststrate JA, Seidell JC. "Body mass index as a measure of body fatness: age- and sex-specific prediction formulas." British Journal of Nutrition, 1991;65(2):105-114. This is a population-level estimation formula and has a typical margin of error of ±3–5% body fat compared to gold-standard methods like DEXA scanning.

Body Fat Category Ranges

Men Women Essential Fat 2–5% 10–13% Athletes 6–13% 14–20% Fitness 14–17% 21–24% Average 18–24% 25–31% Obese 25%+ 32%+

Source: American Council on Exercise (ACE) Body Fat Percentage Categorization.

Body Fat — 3-Site Skinfold Test

Jackson-Pollock

Body Density Formula (Jackson-Pollock, 3-Site)

Sum of skinfolds (S) = Chest + Abdominal + Thigh (mm) Men: Density = 1.10938 − (0.0008267 × S) + (0.0000016 × S²) − (0.0002574 × Age) Women: Density = 1.09949 − (0.0009929 × S) + (0.0000023 × S²) − (0.0001392 × Age)

Siri Equation (Density → Body Fat %)

Body Fat % = ((4.95 ÷ Density) − 4.50) × 100

Sources: Jackson AS, Pollock ML. "Generalized equations for predicting body density of men." British Journal of Nutrition, 1978;40(3):497-504. Jackson AS, Pollock ML, Ward A. "Generalized equations for predicting body density of women." Medicine & Science in Sports & Exercise, 1980;12(3):175-181. Siri WE. "Body composition from fluid spaces and density: analysis of methods." 1961, reprinted in Nutrition, 1993;9(5):480-491.

Age-Based Norms (Excellent / Good / Average / Poor)

Norm tables adapted from American College of Sports Medicine (ACSM) and YMCA fitness testing body composition percentile standards, commonly used alongside Jackson-Pollock skinfold testing in clinical and athletic settings.

AI Body Fat Estimator — Math Equations & Algorithms

AI Page OnlyKatch-McArdle

Step 1 — Derive Lean Body Mass from AI-Estimated Body Fat %

The AI page uses Claude Vision to visually estimate body fat percentage from a photo. That percentage is then used to compute lean body mass:

Lean Body Mass (lbs) = Total Weight (lbs) × (1 − Body Fat % ÷ 100) Example: 183 lbs at 22% body fat LBM = 183 × (1 − 0.22) = 183 × 0.78 = 142.7 lbs lean mass

Step 2 — Basal Metabolic Rate (Katch-McArdle Formula)

Because lean body mass is known (from the AI estimate), the AI page uses the Katch-McArdle equation rather than Mifflin-St Jeor, as it accounts directly for individual muscle mass rather than estimating it from height, weight, and age alone:

BMR (kcal/day) = 370 + (21.6 × Lean Body Mass in kg) Convert LBM to kg: LBM_kg = LBM_lbs × 0.453592 Example: 142.7 lbs LBM → 64.7 kg BMR = 370 + (21.6 × 64.7) = 370 + 1,397.5 = 1,767.5 kcal/day

Source: Katch FI, McArdle WD. Nutrition, Weight Control, and Exercise. 1975. Mathematically equivalent to the Cunningham equation (1991). Preferred over Mifflin-St Jeor when body composition is known, as it removes the variability introduced by estimating lean mass from demographic proxies alone.

Step 3 — Total Daily Energy Expenditure (TDEE)

TDEE (kcal/day) = BMR × Activity Multiplier Sedentary (little/no exercise): × 1.2 Lightly active (1–3 days/week): × 1.375 Moderately active (3–5 days/week): × 1.55 Very active (6–7 days/week): × 1.725 Extra active (athlete/physical job): × 1.9

Step 4 — Goal-Adjusted Calorie Target

Lose body fat: Calorie Goal = TDEE − 500 kcal/day (~1 lb/week deficit) Maintain: Calorie Goal = TDEE Gain/bulk: Calorie Goal = TDEE + 300 kcal/day (lean bulk surplus)

A 500 kcal/day deficit corresponds to approximately 1 lb (0.45 kg) of fat loss per week, based on the 3,500 kcal ≈ 1 lb equivalency. Source: Wishnofsky M. "Caloric equivalents of gained or lost weight." American Journal of Clinical Nutrition, 1958.

