Formulas

Hybrid weekly plan: 2-3 strength + 3-4 endurance + 1-2 mobility. Schoenfeld/Roberts 2023 framework. AM cardio + PM strength, ≥6h separation, polarized intensity.

endurance

Computes the hypertrophy penalty from concurrent cardio plus strength training: cardio above 3 sessions per week cuts muscle gain roughly 10-15%.

Strength Training

Computes Coggan cycling power zones as percentages of FTP, from active recovery near 55% up to anaerobic above 120%, with FTP from a 20-minute test.

endurance

Detraining decay: strength −5-10% by week 4, −15-20% by week 8. VO2max −7%/week initially. Mujika 2010 meta-analysis.

Strength Training

Female athlete energy availability (RED-S): EA = (intake_kcal − exercise_kcal) / FFM_kg, where EA below 30 kcal/kg is clinically low per IOC 2018 consensus.

endurance

Flexibility score: Beighton hypermobility (0-9) + FMS Deep Squat (0-3). Beighton ≥5 suggests hypermobility; FMS ≤2 flags movement dysfunction.

mobility

Food-to-exercise: minutes_to_burn = food_kcal / (MET × mass_kg × 0.0175). MET values from Ainsworth Compendium 2011. Walk 3.5, run 9.8, cycle moderate 7.5.

Fat Loss

HRV deload trigger: morning rMSSD below rolling 7-day baseline by 1.5+ SD for 3 days = deload signal. Plews & Laursen 2017. Use weekly average not daily.

Recovery

Hybrid macro split: protein 2.0-2.2 g/kg, carbs 6-8 g/kg endurance day / 4-5 g/kg lift day, fat 0.8-1.0 g/kg. Roberts 2023. Fuels both strength and endurance demand.

Fat Loss

Intermittent fasting window planner: 16:8 base, ±2h around training. Stockman 2018 meta — fat loss equivalent to caloric restriction, no metabolic advantage.

Fat Loss

Junk volume: sets above MAV produce diminishing returns. Schoenfeld 2017 meta-analysis: ≥10 sets/muscle/week, plateau by ~20 sets. Above MRV is regression.

Strength Training

Katch-McArdle BMR = 370 + 21.6·LBM_kg. Uses lean body mass instead of total mass — more accurate when reliable body-fat data is available.

Fat Loss

Macro cycling: high-carb training days (≥6 g/kg), lower-carb rest days (3-4 g/kg). Burke & Hawley 2018. Protein constant. Fits weekly periodization.

Fat Loss

Marathon elevation pace correction: about 1.5 sec of finish time per metre climbed, 0.75 sec per metre descended (2:1 asymmetric). Daniels rule of thumb, Minetti 2002 consistent.

endurance

Marathon hydration: sweat rate 0.5-2.5 L/h, sodium concentration 460-1840 mg/L. Casa 2007 + ACSM 2007 standards. Replace 70-90% of losses; avoid hyponatremia.

Hydration

Max muscular potential formula: natural FFMI ceiling near 25 for men and 21 for women (Kouri 1995), with monthly muscle gain rates by training age.

Body Composition

Plate-loading math: greedy descending allocation of plates per side. Olympic 20kg bar (45lb US), standard plate set: 25/20/15/10/5/2.5/1.25 kg per side.

Strength Training

Powerlifting attempts: opener 92-93% 1RM, 2nd attempt 97-99%, 3rd attempt 100-103%. Calgary Barbell methodology. Open low to bank a total; close strong for total.

Strength Training

Race-week taper math: cut training volume 41-60% over 8-14 days while holding intensity, then carb-load 7-12 g/kg (Burke 2011) for a ~3% faster race.

endurance

Resting heart rate: morning supine 5-min average. Adult normal 60-100 bpm; trained 40-60. AHA 2019. +5 bpm sustained signals overreaching (Lehmann 1998).

Recovery

Riegel race time prediction: T2 = T1 × (D2/D1)^1.06. Race-time prediction across distances. Valid 5K–marathon, breaks down beyond 30K.

endurance

RPE to % 1RM (Tuchscherer table). RPE 10 = 100% 1RM. Each RPE point ≈ 2-3% drop. Powerlifting autoregulation standard.

Strength Training

Run training paces from a recent race time: get your easy, marathon, threshold, interval, and repetition paces using Daniels' VDOT model.

endurance

90-min sleep cycle planning: bedtime = wake_time − (cycles × 90 min) − 15 min sleep latency. 4-6 cycles per night. Waking at cycle end reduces sleep inertia.

Recovery

Sleep debt formula: rolling 14-day deficit vs need. Van Dongen 2003 showed performance decline at <6h for 14 days = equivalent to 24h total sleep deprivation. AASM 7-9h adult need.

Recovery

Three powerlifting peaking programs: Smolov (13-week squat, 70-90% 1RM), Sheiko (high-frequency 4 days, 70-85%), Texas Method (3-day split, 90-105%). Volume-to-intensity-to-peak progression.

Strength Training

Strength percentile: lookup 1RM-to-population-percentile in DOTS-normalized tables. Symmetric Strength / Open Powerlifting / Strength Level data. Bodyweight + sex + lift specific.

