Race Time Predictor
Equivalent race times from one result, a marathon reality check and five training paces.
Predicted race times
| Distance | Riegel | Daniels–Gilbert | Pace /km |
|---|
Pace is for the Daniels–Gilbert time. Your race is highlighted.
Marathon check
Training paces
| Pace | Per km | Per 400 m | % VO₂ |
|---|
From the Daniels–Gilbert oxygen-cost equation. Ranges: run anywhere between the two paces.
About the Race Time Predictor
Enter a recent race — any distance from 1500 m to the marathon — and this predictor shows your equivalent times for 14 standard distances with two published models: Riegel’s endurance formula (with an exponent you can adjust) and the Daniels–Gilbert oxygen-cost model, which also gives a race-based VO₂max.
From the same model it works out five training paces — easy, marathon, threshold, interval and repetition — per km, per mile and per 400 m. For marathon goals, add your weekly mileage and it adds the Vickers–Vertosick estimate, built from 2,303 recreational runners, which explains why a marathon usually takes longer than the classic formulas suggest. Everything is calculated in your browser.
How to use it
- Pick the race distance (or enter your own in km, miles or metres) and your finish time in hours, minutes and seconds.
- Leave the Riegel exponent at 1.06, or change it: higher values (1.07–1.08) predict slower long races.
- Optionally add your typical weekly running distance and the course type for the marathon estimate; add a second race to get your personal exponent.
- Read the prediction table, the marathon check and the training paces; copy them, download a CSV or print them.
Examples
Race-based VO₂max 40.0 · half marathon 1:50:19 (Riegel 1.06) or 1:50:52 (Daniels–Gilbert) · marathon 3:50:01 or 3:49:34
Easy 6:07–6:43 /km · marathon 5:26 · threshold 5:03 · interval 4:36–4:47 · repetition 4:25 (1:46 per 400 m)
Riegel 1.06 marathon 3:38:55 · Daniels–Gilbert 3:37:50 · Vickers–Vertosick model 3:54:10
Personal exponent 1.070 · Vickers–Vertosick two-race model with 30 miles a week: marathon 3:42:34
Riegel’s formula
T₂ = T₁ × (D₂ ÷ D₁)^k. Peter Riegel showed that across endurance sports, time grows a little faster than distance (American Scientist). With the usual exponent k = 1.06, a 50:00 10 km predicts 3,000 s × (42.195 ÷ 10)^1.06 = 13,801 s = 3:50:01 for the marathon. Riegel cited k = 1.08 for elite runners and 1.05–1.06 for male recreational runners aged 40 to 70 (as reported by Vickers and Vertosick). With two recent races, k = ln(T₂ ÷ T₁) ÷ ln(D₂ ÷ D₁) is your own value, and Use my exponent applies it.
The Daniels–Gilbert model
Jack Daniels and Jimmy Gilbert (Oxygen Power) described running with two equations, with speed v in metres per minute and race time t in minutes:
- Oxygen cost: VO₂ = −4.60 + 0.182258·v + 0.000104·v² (mL/kg/min)
- Fraction of VO₂max you can sustain: %max = 0.8 + 0.1894393·e^(−0.012778·t) + 0.2989558·e^(−0.1932605·t)
Your race-based VO₂max is the cost of your race pace divided by that fraction. 10 km in 50:00 is v = 200 m/min, cost 36.01, fraction 0.900, so 36.01 ÷ 0.900 = 40.0. The predicted time for another distance is the time that gives the same number. It reflects your racing — economy and pacing included — so it is not the same as a VO₂max measured in a lab.
Training paces
The paces come from the same oxygen-cost equation: the speed whose oxygen cost is a set fraction of your race-based VO₂max.
- Easy: 62–70% — most of your running, warm-ups and recovery.
- Marathon: your predicted marathon pace.
- Threshold: 88.8% — the fraction the model says you can hold for 60 minutes, so about the pace you could race for an hour (tempo runs, 5–10 minute repeats).
- Interval: 95–100% — near VO₂max, for repeats of 2–5 minutes.
- Repetition: your predicted mile race pace, for short fast repeats with full recovery.
The threshold, marathon and repetition paces follow directly from the model; the easy and interval ranges are MySmartCoPilot’s own choices. None of them is copied from a published pace table, so treat them as a starting point and adjust them to how the sessions feel.
