Two runners line up for the same autumn marathon. Both are 52. Both ran 44:00 for 10K in September — 4:24 per kilometre, a solid club race. Same distance, same conditions, same result.
One finishes the marathon in 3:22. The other walks in at 3:39.
Neither had a bad day. Their predicted times were different from the start. That 17-minute gap was already written into their race history — specifically, into the ratio between their half marathon time and their marathon time. Here is how that number gets derived, what it means, and why it matters more for masters runners than anyone else.
Where does the formula come from?
Peter Riegel was a research engineer at Battelle Memorial Institute in Columbus, Ohio — and a competitive marathoner. In 1977 he published a prediction model in Runner's World. Four years later he formalised it in the paper "Athletic Records and Human Endurance" in American Scientist (Riegel, American Scientist, Vol. 69, 1981).
The formula is compact:
T₂ = T₁ × (D₂ / D₁)^k
Three inputs: your known time T₁ at distance D₁, the target distance D₂, and the exponent k. Riegel derived k by fitting world records across running, swimming, cycling and speed skating. In his 1981 American Scientist paper, he showed that for performances lasting between 3.5 and 230 minutes, the best-fit exponent was 1.06.
So: you ran 44:00 for 10K (T₁ = 2,640 seconds, D₁ = 10,000 metres). Your predicted half marathon:
T₂ = 2640 × (21,097 / 10,000)^1.06 ≈ 5,831 seconds ≈ 1:37:11
Your predicted marathon:
T₂ = 2640 × (42,195 / 10,000)^1.06 ≈ 12,145 seconds ≈ 3:22:25
Both predictions come from the same 44:00, the same k=1.06, nothing else. The full derivation of age factors used alongside these predictions is on the methodology page.
What does k actually measure?
So k is not fitness. It is not speed. It is the rate at which you slow down as distance increases.
If k were exactly 1.0, you could hold your 10K pace indefinitely — distance would cost nothing. Nobody runs k=1.0 in practice. Energy systems deplete, glycogen stores empty, and running form degrades. Every extra kilometre extracts a small penalty.
At k=1.06, doubling the distance costs about 4.2% extra time (2^0.06 ≈ 1.042). That is Riegel's population average, derived from world records. But in 2016, a PLOS ONE study found that individual runners' personal exponents fit their own race data far better than the universal 1.06 — and that world-record pace clusters closer to k=1.08 (Gassmann et al., PLOS ONE, 2016). The average is a reasonable starting point. It is not your number.
On RaceRecords, credible personal exponents run from 1.045 to 1.12. That looks like a narrow range. It is not.
From a 44:00 10K, those four exponents predict marathons between 3:18 and 3:40 — a spread of 22 minutes. The runners lining up at the start line look identical on paper. Their physiology has already written the result.
Why does the prediction band grow with distance?
The prediction range you see on RaceRecords is k ± 0.015 around the central estimate. That spread is fixed. Its effect is not.
At the half marathon, that same ±0.015 in k produces a window of about 2 minutes either side of the prediction. At the marathon, it produces a window of about 9 minutes. Same spread, four times wider outcome.
Why? Because the distance ratio compounds the exponent's influence. Projecting from 10K to half marathon, the ratio is roughly 2.1. Projecting from 10K to marathon, the ratio is 4.2. The uncertainty doubles with it.
A 2026 Frontiers in Physiology study tested this directly. Among 8,261 runners who had run both the Valencia Half Marathon and the Valencia Marathon in consecutive years, a purpose-built regression model from half marathon data explained 85% of the variance in marathon performance — with a mean absolute error of 5.9%, roughly 10–12 minutes for a 3:30 finisher (Frontiers in Physiology, PMC12856576, February 2026). The model was not naive. It used pacing splits, demographics, and multiple predictors. The error remained real.
How does RaceRecords derive your personal exponent?
If k=1.06 is the population average, your k is the value that fits your own performances. RaceRecords derives it automatically from what it calls a qualifying peak block.
The requirements:
- A peak half marathon, 10-mile, or 15K — a time PR or age-grade PR when it was run
- A peak marathon — also a time PR or age-grade PR when run
- Both within 12 months of each other
- Both within the last 5 years
When those conditions are met, the formula is:
k = ln(T_marathon / T_short) / ln(D_marathon / D_short)
A concrete example. You ran 1:36:00 at a local half marathon last April — a new time PR. Eight months later, your autumn marathon finished at 3:28:00. Also a new PR.
k = ln(12,480 / 5,760) / ln(42,195 / 21,097)
= ln(2.167) / ln(2.000)
= 0.774 / 0.693
≈ 1.116
That is notably above the generic 1.06. Now apply it to your 44:00 10K from September:
- Generic k=1.06: predicts 3:22:25
- Personal k=1.116: predicts 3:39:14 — roughly 17 minutes slower
That is not a pessimistic prediction. It is the prediction grounded in your own data. Both performances — the 1:36 half and the 3:28 marathon — are real peak efforts from the same training block.
