Endurometry Sources & References

The standards, papers and official documents that Endurometry calculators are based on, and what each one is used for.

These are the sources Endurometry calculators actually rely on. Each entry says what we use it for and which calculators depend on it. We only list sources that are used in a calculation or in the methodology — not general reading.

Unit conversion and race distances

Guide for the Use of the International System of Units (SI) — NIST Special Publication 811

A. Thompson, B. N. Taylor · National Institute of Standards and Technology (NIST) · 2008

How Endurometry uses it: Exact definition of the international mile (1 mile = 1,609.344 m), used for every kilometre ↔ mile conversion of distance, pace and speed.

Used by: Running Pace Calculator · Running Pace Converter · KPH to MPH Converter (km/h to mph) · Race Cutoff Time Calculator · Pace Band Generator · Printable Pace Wristband · Pace Chart Generator · Pace, speed and distance · Speed and unit conversion · Course cutoffs

Book of Rules — Competition and Technical Rules (road races)

World Athletics · current edition

How Endurometry uses it: Standard road-race distances — marathon 42.195 km, half marathon 21.0975 km — used as distance presets, worked examples and the cutoff calculator’s course length.

Used by: Running Pace Calculator · Running Pace Converter · Race Time Predictor · Race Cutoff Time Calculator · Pace Band Generator · Printable Pace Wristband · Pace Chart Generator · Pace, speed and distance · Speed and unit conversion · Race time prediction · Course cutoffs

Race prediction

Athletic Records and Human Endurance

Peter S. Riegel · American Scientist · 1981

How Endurometry uses it: Power-law race scaling T2 = T1 × (D2/D1)^k, with k = 1.06 (standard) and k = 1.10 (conservative for longer targets).

Used by: Race Time Predictor · Race time prediction

Oxygen Power: Performance Tables for Distance Runners

Jack Daniels, Jimmy Gilbert · Oxygen Power · 1979

How Endurometry uses it: Oxygen-cost and %VO2max equations used to compute VDOT from a known race, to predict another distance, and to convert a fraction of VDOT into a training pace.

Used by: Race Time Predictor · Training Pace Calculator (VDOT Zones) · Pace Chart Generator · Race time prediction · Training paces (VDOT zones)

Training methodology

Daniels’ Running Formula (training intensities / VDOT paces)

Jack Daniels · Human Kinetics · 2021

How Endurometry uses it: Published training-intensity fractions of VDOT (Easy, Marathon, Threshold, Interval, Repetition) used as the zone bounds on the training-pace calculator and the intensity table on the pace-chart generator.

Used by: Training Pace Calculator (VDOT Zones) · Pace Chart Generator · Training paces (VDOT zones)

Heart rate

The effects of training on heart rate: a longitudinal study

M. J. Karvonen, E. Kentala, O. Mustala · Annales Medicinae Experimentalis et Biologicae Fenniae · 1957

How Endurometry uses it: Heart-rate reserve method HR = (HRmax − HRrest) × % + HRrest, used for Z1–Z5 on the heart-rate calculator and the optional HR table on the training-pace page.

Used by: Training Pace Calculator (VDOT Zones) · Heart Rate Zone Calculator · Heart-rate zones

Age-predicted maximal heart rate revisited

Hirofumi Tanaka, Kevin D. Monahan, Douglas R. Seals · Journal of Applied Physiology · 2001

How Endurometry uses it: Age-predicted max HR ≈ 208 − 0.7 × age. Default estimate on the heart-rate calculator and the only age estimate on the training-pace page, unless a measured max is entered.

Used by: Training Pace Calculator (VDOT Zones) · Heart Rate Zone Calculator · Heart-rate zones

Physical activity and the prevention of coronary heart disease

S. M. Fox, J. P. Naughton, W. L. Haskell · Annals of Clinical Research · 1971

How Endurometry uses it: The familiar HRmax ≈ 220 − age rule of thumb, offered on the heart-rate calculator as a comparison to Tanaka and Gellish.

Used by: Heart Rate Zone Calculator · Heart-rate zones

Longitudinal modeling of the relationship between age and maximal heart rate

R. L. Gellish, B. R. Goslin, R. E. Olson, A. McDonald, G. D. Russi, V. K. Moudgil · Medicine & Science in Sports & Exercise · 2007

How Endurometry uses it: Quadratic age estimate HRmax ≈ 191.5 − 0.007 × age², offered as a third option on the heart-rate calculator.

Used by: Heart Rate Zone Calculator · Heart-rate zones

Energy cost

ACSM’s Guidelines for Exercise Testing and Prescription — metabolic equations (running)

American College of Sports Medicine · Wolters Kluwer · current edition

How Endurometry uses it: ACSM running metabolic equation VO₂ = 0.2v + 0.9v×grade + 3.5 and the 5 kcal per litre O₂ conversion, used for gross and net calories and for treadmill ↔ outdoor pace.

Used by: Running Calorie Calculator · Treadmill Pace Calculator · Running calories (ACSM) · Treadmill and outdoor pace

A 1% treadmill grade most accurately reflects the energetic cost of outdoor running

A. M. Jones, J. H. Doust · Journal of Sports Sciences · 1996

How Endurometry uses it: Empirical finding that 1% treadmill grade at the same displayed speed best matched still-air outdoor cost. Cited as the common indoor 1% convention; the converter itself equalises ACSM VO₂ and does not keep speed constant.

Used by: Treadmill Pace Calculator · Treadmill and outdoor pace

Age grading

Endurometry approximate open-class road age factors (5-year bins, linear interpolation)

Endurometry · 2026

How Endurometry uses it: Endurometry’s own 5-year age-factor knots (linear interpolation, one table for all distances and both sexes). Not official WMA tables; documented on the methodology page. Also used to stretch average-finish seed times with age.

Used by: Age Grading Calculator · Average Running Finish Times · Age grading (Endurometry approximation) · Average finish-time seeds

Body mass and time

Endurometry approximate race-time scaling t ∝ mass^0.67 (allometric rule of thumb)

Endurometry · 2026

How Endurometry uses it: Endurometry’s t ∝ mass^0.67 rescaling. An allometric rule of thumb, not a Daniels table and not ACSM. Documented on the methodology page.

Used by: Weight vs Pace Calculator · Body mass and race time

Average finish times

Endurometry recreational seed baselines (age-30) scaled by Endurometry age factors; Top/Bottom 20% are 0.85× / 1.18× sketches

Endurometry · 2026

How Endurometry uses it: Recreational age-30 seed times and 0.85× / 1.18× sketches used by the average-finish calculator and, until live samples dominate, by /average-times/ articles.

Used by: Average Running Finish Times · Average finish-time seeds

Endurometry Calculation Methodology

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