Research & Scientific References
The Science Behind Our Calculators
Built on Decades of Peer-Reviewed Research
Every calculator on Sport Calculator is grounded in validated scientific research. We cite and reference the work of leading sports scientists, exercise physiologists, and research institutions to ensure accuracy and reliability.
10+
Cited Researchers
50+
Peer-Reviewed Sources
40+
Years of Research
25+
Validated Formulas
Our Commitment to Accuracy
We believe that training tools should be transparent. Unlike black-box calculators that hide their methods, we openly cite the research and formulas behind every calculation.
The scientists and researchers listed on this page are not affiliated with Sport Calculator. We reference their published, peer-reviewed research to build accurate tools. Their work represents decades of rigorous scientific study in exercise physiology, sports nutrition, and performance science.
When you use our calculators, you're benefiting from formulas that have been validated in laboratories, tested on thousands of athletes, and published in respected scientific journals.
Foundational Researchers We Reference
The pioneering scientists whose published research forms the basis of our calculations
Dr. Jack Daniels
Exercise Physiology & Running Coaching
Legendary running coach and exercise physiologist who developed the VDOT system, an integrative index of running performance combining VO₂max, running economy, and lactate threshold. Co-developer (with Jimmy Gilbert) of the Daniels-Gilbert training pace equations, which map VDOT to training intensities.
Key Contributions:
- 2x Olympic medal-winning coach (1968, 1972)
- Coached multiple Olympians and NCAA champions
- Directed elite training centers including Wells College
- High Altitude Training Center director (Flagstaff, AZ)
- Coached 130+ All-Americans
Jimmy Gilbert
Exercise Physiology
Exercise physiologist who co-created (with Dr. Jack Daniels) the Daniels-Gilbert running velocity and VDOT-pace equations. Specialized in oxygen cost modeling, running economy calculations, and performance-VO₂ relationships during foundational endurance-physiology work in the 1970s.
Key Contributions:
- Co-creator of the Daniels-Gilbert VDOT-pace equations
- Assisted in mathematical modeling linking oxygen cost curves to race-pace predictions
- Helped derive speed-VO₂ relationships and tables for VDOT calculators
- Contributed to improved accuracy in estimating training paces from race performances
Dr. Andrew Coggan
Cycling Physiology
Pioneer of power-based cycling training who created the Coggan Power Zones (7-zone model) and architected Functional Threshold Power (FTP) as the anchor for power-based training intensity. Played a central role in developing TrainingPeaks' WKO metrics (TSS®, IF®, NP®).
Key Contributions:
- Creator of the Coggan Power Zones (7-zone model)
- Architect of Functional Threshold Power (FTP)
- Developed NP®, IF®, TSS® metrics for cycling load management
- Consultant for USA Cycling and major power-meter companies
- Performance modeling using power-duration curves
Dr. Phil Maffetone
Sports Medicine & Holistic Endurance Training
Sports medicine physician who developed the MAF Method (Maximum Aerobic Function), known for the 180-age heart-rate formula to target aerobic (fat-oxidation) zones. Emphasizes low-stress, injury-reducing training with focus on metabolic health.
Key Contributions:
- Creator of the MAF Method (180-Age formula)
- Coached 6-time Ironman World Champion Mark Allen
- Pioneer of low heart rate training
- Popularized simple field-friendly tools for aerobic base building
- Emphasized HR-driven feedback for injury prevention and metabolic efficiency
Dr. Martti J. Karvonen
Physiology
Finnish physiology researcher (1918-2009) who created the Karvonen Formula: Target HR = HRrest + %Intensity × (HRmax - HRrest). This uses Heart Rate Reserve (HRR) as the intensity anchor, demonstrating that HRR correlates more tightly with VO₂ reserve than simple %HRmax.
Key Contributions:
- Creator of the Karvonen Formula (HRR method)
- Pioneered Heart Rate Reserve calculations
- Demonstrated HRR-VO₂ reserve correlation
- Research on cardiovascular responses to exercise
- Work on epidemiology of heart disease and population health
Dr. Asker Jeukendrup
Sports Nutrition
World-renowned sports nutritionist who defined modern carbohydrate oxidation limits (≈60 g/h glucose, ≈90 g/h glucose+fructose, up to ~120 g/h in elite). Research leader in multiple transportable carbohydrates and GI absorption, with extensive work on race fueling strategies.
Key Contributions:
- Defined carbohydrate oxidation rate guidelines
- Research leader on multiple transportable carbohydrates
- Former Performance Director at Jumbo-Visma Cycling
- Consultant to Olympic and professional endurance athletes
- Creator of MySportScience platform
Dr. Barbara Ainsworth
Exercise Epidemiology
Exercise epidemiologist and lead author of the Compendium of Physical Activities, the global standard table of MET values used in energy-expenditure models. Provided harmonized MET estimates for over 800 physical activities.
Key Contributions:
- Lead developer of the Compendium of Physical Activities
- Standardized MET values for 800+ activities
- Forms scientific basis for calorie estimations in wearables, apps, and research
- Arizona State University professor
- Over 30 years of exercise science research
K. Mantzios et al.
Research team whose 2022 study quantified temperature-dependent decrements in running performance. Modeled performance loss per °C relative to an optimal temperature (~10-12°C), providing modern, data-driven heat penalty curves for marathon and road racing.
