Methodology & Sources

Transparency is at the heart of BodyMath. Learn about the scientific research and methodologies behind our calculators.

Our Scientific Approach

At BodyMath, we are committed to providing calculators based on peer-reviewed scientific research and established medical knowledge. Our approach prioritizes:

  • Evidence-based formulas: We use calculations from published research and clinical guidelines
  • Peer-reviewed sources: Our methodology references studies published in reputable scientific journals
  • Conservative estimates: When research varies, we err on the side of caution
  • Transparency: We clearly explain the limitations and assumptions of each calculator
  • Regular updates: We review and update our calculators as new research emerges

Calculator-Specific Methodologies

βš–οΈ BMI Calculator

Formula: BMI = weight (kg) / height (m)Β²

Classification: Based on World Health Organization (WHO) standards:

  • Underweight: BMI < 18.5
  • Normal weight: BMI 18.5 - 24.9
  • Overweight: BMI 25.0 - 29.9
  • Obese: BMI β‰₯ 30.0

Limitations: BMI does not account for muscle mass, bone density, age, sex, or ethnicity. Athletes and muscular individuals may have high BMI despite low body fat.

Source: World Health Organization (WHO) BMI classification standards

β˜• Caffeine Half-Life Calculator

Formula: Exponential decay model based on first-order pharmacokinetics

Half-life: Average caffeine half-life is 5 hours in healthy adults (range: 3-7 hours)

Calculations:

  • Amount remaining = Initial dose Γ— 0.5^(time elapsed / half-life)
  • Percentage remaining = (Amount remaining / Initial dose) Γ— 100

Limitations: Caffeine metabolism varies based on genetics (CYP1A2 enzyme), smoking status, pregnancy, liver function, and medications. Individual half-lives can range from 1.5 to 9.5 hours.

Key Sources: Nehlig (2018) in Frontiers in Psychiatry; Blanchard & Sawers (1983) in Clinical Pharmacokinetics

🍷 Alcohol Sleep Impact Calculator

Methodology: Estimates sleep debt based on alcohol's effects on REM sleep and sleep architecture

Key Effects:

  • REM sleep suppression: ~10-20% reduction per drink
  • Sleep fragmentation: Increased awakenings in second half of night
  • Reduced sleep quality: Despite faster sleep onset

Limitations: Individual responses vary based on tolerance, genetics, body composition, and timing of consumption. The calculator provides general estimates, not personalized predictions.

Key Sources: Ebrahim et al. (2013) in Alcoholism: Clinical and Experimental Research; Roehrs & Roth (2001) in Alcohol Research & Health

⚑ Circadian Rhythm Calculator

Methodology: Predicts energy peaks and dips based on sleep/wake schedule and circadian biology

Key Principles:

  • Circadian alertness peaks 2-3 hours after waking and 6-8 hours after waking
  • Post-lunch dip occurs 7-9 hours after waking
  • Evening alertness decline begins 2-3 hours before habitual bedtime
  • Lowest alertness occurs 2-4 AM (biological night)

Limitations: Does not account for individual chronotype (morning lark vs. night owl), sleep debt, light exposure, or caffeine consumption. Predictions are based on population averages.

Key Sources: Refinetti (2016) Circadian Physiology; Monk et al. (1997) in Chronobiology International

🚭 Smoking Cessation ROI Calculator

Methodology: Calculates financial savings and health improvements after quitting smoking

Financial Calculation: Daily cigarettes Γ— Pack size Γ— Pack price Γ— Time period

Health Timeline: Based on American Cancer Society guidelines:

  • 20 minutes: Heart rate and blood pressure normalize
  • 12 hours: Carbon monoxide levels return to normal
  • 2-12 weeks: Circulation improves, lung function increases
  • 1-9 months: Coughing and shortness of breath decrease
  • 1 year: Heart disease risk drops by 50%
  • 5 years: Stroke risk equals that of non-smokers
  • 10 years: Lung cancer risk drops by 50%

Limitations: Health benefits vary by individual factors including age, smoking history, and overall health. Financial savings don't account for healthcare costs or indirect expenses.