Step 5 — Protein Target (Lean Mass Method)

Losing body fat: Protein (g) = 1.2 × Lean Body Mass (lbs) Maintaining/Gaining: Protein (g) = 1.0 × Lean Body Mass (lbs) Example (LBM = 142.7 lbs, goal = lose): Protein = 1.2 × 142.7 = 171.2g ≈ 171g/day

Protein is set per pound of lean body mass rather than total weight because fat tissue requires negligible protein to maintain. The higher multiplier during a deficit (1.2g/lb LBM) helps preserve muscle while losing fat. Source: Jäger R, et al. "International Society of Sports Nutrition Position Stand: protein and exercise." Journal of the International Society of Sports Nutrition, 2017;14:20. Transparent Labs: recommended range 0.8–1.4g/lb LBM for active individuals.

Step 6 — Carbohydrate Target

Carbs (g) = (Calorie Goal × 0.50) ÷ 4 Carbohydrates provide 4 kcal per gram. Allocating 50% of total calories to carbs sits at the midpoint of the USDA Acceptable Macronutrient Distribution Range (AMDR) of 45–65%. Example (calorie goal = 1,767 kcal): Carbs = (1,767 × 0.50) ÷ 4 = 883.5 ÷ 4 = 220.9g ≈ 221g/day

Step 7 — Fat Target

Losing body fat: Fat (g) = 0.8 × Total Body Weight (lbs) Gaining/bulking: Fat (g) = 1.5 × Total Body Weight (lbs) Example (183 lbs, goal = lose): Fat = 0.8 × 183 = 146.4g ≈ 146g/day

Step 8 — Added Sugar & Sodium Limits

Added Sugar limit — AHA ideal: Men: ≤ 36g/day (≈ 150 kcal, 9 tsp) Women: ≤ 25g/day (≈ 100 kcal, 6 tsp) Sodium limit — AHA ideal: All adults: ≤ 1,500 mg/day

Source: American Heart Association, "Added Sugars" and "How Much Sodium Should I Eat Per Day?". The AHA's stricter ideal targets are used rather than the FDA/DGA general limits (50g sugar, 2,300mg sodium) for better cardiovascular health outcomes.

Step 9 — Exercise Calorie Burn Formula

Calories Burned = 9.8 × Weight (kg) × Duration (hours) × Intensity Multiplier Convert weight: Weight_kg = Weight_lbs ÷ 2.205 Calibration reference (150 lb person, 30 minutes): 9.8 × 68.04 kg × 0.5 hrs = 333.4 kcal (base) Each exercise has a low/high multiplier derived from its known calorie range at the 150 lb / 30 min baseline, then scaled proportionally to the user's actual body weight. Example: Running, 30 min, 183 lbs Base = 9.8 × (183÷2.205) × 0.5 = 9.8 × 83.0 × 0.5 = 406.7 kcal

Formula consistent with MET (Metabolic Equivalent of Task) methodology. Base constant (9.8) calibrated against published 30-min calorie ranges for a 150 lb person. Calorie range data sourced from: TODAY.com; Byrdie; Medical News Today; The Training Room; Compendium of Physical Activities (Ainsworth BE, et al., 2011 update).

Step 10 — Predicted Weekly Weight Change

Net Weekly Surplus/Deficit = Σ (Daily Calories Consumed) − (Calorie Goal × Days Logged) Predicted Weight Change (lbs) = Net Weekly Surplus/Deficit ÷ 3,500 Example: 5 days logged, avg 1,500 kcal/day, goal 1,767 kcal/day Net = (5 × 1,500) − (5 × 1,767) = 7,500 − 8,835 = −1,335 kcal Predicted loss = 1,335 ÷ 3,500 = −0.38 lbs this week

Based on the Wishnofsky 3,500 kcal ≈ 1 lb rule. This is a projection, not a guarantee — actual weight change also depends on water retention, muscle gain, and metabolic adaptation.

Calorie Goal Calculation