Race time predictor
Race times predicted from one you have already run — and, if you give two, fitted to your fade rate rather than the average of everybody’s, which is where the usual answer goes wrong. Nothing you type here leaves your browser — it is worked out on your own device, so there is nothing to send and nothing to log.
Riegel's formula, and the exponent that is all of it
Pete Riegel published this in Runner’s World in 1977, and almost every race predictor on the web is still it:
T₂ = T₁ × (D₂ ÷ D₁)1.06
The exponent is the entire model. At 1.06, doubling the distance multiplies your time by 21.06 = 2.085, so you slow down as the race gets longer by a fixed proportion. It was fitted to observed race times across many runners and many distances, and as an average it is good.
And it is worst at the distance you came here for
Nobody opens a race predictor to find out their 10 km time.
Vickers and Vertosick tested Riegel against 2,303 recreational runners and found it “dramatically underestimated marathon time, giving times at least 10 min too fast for half of runners”. Their own models, which use weekly training mileage as well as race times, put about 75% of runners within ten minutes where Riegel managed 50%.
So the marathon figure is not merely uncertain, it is biased, and it is biased in the direction that gets people into trouble. This page says so next to the number rather than underneath it.
Your own exponent is computable, and nobody computes it
Riegel’s 1.06 is an average. Yours is not a mystery: give two of your own race times and it falls straight out of the arithmetic.
n = log(T₂ ÷ T₁) ÷ log(D₂ ÷ D₁)
A runner who does 25:00 for 5 km and 52:00 for 10 km has an exponent of 1.057 — slightly better than average at holding pace. A runner who does the same 25:00 for 5 km but 55:00 for 10 km has an exponent of 1.138.
Riegel gives both of them the same marathon prediction, because it only looked at the 5 km. Their own exponents put them forty-four minutes and fifty seconds apart — 3:58:02 against 4:42:53. One of them is being handed a race plan that does not belong to them.
What no formula here knows about you
Your training. The single strongest predictor Vickers and Vertosick found was weekly mileage, and it appears in none of the classic formulas. A 5 km time tells you what you can do for twenty minutes; the marathon asks a different question of a body.
The day. Heat, course profile and whether you went out too fast all move a marathon by more than the difference between any two of these predictions.
Treat the shorter distances as reasonable and the marathon as a ceiling you have not yet earned.
Where this comes from
Riegel, P. (1977). Runner’s World. · Vickers, A. J., & Vertosick, E. A. (2016). “An empirical study of race times in recreational endurance runners.” 2,303 runners; the marathon comparison used the 156 who reported a marathon plus two other distances.
The marathon here is 42,195 m and the half is 21,097.5 m, which are the defined distances. Rounding the marathon to 42 km costs a three-hour runner 50 seconds — and that is more than this site rounds away anywhere else.