Running / 006
Race time predictor
One recent race in, predicted times and paces for every standard distance out — using Riegel's published formula, with its assumptions stated rather than buried.
Read the guide: every 5K from 15:00 to 40:00 with its 10K, half and marathon equivalents
Predicted marathon
RiegelEvery standard distance
The race you entered| Distance | Predicted time | Pace /km | Pace /mi |
|---|
Next / From prediction to plan
Turn a target
into splits.
Riegel's formula
Every figure on this page comes from one equation: T2 = T1 × (D2 ÷ D1)1.06, where T1 is the time you ran over distance D1, and T2 is the predicted time over D2. Peter Riegel published it in American Scientist in 1981, in a paper called "Athletic Records and Human Endurance", having fitted the exponent to records across a spread of distances and sports.
The exponent is the whole idea. If it were exactly 1, pace would be constant and doubling the distance would double the time. At 1.06 the time grows slightly faster than the distance, which is the mathematical way of saying you slow down as races get longer. Twenty minutes for 5K predicts 20:00 × 21.06 = 20:00 × 2.0849, which is 2,502 seconds, or 41:42 for 10K. Forty-five minutes for 10K predicts 45:00 × 2.109751.06, which is 5,957 seconds, or 1:39:17 for a half.
Rounding. The exponent is applied exactly; only what you read on screen is rounded, each time and pace to the nearest second, halves upward. Ask it to predict the distance you entered and it hands back your own time untouched, since a ratio of one stays one whatever power it is raised to.
What it assumes, and where it breaks
Riegel framed the formula for efforts lasting between roughly three and a half minutes and four hours. Below that, races are decided by anaerobic capacity the exponent does not describe; above it, fueling and damage start to matter more than aerobic fitness does. It also assumes you are trained for the distance being predicted, which is the assumption that quietly breaks most often. A 5K runner with no long runs in their legs is not going to run the marathon this formula predicts, and the formula has no way of knowing that.
Reliability falls as the ratio between the two distances grows. One step along the table from your input is a reasonable working number. A marathon predicted from a mile is arithmetic rather than forecasting. Individual physiology pulls in both directions too: endurance-leaning runners tend to beat the prediction at longer distances, speed-leaning runners fall short of it, and nothing in a single exponent can tell which you are.
These are predictions from a published formula, not a training plan and not advice. A number on this page is not evidence that your body is prepared for the distance attached to it, and the marathon in particular demands preparation no equation can supply. Build up gradually, and get medical advice before racing an unfamiliar distance — particularly with a cardiac or respiratory condition, on the back of an injury, or without the training behind you.
Common questions
How accurate is a race time predictor?
It is most trustworthy close to the distance you put in and least trustworthy far from it. Riegel's exponent describes how a typical trained runner slows as distance grows, and individuals sit either side of typical: endurance-leaning runners beat the prediction at longer distances, speed-leaning runners fall short of it. A 5K result predicting a marathon is extrapolating more than eight-fold and should be read as a rough ceiling.
What is Riegel's formula?
T2 = T1 × (D2 ÷ D1) raised to the power 1.06, where T1 is your known time over distance D1 and T2 is the prediction over D2. Peter Riegel published it in American Scientist in 1981 after fitting the exponent to records across a range of distances. An exponent above 1 is what makes the prediction slow down as the distance grows: doubling the distance costs slightly more than doubling the time.
Why does the marathon prediction look too fast?
Because the formula assumes you are trained for the distance it is predicting, and almost nobody is equally trained for 5K and for a marathon. The marathon also introduces failure modes that shorter races do not have — fueling, cramp, the wall — none of which an exponent can model. Treat a marathon prediction from a short race as what you might run on ideal preparation, not as a target to set off at.
What are the limits of the formula?
Riegel framed it for efforts between roughly 3.5 minutes and 4 hours, which brackets out a flat-out 800 and a long ultra at the other end. It also assumes both races are run on comparable terrain in comparable conditions, by someone trained for both, and it knows nothing about hills, heat, altitude or how the day went.
Why not use VDOT tables instead?
Those tables are copyrighted material and cannot be reproduced here. Riegel's formula is a published equation that can be stated in full, checked against its source, and recomputed by anyone — which suits a page whose point is showing the arithmetic rather than hiding it behind a lookup.