Key Sources: American Cancer Society smoking cessation guidelines; U.S. Surgeon General reports on smoking and health

😴 Sleep Apnea Risk Assessment

Methodology: Risk assessment based on validated clinical screening tools

Risk Factors Evaluated:

  • Loud snoring
  • Observed breathing pauses during sleep
  • Excessive daytime sleepiness
  • High blood pressure
  • BMI over 35
  • Age over 50
  • Neck circumference (males >17", females >16")
  • Male gender

Limitations: This is a screening tool, not a diagnostic test. Only a sleep study (polysomnography) can definitively diagnose sleep apnea. High-risk results warrant consultation with a sleep specialist.

Key Sources: Based on STOP-BANG questionnaire and American Academy of Sleep Medicine guidelines

πŸ’€ Sleep Debt Calculator

Methodology: Calculates cumulative sleep deficit based on recommended sleep duration minus actual sleep

Formula: Sleep Debt = (Recommended Sleep βˆ’ Actual Sleep) Γ— Days

Recommendations by Age:

  • Adults (18-64): 7-9 hours per night
  • Older adults (65+): 7-8 hours per night
  • Teenagers (14-17): 8-10 hours per night

Limitations: Individual sleep needs vary. Some people function well on less sleep while others need more. Quality of sleep matters as much as quantity.

Key Sources: National Sleep Foundation sleep duration recommendations; Walker (2017) Why We Sleep

😴 Nap Optimizer

Methodology: Recommends nap duration and timing based on sleep cycle architecture and circadian rhythm

Nap Types:

  • Power nap (10-20 min): Light sleep stages, quick refresh
  • Recovery nap (60 min): Includes slow-wave sleep for memory
  • Full cycle (90 min): Complete sleep cycle, avoids inertia

Limitations: Optimal nap timing depends on individual chronotype and sleep pressure. Napping too late can interfere with nighttime sleep.

Key Sources: Milner & Cote (2009) in Sleep Medicine Reviews; Brooks & Lack (2006) in Sleep

✈️ Jet Lag Recovery Calculator

Methodology: Calculates adaptation schedule based on time zone shift and circadian phase response curves

Recovery Rate: Approximately 1 day per time zone crossed (faster for westward travel)

Light Exposure Timing:

  • Eastward travel: Morning light exposure advances circadian rhythm
  • Westward travel: Evening light exposure delays circadian rhythm
  • Avoid light at opposite times to prevent counter-adjustment

Limitations: Individual adaptation rates vary. Age, direction of travel, and prior sleep debt affect recovery time.

Key Sources: Eastman & Burgess (2009) in Sleep Medicine Clinics; Waterhouse et al. (2007) in The Lancet

πŸ”₯ TDEE Calculator

Formula: Mifflin-St Jeor equation for Basal Metabolic Rate (BMR)

  • Men: BMR = (10 Γ— weight in kg) + (6.25 Γ— height in cm) βˆ’ (5 Γ— age) + 5
  • Women: BMR = (10 Γ— weight in kg) + (6.25 Γ— height in cm) βˆ’ (5 Γ— age) βˆ’ 161

Activity Multipliers:

  • Sedentary: BMR Γ— 1.2
  • Lightly active: BMR Γ— 1.375
  • Moderately active: BMR Γ— 1.55
  • Very active: BMR Γ— 1.725
  • Extremely active: BMR Γ— 1.9

Limitations: Equations provide estimates; actual needs vary based on body composition, genetics, and metabolic adaptation.

Key Sources: Mifflin et al. (1990) in American Journal of Clinical Nutrition

πŸ₯— Macronutrient Calculator

Methodology: Calculates protein, carbohydrate, and fat targets based on calorie goals and diet type

Caloric Values:

  • Protein: 4 calories per gram
  • Carbohydrates: 4 calories per gram
  • Fat: 9 calories per gram

Preset Ratios: Based on common dietary approaches (balanced, low-carb, high-protein, keto, etc.)

