Formula
Formulas
Formulas resources — 55 formulas for fitness performance, with sourced formulas and named limits.
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endurance
Hybrid Training Planner Formula
Hybrid weekly plan: 2-3 strength + 3-4 endurance + 1-2 mobility. Schoenfeld/Roberts 2023 framework. AM cardio + PM strength, ≥6h separation, polarized intensity.
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Strength Training
Concurrent Training Interference Formula
Concurrent training interference dose-response: >3 cardio sessions/week reduces hypertrophy ~10-15%. Wilson 2012 + Schumann 2022 meta.
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endurance
Cycling FTP Power Zones Formula
Cycling Coggan power zones from FTP: Z1 ≤55%, Z2 56-75%, Z3 76-90%, Z4 91-105%, Z5 106-120%, Z6 121-150%, Z7 >150%. 20-min test minus 5% = FTP estimate.
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endurance
Daniels' VDOT Training Paces Formula
Daniels VDOT: ease 65-78%, marathon 79-83%, threshold 86-92%, interval 95-100%, repetition 105-110% of VO2max-equivalent pace. Validated lookup from race-time-to-paces.
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Strength Training
Detraining Decay Formula
Detraining decay: strength −5-10% by week 4, −15-20% by week 8. VO2max −7%/week initially. Mujika 2010 meta-analysis.
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endurance
Female Athlete Formula Suite
Female athlete energy availability (RED-S): EA = (intake_kcal − exercise_kcal) / FFM_kg. EA <30 = clinically low. IOC 2018 consensus.
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mobility
Flexibility Score Formula
Flexibility score: Beighton hypermobility (0-9) + FMS Deep Squat (0-3). Beighton ≥5 suggests hypermobility; FMS ≤2 flags movement dysfunction.
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Fat Loss
Food-to-Exercise Conversion Formula
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.
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Recovery
HRV Deload Trigger Formula
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.
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Fat Loss
Hybrid Athlete Macro Split Formula
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.
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Fat Loss
Intermittent Fasting Window Formula
Intermittent fasting window planner: 16:8 base, ±2h around training. Stockman 2018 meta — fat loss equivalent to caloric restriction, no metabolic advantage.
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Strength Training
Junk Volume Threshold Formula
Junk volume: sets above MAV produce diminishing returns. Schoenfeld 2017 meta-analysis: ≥10 sets/muscle/week, plateau by ~20 sets. Above MRV is regression.
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Fat Loss
Katch-McArdle Formula
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.
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Fat Loss
Macro Cycling Formula
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.
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endurance
Marathon Pace Elevation Formula
Marathon elevation pace correction: +12-15 sec per 1000m elevation gain (uphill), -4-6 sec downhill. Minetti 2002 + Townshend 2009 validated.
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Hydration
Marathon Sweat Rate + Electrolyte Formula
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.
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Body Composition
Natural Muscle Gain Potential Formula
Natural max FFMI ≈ 25 (men), 21 (women). Helms 2018 + Kouri 1995. Muscle gain rate: 0.5-1.0% bodyweight/month novice, 0.25-0.5% intermediate, <0.1% near ceiling.
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Strength Training
Plate Loading Formula
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.
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Strength Training
Powerlifting Meet Day Attempt Selector Formula
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.
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endurance
Race-Week Taper Formula
Race taper: 41-60% volume reduction over 8-14 days while maintaining intensity. Mujika & Padilla 2003 meta-analysis. ~3% performance gain.
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Recovery
Resting Heart Rate Formula + Interpretation
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).
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endurance
Riegel Race Time Formula
Riegel race time prediction: T2 = T1 × (D2/D1)^1.06. Race-time prediction across distances. Valid 5K–marathon, breaks down beyond 30K.
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Strength Training
RPE to Percentage Formula (Tuchscherer)
RPE to % 1RM (Tuchscherer table). RPE 10 = 100% 1RM. Each RPE point ≈ 2-3% drop. Powerlifting autoregulation standard.
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Recovery
Sleep Cycle Formula (90-Min)
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.
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Recovery
Sleep Debt Formula
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.
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Strength Training
Smolov / Sheiko / Texas Method Formula
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.
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Strength Training
Strength Percentile Formula
Strength percentile: lookup 1RM-to-population-percentile in DOTS-normalized tables. Symmetric Strength / Open Powerlifting / Strength Level data. Bodyweight + sex + lift specific.
