Our Methodology

How we build, validate, and maintain accurate running calculators.

Evidence-Based Calculation

Every calculator on RunDida is built on established sports science research and validated coaching frameworks. We do not invent formulas. Instead, we implement well-documented models from peer-reviewed literature and translate them into accessible, interactive tools.

Each tool page includes a Sources section citing the specific papers, textbooks, and research that underpin the calculations. This transparency allows coaches, athletes, and researchers to verify our implementations against the original literature.

Core Formulas and Their Sources

Pace and VDOT Calculations

Our pace calculator and training pace zones are based on the VDOT system developed by Dr. Jack Daniels and Jimmy Gilbert, first published in Oxygen Power (1979) and refined in Daniels' Running Formula (Human Kinetics, 3rd Edition, 2014). The system models two physiological relationships: the oxygen cost of running at a given velocity, and the sustainable fraction of VO2max over a given duration. We implement the exact polynomial and exponential equations from the original research.

Heart Rate Zone Training

The heart rate zone calculator implements the Karvonen method, which uses heart rate reserve (HRR) rather than simple percentage of maximum heart rate. This approach, validated by Karvonen, Kentala, and Mustala (1957) and refined by the American College of Sports Medicine, provides more physiologically accurate zone boundaries because it accounts for individual resting heart rate differences.

Race Time Prediction

Our race time predictor and race equivalence calculator use Peter Riegel's endurance prediction formula, published in American Scientist (1981). The power law relationship T2 = T1 × (D2/D1)exponent has been validated across millions of race results. We extend the standard model with training-level-adjusted fatigue exponents based on research by Vickers and Vertosick (BMC Sports Science, 2016), which analyzed over 2 million race results to determine population-specific exponents.

VO2max Estimation

The VO2max calculator uses the Cooper 12-minute test regression model and the Daniels VDOT-to-VO2max relationship. Both methods have been validated against direct laboratory measurement (gas exchange analysis) and provide estimates within 5-10% of measured values for trained runners.

Energy Expenditure and Nutrition

Our calorie calculator, gel calculator, and carb loading planner use MET values from the Compendium of Physical Activities (Ainsworth et al., Medicine & Science in Sports & Exercise, 2011) and carbohydrate oxidation rates from Jeukendrup's research on exercise nutrition (Journal of Sports Sciences, 2011).

Glycogen Depletion Modeling

The marathon wall predictor models glycogen storage capacity (approximately 14g per kg of lean body mass for muscle glycogen, plus 80-110g liver glycogen) and depletion rates based on exercise intensity. The substrate utilization model draws from Rapoport's metabolic analysis of marathon performance (PLoS Computational Biology, 2010) and Burke et al.'s research on carbohydrate for competition (Journal of Sports Sciences, 2011).

Training Periodization

Our training plan generator, taper calculator, and training start date calculator implement periodization models from Tudor Bompa's Periodization: Theory and Methodology of Training (6th Edition, 2019) and taper research by Mujika and Padilla (Medicine & Science in Sports & Exercise, 2003), which demonstrated that a well-executed taper can improve race performance by 2-3%.

Validation Process

Each calculator undergoes a multi-step validation process before publication:

  1. Formula verification — equations are checked against the original source publications to ensure accurate implementation
  2. Boundary testing — inputs at extreme ranges (very fast, very slow, minimum and maximum values) are tested to ensure sensible outputs
  3. Cross-validation — results are compared against established reference tables (e.g., Daniels' VDOT tables, published heart rate zone charts) and competing tools
  4. Unit consistency — all calculators support both metric (km, kg) and imperial (miles, lbs) units with accurate conversion
  5. Mobile testing — all calculators are verified on mobile devices (iOS Safari, Android Chrome) for usability and accuracy

Limitations and Disclaimers

Running calculators provide estimates based on population-level models. Individual results vary based on genetics, training history, environmental conditions, health status, and other factors that mathematical models cannot fully capture. Our tools are designed to inform your training decisions, not replace professional coaching or medical advice.

Specific limitations include:

  • Race time predictions assume the input race was a genuine maximum effort in favorable conditions
  • Heart rate zones are approximate; individual lactate threshold testing provides more precise boundaries
  • VO2max estimates from performance data may differ 5-10% from laboratory-measured values
  • Calorie calculations use average MET values that vary by running economy and body composition
  • Weather-based recommendations use general guidelines; individual heat and cold tolerance varies significantly

Privacy and Data

All calculations run entirely in your browser using client-side JavaScript. No personal data, race results, or calculation inputs are transmitted to RunDida servers. Results stored via browser localStorage (such as packing list checkboxes) remain on your device and are never shared. See our About page for contact information.

Explore Our Tools

Browse our complete collection of running calculators, explore major marathon profiles, or return to the homepage to use the marathon countdown.