RunPaceLab

Methodology

How formulas are sourced, implemented, and tested on RunPaceLab.

Editorial process

Articles on RunPaceLab follow this process:

  1. Source identification: The original paper, textbook, or official source for the formula or concept is located. For well-known formulas, this typically means going back to the original publication — Karvonen’s 1957 paper, Riegel’s 1981 paper, Daniels’ textbook — rather than relying on secondary summaries.
  2. Formula implementation: The formula is implemented in TypeScript from the primary source. Implementation notes cite the source equation. Unit tests verify correctness against known values.
  3. Article drafting: Articles are researched from primary sources and drafted with AI assistance (specifically, Claude by Anthropic). The AI drafts article structures and initial prose; the author edits every article, verifies claims against sources, and adjusts for tone and accuracy.
  4. Fact-checking: Quantitative claims are cross-checked against primary sources. No claim is published on the basis of AI output alone — each is traced to a source.
  5. Publication and dating: Articles carry a “last updated” date. When a formula or source is updated, the article is revised and the date updated.

This site does not have a physiologist, coach, or external expert reviewer. The author is a runner and developer, not a credentialled exercise scientist. The editorial authority is “I read the papers and implemented the formulas.” That is stated plainly and not exaggerated.

AI use disclosure

RunPaceLab uses AI assistance in article drafting. Specifically: initial article structures and draft prose are generated with the help of Claude (Anthropic’s AI assistant). The author then reviews, edits, and fact-checks every article against the primary sources before publication.

This approach is consistent with Google’s published guidance on AI-generated content (2023): scaled AI content published without human editorial oversight violates Google’s guidelines; AI-assisted writing that goes through human editorial review and is factually accurate is explicitly permitted. All content on this site has been reviewed and edited by the author.

Formula implementations (TypeScript code) and unit tests are written by the author, not generated by AI. The code is tested independently.

Formula sources and implementation notes

Pace conversion

Conversion between min/km, min/mile, and km/h uses the internationally defined conversion factor: 1 mile = 1.60934 kilometres (exact by international agreement since 1959).

min/mile = min/km × 1.60934
km/h = 60 / (min/km × 60)

There is no approximation or rounding in this conversion. Displayed times are formatted to the nearest second.

Finish time prediction — Riegel formula

The Riegel formula, published in Robert Riegel’s 1981 article “Athletic Records and Human Endurance” (American Scientist, Vol. 69, pp. 285–290), predicts race performance at one distance from a known performance at another:

T₂ = T₁ × (D₂ / D₁)^1.06

Where T₁ is the known race time, D₁ is the known distance, T₂ is the predicted time, and D₂ is the target distance. The exponent 1.06 was fitted to world record progressions across distances from 1 mile to 100 miles.

Known limitations: The formula was fitted to competitive runners; the exponent may be slightly too high (overestimating fatigue) for recreational runners in shorter to longer predictions, and too low (underestimating fatigue) for runners who are poorly trained in endurance. Large distance gaps (predicting a marathon from a 1K time trial) produce unreliable results.

VDOT and VO2 max — Daniels-Gilbert equation

The VDOT calculator implements the Daniels-Gilbert equation from:

  • Daniels, J. and Gilbert, J. (1979). Oxygen Power: Performance Tables for Distance Runners. Tafnews Press.
  • Daniels, J. (2021). Daniels’ Running Formula, 4th Edition. Human Kinetics.

VO2 at a given velocity v (metres per minute):

VO2 = −4.60 + 0.182258v + 0.000104v²

The percentage of VO2 max sustainable at race duration t (minutes):

%VO2max = 0.8 + 0.1894393 × e^(−0.012778t) + 0.2989558 × e^(−0.1932605t)

VDOT = VO2 / %VO2max. Race time predictions use the inverse of this computation.

Known limitations: VDOT is a performance-derived estimate, not a laboratory VO2 max measurement. Running economy differences between athletes mean two runners with the same VDOT may have laboratory VO2 max values that differ by 5–10 ml/kg/min. VDOT predictions are most accurate within adjacent standard distances for well-trained runners.