Key Contributions:
- 2022 study quantifying temperature-dependent running performance decrements
- Modeled performance loss per °C vs optimal temperature
- Provides modern heat penalty curves for marathon/road racing
Wehrlin & Hallén
Altitude physiology researchers who demonstrated quantitative reductions in VO₂max with increasing altitude, including percentage loss per 1000m. One of the most widely cited models for altitude-related endurance decreases.
Key Contributions:
- Quantified VO₂max reductions with increasing altitude
- Established % loss per 1000m elevation
- Widely cited model for altitude-related endurance decreases
- Equations useful for race prediction and acclimatization planning
Dalleck & Kravitz
Exercise physiology researchers (2007) who created validated metabolic prediction equations estimating VO₂ for elliptical trainers. Enables accurate cross-modal calorie and intensity comparisons between elliptical and treadmill running.
Key Contributions:
- Created validated metabolic prediction equations for elliptical trainers
- Enables cross-modal calorie and intensity comparisons
- Based on oxygen-cost testing across resistance and cadence
McArdle, Katch & Katch
Authors of "Exercise Physiology: Nutrition, Energy, and Human Performance," the field's most widely used reference textbook. Provides sex- and age-specific VO₂max norm tables foundational for teaching cardiorespiratory physiology.
Key Contributions:
- Authors of the definitive Exercise Physiology textbook
- Provides sex- and age-specific VO₂max norm tables
- Foundational reference for cardiorespiratory physiology
- Standard teaching resource for endurance performance
Mifflin & St. Jeor
Developers of the Mifflin-St. Jeor Equation (1990), considered the most accurate resting metabolic rate (RMR) equation for non-obese adults. Replaced Harris-Benedict for many dietitians due to improved accuracy.
Key Contributions:
- Developed the Mifflin-St. Jeor Equation (1990)
- Most accurate RMR equation for non-obese adults
- Replaced Harris-Benedict for improved accuracy
- Basis of modern TDEE estimators with activity factors
Santos-Lozano et al.
Endurance pacing researchers whose 2014 marathon pacing analysis identified patterns of pace decay, positive splits, and sex differences in pacing. One of the largest datasets of real-world marathon pacing.
Key Contributions:
- 2014 marathon pacing analysis
- Identified patterns of pace decay and positive splits
- Analyzed sex differences in pacing
- One of the largest real-world marathon pacing datasets
- Empirical basis for pacing algorithms in prediction models
Burke et al.
Authors of the IOC Consensus Statements on carbohydrate needs, setting widely adopted endurance fueling guidelines: 30-60 g/h, 60-90 g/h, up to 120 g/h depending on duration and modality.
Key Contributions:
- Authors of IOC Consensus Statements on carbohydrate needs
- Established endurance fueling guidelines (30-60, 60-90, up to 120 g/h)
- Duration and modality-specific recommendations
El Helou et al.
Marathon environmental physiology researchers who analyzed marathon performance under varying humidity and environmental stress. Developed empirical models linking humidity to pace degradation.
Key Contributions:
- Analyzed marathon performance under humidity and environmental stress
- Developed empirical models linking humidity to pace degradation
- Used in weather-adjusted marathon prediction tools
Jenkins et al.
Exercise physiology researchers who studied thermoregulatory strain and performance under humid conditions. Quantified relationships among humidity, core temperature rise, and sustainable workload.
Key Contributions:
- Studied thermoregulatory strain under humid conditions
- Quantified humidity-core temperature-workload relationships
Maughan et al.
Researchers with extensive work on hydration, electrolytes, and heat stress in endurance sport. Contributors to ACSM hydration and heat-stress guidelines.
Key Contributions:
- Extensive research on hydration and electrolytes
- Heat stress in endurance sport research
- Contributors to ACSM hydration and heat-stress guidelines
Research Organizations & Standards
Established institutions whose guidelines and data inform our calculations
American College of Sports Medicine (ACSM)
The largest sports medicine and exercise science organization in the world. Their metabolic equations and exercise guidelines form the foundation of many calorie and performance calculations.
Used For:
- Metabolic equations
- Fluid replacement guidelines
- Exercise intensity standards
Compendium of Physical Activities
A comprehensive database of MET (Metabolic Equivalent of Task) values maintained by researchers at Arizona State University. Updated regularly based on oxygen consumption studies.
Used For:
- MET values for 800+ activities
- Calorie burn standardization
- Activity intensity classification
National Weather Service (NWS)
Provides the heat index equation used to calculate perceived temperature and its impact on athletic performance in hot conditions.
Used For:
- Heat index formula
- Weather safety guidelines
Transparent & Science-Based
Every calculator explains its methodology. No hidden formulas, no mystery algorithms — just transparent, peer-reviewed science you can trust for your training.
Important Note
The researchers and organizations listed on this page are not affiliated with, do not endorse, and have no connection to Sport Calculator. We reference their publicly available, peer-reviewed research and published formulas to build accurate training tools. All credit for the underlying science belongs to these researchers and their institutions. For the original research, please refer to the cited publications and official sources.