I calibrated my own exponent last year after a 1:26 half and a 3:15 marathon. The result came back at 1.09. Not catastrophic, but enough to explain why my 40:00 10Ks kept predicting a sub-3 marathon I have never actually run.
Why does this matter more for masters runners?
Masters runners have something younger runners typically lack: meaningful race history. A 55-year-old who has raced seriously for a decade probably has several qualifying blocks available — multiple HM+marathon pairs that reveal a consistent endurance profile.
That matters for two reasons specific to masters running.
First, the personal exponent is most valuable at the distances where individual variation is largest. Most masters athletes in serious age-group competition focus on half marathons and marathons. Predictions at 5K and 10K are already reasonably accurate with generic k — the distance ratio is small, the uncertainty window is tight. Long-distance predictions are where individual physiology shows up most clearly, and that is exactly where masters runners compete.
Second, the underlying physiology shifts in a specific direction with age. In 2022, a systematic review found that VO₂max declines by roughly 5–15% per decade in trained masters athletes — about half the rate seen in sedentary adults (MDPI Encyclopedia systematic review, 2022). But running economy — how efficiently you convert oxygen to forward motion — is well preserved. In 2024, a study of well-trained masters men found no significant decline in running economy relative to matched younger athletes through their late fifties (Sport Sciences for Health, PMC11178332, 2024).
The implication for k: as the speed ceiling lowers with age, the ability to sustain pace across long distances holds up. Some masters runners develop lower k values over their careers — better relative marathon performance than their short-race times would predict. Their personal exponent is the only way to see this in the data.
A 2023 study of masters runners with a mean age of 57 found that the best predictors of long-distance performance were peak aerobic capacity and three-year peak weekly training volume — not short-race speed alone (Lee et al., Journal of Human Sport and Exercise, PMC10695480, 2023). Peak training volume accumulates over years. If you have built it, your k probably reflects it.
The broader pattern — why masters runners thrive at longer distances and how the geography of elite performance shifts with age — is in where masters runners thrive globally.
How to read it in RaceRecords
The Equivalent Times page shows a prediction for each standard road and track distance. The central number is the bold time. The lighter range around it is k ± 0.015 around that centre.
If your personal exponent is active, a small indicator shows which qualifying pair was used and the exact k value RaceRecords derived. You can turn it off in Settings → Predictions to revert to the generic 1.06 band — useful if you suspect a past race was mismeasured or run through injury.
The cross-distance grid (the matrix of sources vs targets) uses generic k=1.06 for all central values. That is deliberate. The grid is a quick comparison across many distance pairs, not a personalised forecast. The personal exponent only engages on the individual target-distance panels.
If you don't have a qualifying pair, RaceRecords tells you directly: "You don't have a qualifying block in range yet — predictions use the standard formula." The most common reasons are no marathon on file, or your most recent half and marathon are more than 12 months apart. Run both in the same training block, peak at both, and the exponent computes itself.
The half marathon is the preferred short anchor because it gives the most informative signal for marathon prediction — closer in distance, smaller distance ratio, less noise. The 10-mile and 15K work if no half is available. All three must be run as genuine peak efforts.
The number is yours
Riegel's formula is 47 years old. It still works because the physiology behind it is stable: all runners slow as distance increases, and most slow at roughly the same rate.
But roughly is not exactly. And for a masters runner planning a racing year — deciding between another half or a full, setting a goal time, pacing a campaign around a race that costs three weeks of recovery — exactly is what matters.
The personal exponent is not magic. It is one data point derived from your own history and applied forward. A study tells you the population average. Your race history tells you where you sit in it.
Either way, the number is yours.
See your own equivalent times on the Equivalent Times page. If you want to check a single race without an account, the calculator gives you a prediction in seconds.
For the score that sits alongside these predictions, read What Your Age-Graded Percentage Actually Means.
Sources
- Riegel, "Athletic Records and Human Endurance," American Scientist Vol. 69, 1981 — retrieved 2026-05-25, https://adsabs.harvard.edu/abs/1981AmSci..69..285R
- Gassmann et al., PLOS ONE, individual runners' personal exponents study, 2016 — retrieved 2026-05-25, https://pmc.ncbi.nlm.nih.gov/articles/PMC4919094/
- Frontiers in Physiology, half marathon as predictor of marathon performance (Valencia study), 2026 — retrieved 2026-05-25, https://pmc.ncbi.nlm.nih.gov/articles/PMC12856576/
- MDPI Encyclopedia, systematic review on VO₂max decline in masters athletes, 2022 — retrieved 2026-05-25, https://encyclopedia.pub/entry/27007
- Sport Sciences for Health, running economy in well-trained masters men, 2024 — retrieved 2026-05-25, https://pmc.ncbi.nlm.nih.gov/articles/PMC11178332/
- Lee et al., Journal of Human Sport and Exercise, masters runner performance predictors, 2023 — retrieved 2026-05-25, https://pmc.ncbi.nlm.nih.gov/articles/PMC10695480/