How accurate is the Riegel formula?

For well-trained runners predicting between 5K and the half marathon, it is often within a few percent. It gets less reliable the further you extrapolate, and for the marathon it tends to be optimistic for runners who don’t do regular long runs.

What marathon time does a 45-minute 10K predict?

With the standard exponent of 1.06, a 45:00 10K predicts 1:39:17 for the half marathon and 3:27:01 for the marathon. With 1.08, which suits runners with lower mileage, the marathon prediction is 3:33:03.

Which race should I use for the prediction?

Use your most recent all-out race, ideally the half marathon if you are predicting a marathon. The closer the source distance is to your goal, the better the prediction. Hilly or hot races will make predictions look slow.

Why is my actual marathon slower than predicted?

Riegel’s formula only models how pace drops with distance. It knows nothing about your long runs, fuelling, the weather or the course. In the marathon, those factors often cost more time than the formula expects.

What does the fatigue exponent mean?

It controls how much you slow down as the race gets longer. Riegel found about 1.06 across world-class running records. A higher value such as 1.07 or 1.08 predicts a bigger slowdown, which often fits recreational runners better over the marathon.

04 Free tool

Race time predictor

Enter a recent race result and see what it predicts for other distances, using Peter Riegel's formula. Then read why the marathon number deserves a pinch of salt.

Marathon: 3:27:01
Half marathon: 1:39:17

Predicted times
Race	Predicted	Pace
1 mile	6:29	4:02/km6:29/mi
5K	21:35	4:19/km6:57/mi
10Kyour race	45:00	4:30/km7:15/mi
10 miles	1:14:31	4:38/km7:27/mi
Half marathon	1:39:17	4:42/km7:34/mi
Marathonrough	3:27:01	4:54/km7:54/mi
50Krough	4:07:49	4:57/km7:59/mi

Predictions longer than about 230 minutes are outside the formula’s tested range. Fuelling, heat and training volume dominate at these durations, so treat them as optimistic.
Predicting more than four times your race distance is a big stretch. A marathon predicted from a 5K is usually too fast unless you do regular long runs.
Predicting shorter races from longer ones assumes you have the speed to match; many endurance-trained runners don’t.

The formula

In the late 1970s the engineer and runner Peter Riegel showed that world records at every distance, from the mile to the marathon, fall on one simple curve. His best-known write-up appeared in American Scientist in 1981:

T₂ = T₁ × (D₂ ÷ D₁)^1.06

T₁ and D₁ are your race time and distance; D₂ is the distance you want a prediction for. The exponent 1.06 captures how much slower you get as the race gets longer: double the distance and your time slightly more than doubles. A 20:00 5K, for example, predicts 41:42 for 10K.

Where it breaks down

The formula describes elite athletes running races they trained specifically for. For everyone else, it's a best-case estimate. Be sceptical when:

You extrapolate a long way. A marathon predicted from a 5K assumes you have the endurance to match your speed. Runners who don't do regular long runs usually finish slower than predicted.
The prediction runs past about 3 hours 50 minutes. Riegel fitted his curve to efforts between roughly 3.5 and 230 minutes. Beyond that, fuelling, heat and walking breaks matter more than any curve.
The source race wasn't all-out, or was hilly, hot or windy. Garbage in, garbage out.
You're predicting down in distance. A good marathoner won't necessarily have the raw speed for a matching mile.

The tool flags these cases with a “rough” tag and a note explaining why.

Using the prediction

Treat the result as a ceiling for your goal, not the goal itself. A sensible marathon plan uses the prediction from a recent half, adds a margin if your long runs have been patchy, and then paces from that number: put it straight into the pace table to get your splits, and into the nutrition planner to plan your gels for that time.

If you raced recently at two distances, compare them. If your 10K predicts a faster half than you actually ran, your endurance is the limiter, so raise the exponent to 1.07 or 1.08 for a more realistic marathon number.

Questions runners ask

How accurate is the Riegel formula?: For well-trained runners predicting between 5K and the half marathon, it is often within a few percent. It gets less reliable the further you extrapolate, and for the marathon it tends to be optimistic for runners who don’t do regular long runs.
What marathon time does a 45-minute 10K predict?: With the standard exponent of 1.06, a 45:00 10K predicts 1:39:17 for the half marathon and 3:27:01 for the marathon. With 1.08, which suits runners with lower mileage, the marathon prediction is 3:33:03.
Which race should I use for the prediction?: Use your most recent all-out race, ideally the half marathon if you are predicting a marathon. The closer the source distance is to your goal, the better the prediction. Hilly or hot races will make predictions look slow.
Why is my actual marathon slower than predicted?: Riegel’s formula only models how pace drops with distance. It knows nothing about your long runs, fuelling, the weather or the course. In the marathon, those factors often cost more time than the formula expects.
What does the fatigue exponent mean?: It controls how much you slow down as the race gets longer. Riegel found about 1.06 across world-class running records. A higher value such as 1.07 or 1.08 predicts a bigger slowdown, which often fits recreational runners better over the marathon.