Why long-race predictions are often too fast
Both models assume you are equally well trained for every distance. Riegel’s formula came from world-record times — the best performances of specialists at each distance. Vickers and Vertosick (2016) collected race times from 2,303 recreational runners: Riegel’s formula worked well up to the half marathon but “dramatically underestimated” marathon times — 10 minutes or more too fast for about half of the runners and more than 20 minutes too fast for nearly a quarter. Their models add typical weekly mileage; with them, the share of runners predicted 10 minutes or more too fast fell to about a quarter:
- One race of 5 km, 5 miles, 10 km, 10 miles or a half marathon (the survey distances; of two races, the one that is a survey distance): v_R = 42,195 ÷ (T × (42,195 ÷ D)^1.07); v = 0.16018617 + 0.83076202·v_R + 0.06423826·(miles a week ÷ 10); marathon = 42,195 ÷ v (metres, seconds, m/s).
- Two races of those distances: k = ln(T₂ ÷ T₁) ÷ ln(D₂ ÷ D₁); k_marathon = 1.4510756 − 0.23797948·k − 0.01410023·(miles ÷ 10); marathon = T₂ × (42,195 ÷ D₂)^k_marathon.
Times from a hilly, hot or windy course, or a cool, calm and flat one, are first corrected with the paper’s published adjustment for that distance.
Sources
- Riegel PS. Athletic records and human endurance. American Scientist 69(3):285-90 (PubMed 7235349)
- Daniels J, Gilbert J. Oxygen Power: Performance Tables for Distance Runners. Tempe, AZ: 1979 — equations as reproduced in Lan FY et al., J Occup Environ Med 62(7):466-71 (PMC7765687) and Smyth B et al., User Model User-adapt Interact 32:787-838 (PMC9701182)
- Vickers AJ, Vertosick EA. An empirical study of race times in recreational endurance runners. BMC Sports Sci Med Rehabil 8:26 — models and course adjustments from its Additional file 1
- World Athletics. World records (men’s 1500 m to marathon), used only to reject impossible times
Limitations
- Predictions assume equal training for every distance, good conditions and an even, well-judged race; heat, hills and pacing mistakes all slow real races.
- The further the target distance is from your race, the less reliable the prediction — especially up to the marathon.
- The Vickers–Vertosick models were built from volunteers who reported their own times and mileage, for 5 km to half-marathon races and marathons.
- Races from 1500 m to the marathon, finish times of 3 minutes to 7 hours and paces faster than 12:00 per km are accepted. Times faster than world-record level are refused as typing mistakes: the men’s world records from 1500 m to the marathon (World Athletics) work out to a race-based VO₂max of 83–87, so anything above 88 is rejected.
Privacy
Everything happens in your browser. What you enter or open here is not uploaded or stored by MySmartCoPilot.
Frequently asked questions
How do I predict my marathon time from a half marathon?
Riegel’s formula multiplies the half-marathon time by 2^1.06 ≈ 2.085: 1:45:00 predicts about 3:38:55. Many recreational runners are slower than that; add your weekly mileage and the Vickers–Vertosick model gives a more realistic figure (3:54:10 for 30 miles a week in this example).
Which prediction is more accurate, Riegel or Daniels–Gilbert?
From a 5 km or 10 km result they agree to within about half a minute up to the half marathon; for the marathon they can differ by several minutes, more so for slower runners. Neither knows how much you train, which matters most for the marathon; for that distance the Vickers–Vertosick estimate, which uses weekly mileage, matched real marathon times better in its validation group.
What exponent should I use in Riegel’s formula?
1.06 is the usual default. If you have two recent races of different distances, the calculator works out your own exponent; values above 1.06 mean you slow down more than average as races get longer.
Is the race-based VO₂max my real VO₂max?
Not exactly: it is the oxygen uptake the Daniels–Gilbert equations need to explain your race, so it also reflects your running economy and pacing. A lab test measures VO₂max directly; the VO₂ max calculator estimates it from field tests.
What pace should my easy runs be?
Slower than you might think: here about 62–70% of your race-based VO₂max, which for a 50:00 10 km runner is about 6:07–6:43 per km. Easy runs should feel conversational.