Strength Training

Treadmill grade adjustment: 0% treadmill = outdoor pace + 12 sec/km (no wind resistance). +1% grade adds ~3.3% energy cost (Jones & Doust 1996). 1-2% grade simulates outdoor effort.

endurance

Velocity-based 1RM: load-velocity profile, MVT (minimum velocity threshold) per lift. González-Badillo 2010 method. Bench 0.17 m/s, squat 0.30 m/s, deadlift 0.15 m/s.

Strength Training

Wendler 5/3/1: training max = 90% true 1RM. 4-week cycle: 5/5/5+, 3/3/3+, 5/3/1+, deload. Add 5 lb upper / 10 lb lower per cycle. Jim Wendler Beyond 5/3/1.

Strength Training

BMI = weight in kilograms divided by height in meters squared. Quick screening number, blind to body composition. Cutoffs are 18.5 / 25 / 30 (WHO).

Body Composition

BMR = 10·mass_kg + 6.25·height_cm − 5·age + sex_constant. Mifflin-St Jeor 1990. Sex constant: +5 male, −161 female. Used as the baseline for TDEE and deficit math.

Fat Loss

US Navy circumference-based body fat. Men: 86.010·log10(waist−neck) − 70.041·log10(height) + 36.76. Women: 163.205·log10(waist+hip−neck) − 97.684·log10(height) − 78.387.

Body Composition

Body recomposition formula: target_weight = LBM / (1 − target_BF%/100). weekly_fat_loss = (current_weight − target_weight) / weeks.

Body Composition

The calorie deficit formula: daily deficit = TDEE minus intake, with 1 lb fat about 3,500 cal and 1 kg about 7,700 cal, plus a worked weekly-loss example.

Fat Loss

Calories burned = MET × body weight (kg) × hours. METs come from the Compendium of Physical Activities; 1 MET is about 1 kcal per kg per hour.

Cardio Conditioning

Creatine loading formula: 0.3 g/kg/day for 5–7 days, split 4× daily. Maintenance: 0.03 g/kg/day or 3–5 g flat. Same saturation in ~7 vs ~28 days.

Nutrition Planning

Daily water intake formula: water_ml = 30·mass_kg (sedentary) to 35·mass_kg (active). Add 350–500 ml/hour exercise. Food covers ~20%.

Nutrition Planning

DOTS = total_kg × (500 / (a + b·bw + c·bw² + d·bw³ + e·bw⁴)). Sex-specific polynomial coefficients.

Strength Training

FFMI formula: FFMI = LBM_kg / (height_m)² + 6.1·(1.8 − height_m). The +6.1·(1.8−h) normalizes to a 1.8 m reference. Natural ceiling ~25 male, ~22 female.

Body Composition

Heart rate zone formula (Karvonen): target_HR = (HRmax − HRrest) × intensity_pct + HRrest. HRmax ≈ 208 − 0.7·age (Tanaka).

Cardio Conditioning

Ideal weight formula from the Devine 1974 equation: men 50 + 2.3 kg per inch over 60, women 45.5 + 2.3, plus Robinson, Miller and Hamwi variants.

Body Composition

Lean body mass formula (Boer 1984). Male: LBM = 0.407·mass_kg + 0.267·height_cm − 19.2. Female: LBM = 0.252·mass_kg + 0.473·height_cm − 48.3.

Body Composition

Macronutrient ratio formula: protein 1.6–2.2 g/kg, fat 0.6–1.0 g/kg (≥20% of calories), carbs = (total cal − protein·4 − fat·9) / 4.

Nutrition Planning

One-rep max formula (Epley): epley 1985: 1RM = weight × (1 + reps / 30). Most accurate for 3–8 reps. Brzycki and Lombardi are common alternatives.

Strength Training

Progressive overload formula: next-week target = current load × (1 + overload_rate). Typical 2.5% novice / 1.5% intermediate / 0.5% advanced.

Strength Training

protein_g = mass_kg × goal_factor. Goal factors: 0.8 sedentary (RDA), 1.6 trained baseline, 1.8 deficit / hypertrophy, 2.2 advanced cut or older lifter.

Nutrition Planning

Running pace formula: pace = time / distance, plus Riegel T2 = T1 x (D2/D1)^1.06 for race-equivalent paces. Worked 10K-to-half-marathon example.

endurance

sweat_rate_L_per_hour = (mass_pre − mass_post + fluid_consumed_L − urine_L) / duration_hours.

endurance

Swim pace formula: pace_per_100m = total_seconds × 100 / total_distance_m. Open-water surcharge: typically +5–15 sec per 100 m.

endurance

TDEE = BMR × activity factor. Factors: 1.2 sedentary, 1.375 light, 1.55 moderate, 1.725 very active, 1.9 athlete. Drives fat-loss deficit and lean-gain surplus math.

Fat Loss

Cooper 12-min run: VO₂max = (distance_m − 504.9) / 44.73. Other estimates: Rockport walk, 1.5-mile run, Storer cycle ergometer.

Cardio Conditioning

Computes waist-to-hip ratio as waist circumference divided by hip circumference; WHO cardiometabolic risk cutoffs are 0.90 for men and 0.85 for women.

Body Composition

Walking calories ≈ MET × 3.5 × mass_kg × minutes / 200, with MET = 2.0 stroll / 3.5 brisk / 5.0 fast / 6.3 power walk. Apply 1 + 0.02·grade for incline.

Cardio Conditioning

Workout volume formula: volume load = sets × reps × weight. Hard sets = total sets within 2 reps of failure per muscle group per week.

Strength Training