Marathon Finish Predictor
h:mm:ss
Projected marathon
3:38:55 – 3:43:08
The two formulas disagree by 4:13
- Riegel — t₂ = t₁ × (d₂/d₁)^1.063:38:55
- Cameron — Distance-dependent correction3:43:08
- Distance multiple2× the race you ran
How this was worked out
- The race you ran21,098 m in 1:45:00 = 6,300 s
- Riegel, worked6,300 × (42,195 ÷ 21,098)^1.06 = 13,135 s = 3:38:55
- Cameron, workedf(21,098) = 13.1752, f(42,195) = 12.4001; 6,300 × 2 × (13.1752 ÷ 12.4001) = 13,388 s = 3:43:08
- The gap between them3:43:08 − 3:38:55 = 4:13, and both ends of it are optimistic
Riegel stated the equation for events of roughly three and a half minutes to three and a half hours, and a projection of 3:43:08 is past the top of that range. This is a 2-fold jump in distance, and the further outside the fitted range the answer sits, the more of it is extrapolation rather than arithmetic.
Both numbers are optimistic, and the marathon is where they are most optimistic. Vickers and Vertosick surveyed 2,303 recreational runners (BMC Sports Science, Medicine and Rehabilitation, 2016) and found Riegel well calibrated up to the half marathon but at least ten minutes too fast at the marathon for half of them. Neither formula has an input for weekly mileage or longest run, so both answer as though whatever endurance produced the short race carries all the way — and for anyone whose long runs do not support the distance, it does not.
Riegel: t₂ = t₁ × (d₂/d₁)^1.06, from Peter Riegel, “Athletic Records and Human Endurance”, American Scientist 69 (1981), fitted to world records and stated for events of roughly 3.5 minutes to 3.5 hours. Cameron applies a distance-dependent correction, f(x) = 13.49681 − 0.000030363x + 835.7114/x^0.7905 with x in metres, instead of one fixed exponent. They are shown separately because the gap between them is information; averaging them would only hide it.
Riegel, and one exponent for everything
Peter Riegel published his endurance equation in American Scientist in 1981, under the title “Athletic Records and Human Endurance”. Fitting record performances across running, swimming, cycling and walking, he found that time rises with distance raised to the power 1.06: double the distance and the time goes up by roughly 8.5 per cent more than double. Written out, t₂ = t₁ × (d₂/d₁)^1.06, and that single exponent is the whole model.
Riegel was explicit about where it applied — events lasting somewhere between three and a half minutes and three and a half hours, fitted to records rather than to ordinary training. A marathon sits at the far edge of that window for a fast runner and well outside it for most of the field, which is precisely where the equation is asked to work hardest.
Cameron, and a correction that moves
The formula attributed to Dave Cameron takes a different shape. Instead of one exponent, it scales the two distances through a correction function, f(x) = 13.49681 − 0.000030363x + 835.7114/x^0.7905 with x in metres, and multiplies the ratio of those two corrections by the ratio of the distances.
The practical effect is that the penalty is not assumed to be the same everywhere. Stepping from five to ten kilometres and stepping from a half marathon to a full one are treated as different problems, and at the marathon end Cameron is usually the more cautious of the two. From a 1:45 half marathon, Riegel projects 3:38:55 and Cameron 3:43:08 — four minutes apart, which is a useful reminder that a projection is a region rather than a point.
Both of them run fast, and there is evidence
This is the part worth reading twice. In 2016 Andrew Vickers and Emily Vertosick published a survey of 2,303 recreational endurance runners in BMC Sports Science, Medicine and Rehabilitation. Riegel held up well for distances up to the half marathon. At the marathon it did not: the predicted times were at least ten minutes too fast for half the runners in the sample, and adding training volume to the model cut the error substantially.
The reason is structural rather than a flaw in the arithmetic. Neither formula has anywhere to put your weekly mileage, your longest run, the temperature or whether you have ever run beyond thirty kilometres. Both take a short race as evidence of endurance that extends smoothly, and for anyone whose long runs do not support the distance, it does not extend at all. That is the honest headline: these numbers describe what your speed would be worth if your endurance matched it.
Reading the range
Take the slower of the two figures as the optimistic end of a realistic band, not as a target, and widen it further if your training has been short on long runs, the forecast is warm, or the course climbs. Runners who go out on the faster number and hold it are usually the ones who were already running the mileage that would have justified it.
The distance multiple shown alongside the answers is the sanity check. Predicting a half from a ten kilometre race is a stretch of about two; predicting a marathon from a parkrun is a stretch of more than eight, and no formula fitted to race results can make that jump on your behalf.
Riegel against Cameron, and what your watch says
Which of the two formulas should I trust?
Neither on its own. They are shown side by side because the gap between them carries information about how uncertain the extrapolation is, and averaging them into one number would present a false precision that neither author claimed.
Why is there no adjustment for how much I train?
Because neither published formula includes one, and inventing a coefficient to bolt on would make the output an opinion rather than a citation. The research showing training volume matters is described above so you can apply that judgement yourself.
Can I predict a short race from a long one?
The arithmetic runs in both directions and the tool will do it, but the result is less useful. Speed at five kilometres depends on qualities a marathon does not test, so a backwards projection tends to understate what a well-trained runner can produce over a short distance.
Does it know about hills, heat or altitude?
No. Both formulas were fitted to race times without any environmental input at all, so a projection describes a flat course in reasonable conditions. Heat in particular can cost more than the entire gap between the two predictions shown.
Why does the same race give a different answer here than on my watch?
Most watch estimates use physiological modelling built on heart rate and recent training load rather than a published race-equivalence formula. They are answering a related but different question, and they have data about you that a page taking one race time does not.