Limitations: Optimal macros depend on individual goals, activity type, and metabolic health. These are starting points for experimentation.

Key Sources: Dietary Guidelines for Americans; Position statements from Academy of Nutrition and Dietetics

πŸ’§ Water Intake Calculator

Base Formula: 30-35 mL per kg of body weight, adjusted for activity and climate

Adjustments:

  • Exercise: +500-1000 mL per hour of activity
  • Hot climate: +500-750 mL per day
  • Caffeine: Additional water to offset diuretic effect

Limitations: Individual needs vary based on diet, health conditions, and environment. Thirst is generally a reliable indicator for healthy adults.

Key Sources: National Academies of Sciences Dietary Reference Intakes; Armstrong (2012) in Nutrition Reviews

πŸ“ Body Fat Calculator

Method 1 - US Navy Formula:

  • Men: 86.010 Γ— log10(waist βˆ’ neck) βˆ’ 70.041 Γ— log10(height) + 36.76
  • Women: 163.205 Γ— log10(waist + hip βˆ’ neck) βˆ’ 97.684 Γ— log10(height) βˆ’ 78.387

Method 2 - BMI-based: Estimates using Deurenberg formula based on BMI, age, and sex

Limitations: Circumference methods are estimates with Β±3-4% error. DEXA scans provide the most accurate body composition analysis.

Key Sources: Hodgdon & Beckett (1984) US Navy body composition equations; Deurenberg et al. (1991)

πŸ‹οΈ One Rep Max Calculator

Methodology: Average of 5 validated 1RM prediction formulas

Formulas Used:

  • Brzycki: weight Γ— (36 / (37 βˆ’ reps))
  • Epley: weight Γ— (1 + 0.0333 Γ— reps)
  • Lander: (100 Γ— weight) / (101.3 βˆ’ 2.67123 Γ— reps)
  • Lombardi: weight Γ— reps^0.10
  • O'Conner: weight Γ— (1 + 0.025 Γ— reps)

Limitations: Accuracy decreases above 10 reps. Formulas work best for compound lifts. Individual variation exists based on training experience and muscle fiber composition.

Key Sources: LeSuer et al. (1997) in Journal of Strength and Conditioning Research

πŸ”₯ Calorie Burn Calculator

Formula: Calories = MET Γ— weight (kg) Γ— duration (hours)

MET Values: Metabolic Equivalent of Task values from the Compendium of Physical Activities

  • Walking (3 mph): 3.5 METs
  • Running (6 mph): 9.8 METs
  • Cycling (moderate): 8.0 METs
  • Swimming (laps): 8.0 METs
  • Weight training: 3.0-6.0 METs

Limitations: MET values are averages; actual burn depends on intensity, fitness level, and efficiency. Does not account for EPOC (afterburn effect).

Key Sources: Ainsworth et al. (2011) Compendium of Physical Activities

⏰ Intermittent Fasting Calculator

Methodology: Tracks fasting duration and maps metabolic states based on time since last meal

Fasting Stages:

  • 4-8 hours: Blood sugar normalizes, insulin drops
  • 12 hours: Glycogen depletion, ketosis begins
  • 16-18 hours: Autophagy increases
  • 24 hours: Enhanced autophagy, growth hormone surge

Limitations: Metabolic responses vary by individual. Timing of benefits is approximate. Not suitable for everyoneβ€”consult healthcare provider before starting.