Heart rate zones — Karvonen method

The Karvonen method, from Karvonen, M., Kentala, K., and Mustala, O. (1957). “The effects of training on heart rate: a longitudinal study.” Annales Medicinae Experimentalis et Biologiae Fenniae, 35(3), pp. 307–315:

Target HR = ((HRmax − HRrest) × intensity%) + HRrest

Zone boundaries: Z1 at 50%, Z2 at 60%, Z3 at 70%, Z4 at 80%, Z5 at 90% of heart rate reserve.

Default HRmax estimation uses 220 − age (Fox formula), which has a standard deviation of approximately ±10–12 bpm and is less accurate for older adults. The Tanaka formula (208 − 0.7 × age), from Tanaka et al. (2001), provides marginally better accuracy for ages 40+. The calculator allows entry of a measured HRmax to override the estimate.

Known limitations: HRmax formulas are population averages. Individual variation is large. Heart rate zones based on estimated HRmax may be significantly off. Lactate threshold-based zone definitions (LTHR) may be more practically accurate for structured training, but require a threshold test to establish.

Heart rate zones — %HRmax method

Zone definitions as percentages of maximum heart rate per ACSM (American College of Sports Medicine) guidelines:

  • Zone 1: 50–60% HRmax
  • Zone 2: 60–70% HRmax
  • Zone 3: 70–80% HRmax
  • Zone 4: 80–90% HRmax
  • Zone 5: 90–100% HRmax

Calorie burn — MET-based method

MET values from: Ainsworth, B.E., et al. (2011). “2011 Compendium of Physical Activities: A Second Update of Codes and MET Values.” Medicine & Science in Sports & Exercise, 43(8), pp. 1575–1581.

kcal = MET × weight_kg × duration_hours

MET values by pace band (from the Compendium):

  • 6–8 km/h: MET 7.0 (jogging, light effort)
  • 8–10 km/h: MET 10.0 (running, moderate effort)
  • 10–12 km/h: MET 11.5 (running, vigorous effort)
  • 12–14 km/h: MET 13.0 (running, fast)
  • >14 km/h: MET 14.5 (running, very fast)

Known limitations: MET values represent population averages. Individual variation in running economy means actual calorie burn can differ by ±15–20% from the estimate. Estimates represent net calorie burn above resting metabolism during the run, not total daily calorie expenditure.

Boston Qualifier standards

Qualifying times and age group definitions from the Boston Athletic Association (BAA) official qualifying standards, available at boston.athletics.org. These are updated annually; this calculator reflects the 2026 and 2027 qualifying standards as published. Historical cutoff data from BAA registration results.

Splits calculation

Even splits: constant pace = target_time / total_distance. Negative/positive splits: the specified split percentage is applied to the first half pace, with the second half adjusted proportionally so that the total time meets the target. Checkpoint times are computed by cumulative sum of per-kilometre split times. This is a custom implementation with no single authoritative source.

Testing

All formula functions are unit tested. Tests verify:

  • Known values from the original papers and textbooks
  • Edge cases (zero inputs, very fast and very slow paces)
  • Format conversion round-trips
  • Consistency between the calculator UI and the underlying formula functions

Update policy

Formula implementations are reviewed when:

  • A source is updated (e.g., new BAA qualifying standards are published)
  • New research significantly revises an established formula
  • A user reports an error that is confirmed
  • The author identifies an error in a periodic review

The “last updated” date on each guide page reflects when that page’s content was most recently reviewed. Changes to formulas are noted in the methodology section of the relevant guide.

What this site is not

Running science is a complex field, and this site covers a narrow slice of it: the mathematics and tooling side. It does not cover:

  • Training plan design or periodisation
  • Injury prevention or rehabilitation
  • Nutrition, supplementation, or weight management
  • Coaching methodology
  • Mental performance or psychology

These topics require expertise and credentials the author does not have. Content that touches on any of these areas notes the limitation clearly and directs readers to appropriate qualified sources.