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endurance
Treadmill to Outdoor Pace Conversion Formula
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.
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Strength Training
Velocity-Based 1RM Formula
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.
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Strength Training
Wendler 5/3/1 Formula
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.
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Body Composition
BMI Formula
BMI = weight in kilograms divided by height in meters squared. Quick screening number, blind to body composition. Cutoffs are 18.5 / 25 / 30 (WHO).
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Fat Loss
BMR Formula (Mifflin-St Jeor)
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.
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Body Composition
Body Fat Percentage Formula (US Navy)
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.
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Body Composition
Body Recomposition Formula
Body recomposition formula: target_weight = LBM / (1 − target_BF%/100). weekly_fat_loss = (current_weight − target_weight) / weeks.
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Fat Loss
Calorie Deficit Formula
Calorie deficit formula: daily deficit = TDEE − target_intake. 1 lb fat ≈ 3,500 cal; 1 kg ≈ 7,700 cal.
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Cardio Conditioning
Calories Burned Formula (MET)
Calories burned = (MET × 3.5 × mass_kg / 200) × minutes. METs come from the Compendium of Physical Activities.
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Nutrition Planning
Creatine Loading Formula
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.
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Nutrition Planning
Daily Water Intake Formula
Daily water intake formula: water_ml = 30·mass_kg (sedentary) to 35·mass_kg (active). Add 350–500 ml/hour exercise. Food covers ~20%.
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Strength Training
DOTS Score Formula
DOTS = total_kg × (500 / (a + b·bw + c·bw² + d·bw³ + e·bw⁴)). Sex-specific polynomial coefficients.
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Body Composition
FFMI Formula (Kouri-adjusted)
FFMI = LBM_kg / (height_m)² + 6.1·(1.8 − height_m). The +6.1·(1.8−h) is Kouri's normalization to a 1.8 m reference. Natural ceiling ~25 (male), ~22 (female).
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Cardio Conditioning
Heart Rate Zone Formula (Karvonen)
Heart rate zone formula (Karvonen): target_HR = (HRmax − HRrest) × intensity_pct + HRrest. HRmax ≈ 208 − 0.7·age (Tanaka).
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Body Composition
Ideal Body Weight Formula (Devine)
Ideal body weight formula (Devine 1974). Male: IBW = 50 + 2.3·(height_in − 60). Female: IBW = 45.5 + 2.3·(height_in − 60). Kg output.
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Body Composition
Lean Body Mass Formula (Boer)
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.
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Nutrition Planning
Macronutrient Ratio Formula
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.
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Strength Training
One-Rep Max Formula (Epley)
One-rep max formula (Epley): epley 1985: 1RM = weight × (1 + reps / 30). Most accurate for 3–8 reps. Brzycki and Lombardi are common alternatives.
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Strength Training
Progressive Overload Formula
Progressive overload formula: next-week target = current load × (1 + overload_rate). Typical 2.5% novice / 1.5% intermediate / 0.5% advanced.
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Nutrition Planning
Protein Intake Formula
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.
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endurance
Running Pace Formula
Running pace formula: pace = total_time / total_distance. Cross-distance prediction: T₂ = T₁ × (D₂ / D₁)^1.06 (Riegel).
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endurance
Sweat Rate Formula
sweat_rate_L_per_hour = (mass_pre − mass_post + fluid_consumed_L − urine_L) / duration_hours.
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endurance
Swim Pace Formula
Swim pace formula: pace_per_100m = total_seconds × 100 / total_distance_m. Open-water surcharge: typically +5–15 sec per 100 m.
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Fat Loss
TDEE Formula
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.
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Cardio Conditioning
VO₂ Max Formula (Cooper Test)
Cooper 12-min run: VO₂max = (distance_m − 504.9) / 44.73. Other estimates: Rockport walk, 1.5-mile run, Storer cycle ergometer.
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Body Composition
Waist-to-Hip Ratio Formula
WHR = waist_circumference / hip_circumference. WHO risk cutoffs: men >0.90, women >0.85.
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Cardio Conditioning
Walking Calorie Formula
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.
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Strength Training
Workout Volume Formula
Workout volume formula: volume load = sets × reps × weight. Hard sets = total sets within 2 reps of failure per muscle group per week.