Key Sources: de Cabo & Mattson (2019) in New England Journal of Medicine; Patterson & Sears (2017) in Annual Review of Nutrition

🧬 Biological Age Calculator

Methodology: Estimates biological age based on lifestyle factors known to affect aging markers

Factors Assessed:

  • Exercise frequency: Up to βˆ’2 years
  • Sleep quality: Up to βˆ’1 year
  • Chronic stress: Up to +3 years
  • Smoking: Up to +8 years
  • Alcohol consumption: Up to +2 years
  • Diet quality: Up to Β±1 year
  • Social connections: Up to Β±1 year
  • BMI: Up to +2 years

Limitations: This is an estimate based on lifestyle factors. True biological age requires clinical testing (DNA methylation, blood biomarkers). Use as a motivational tool, not a medical assessment.

Key Sources: Levine et al. (2018) in Aging; multiple longevity studies on lifestyle factors

❀️ Heart Risk Calculator

Methodology: 10-year cardiovascular disease risk estimation inspired by the Framingham Risk Score

Risk Factors:

  • Age and sex
  • Total cholesterol and HDL cholesterol
  • Systolic blood pressure
  • Smoking status
  • Diabetes status
  • Blood pressure medication use
  • Family history of heart disease

Limitations: Simplified model for educational purposes. Clinical risk assessment (ASCVD Risk Calculator) should be used for medical decisions. Does not account for all risk factors.

Key Sources: D'Agostino et al. (2008) in Circulation; Framingham Heart Study

😀 Stress Score Calculator

Methodology: Assesses stress across 10 life domains with weighted scoring

Factors Assessed:

  • Work/school pressure
  • Job/financial security
  • Relationship quality
  • Financial concerns
  • Health worries
  • Sleep quality
  • Recent life changes
  • Sense of control
  • Social support
  • Relaxation time

Limitations: Self-reported assessment for general awareness. Not a clinical diagnostic tool. Validated instruments like PSS-10 should be used for clinical purposes.

Key Sources: Cohen's Perceived Stress Scale framework; Holmes-Rahe Stress Inventory concepts

πŸ“± Screen Time Impact Calculator

Methodology: Calculates health impact based on screen time categories and mitigating factors

Categories Tracked:

  • Work/school screen time
  • Social media usage
  • Streaming/video consumption
  • Gaming
  • General browsing
  • Screen time before bed

Health Effects Assessed: Eye strain, sleep disruption, sedentary behavior, mental health impacts, posture issues

Limitations: Impact varies by individual. Quality and type of screen use matters. Not all screen time is equally harmful.

Key Sources: American Academy of Ophthalmology guidelines; research on digital wellness and sleep hygiene

General Research Sources

Our calculators draw from research published in leading medical and scientific journals, including:

  • New England Journal of Medicine
  • The Lancet
  • JAMA (Journal of the American Medical Association)
  • Sleep
  • Chronobiology International
  • Alcoholism: Clinical and Experimental Research
  • Clinical Pharmacokinetics
  • Journal of Clinical Sleep Medicine

We also reference guidelines from authoritative health organizations including the World Health Organization (WHO), American Heart Association, American Cancer Society, and American Academy of Sleep Medicine.

Calculation Accuracy & Precision

All mathematical calculations are performed with appropriate precision:

  • Rounding: Results are rounded to clinically meaningful precision
  • Unit conversions: Conversions between metric and imperial units follow standard conversion factors
  • Time calculations: Pharmacokinetic models use exponential decay functions
  • Statistical methods: Population averages and ranges are based on published data

Continuous Improvement

Scientific knowledge evolves, and so do our calculators. We are committed to:

  • Regularly reviewing new research in relevant fields
  • Updating calculator formulas when better evidence becomes available
  • Incorporating user feedback to improve clarity and usefulness
  • Expanding our calculator library to cover additional health topics
  • Maintaining transparency about our methodology and sources

Important Reminder

While our calculators are based on scientific research, they provide general estimates and should not replace professional medical advice. Individual biology, health conditions, and circumstances can significantly affect outcomes. Always consult with qualified healthcare providers for personalized medical guidance.

Questions About Our Methodology?

If you have questions about the science behind our calculators or would like more details about our sources, please contact us at:

Email: reach@bodymath.fyi