How do you predict a marathon time from a half marathon?

Multiply the half time by 2.084 (that is 2^1.06, the Riegel adjustment for doubling the distance). A 2:00 half predicts 4:10; a 1:30 half predicts 3:08. Enter the race above and the page shows the arithmetic and the pace to run.

What marathon time does a 10K predict?

Multiply the 10K time by (42.195 ÷ 10)^1.06 = 4.60. A 50:00 10K predicts 3:50:00; a 40:00 10K predicts 3:04:00. The prediction from a 10K is rougher than from a half, because the marathon is four times as far.

What is the Riegel formula?

T₂ = T₁ × (D₂ ÷ D₁)^1.06, published by Peter Riegel in 1981 after fitting record times from the mile to the marathon. The 1.06 says that time grows slightly faster than distance — each doubling costs about 4% in pace.

Why did my marathon come out slower than the prediction?

Usually mileage. The formula assumes the same fitness expressed over a longer distance; without the long runs, glycogen runs out around 30–35 km and pace collapses. Heat, hills and a fast first half do the rest. Predict from a recent half run in similar conditions and train the distance.

What 5K time predicts a sub-4-hour marathon?

About 25:00 by Riegel's formula, which predicts 3:59:47. Most runners need a faster 5K than that, because marathons tend to come out slower than the prediction.

Race Time Predictor (Riegel Formula: 5K, 10K, Half and Marathon)

Predict a marathon, half, 10K or 5K time from a recent race with Riegel's formula, with the pace and the working.

Inputs

Recent race distance(km)

1 km100 km

Hours

024

Minutes

059

Seconds

059

Predict distance(km)

1 km100 km

Riegel exponent

11.2

1.06 is Riegel's figure for runners. Well-trained marathoners sometimes fit 1.07–1.08; use 1.06 unless you know otherwise.

Units

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Predicted 42.195 km

3:38:53

Equivalent performances (Riegel)

Distance	Predicted time	Pace
5K	22:49	4:34/km
10K	47:35	4:45/km
15K	1:13:08	4:53/km
Half marathon	1:44:59	4:59/km
Marathon	3:38:53	5:11/km

Working: 1:45:00 × (42.195 ÷ 21.1)^1.06 = 1:45:00 × 2.0847 = 3:38:53
Predicted pace: 5:11/km (8:21/mi)
Pace of the race you entered: 4:59/km
Slowdown: 4.2% slower per km over the longer distance

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What each Race Time input means

Recent race distance: The distance of a race you have run recently, all out, in km or miles.
Hours: Hours in that race time.
Minutes: Minutes in that race time.
Seconds: Seconds in that race time.
Predict distance: The distance to predict: 42.195 km for a marathon, 21.0975 for a half, 10 or 5.
Riegel exponent: Riegel's 1.06 by default. Raise it to 1.07–1.08 for a more cautious marathon prediction if you are not a high-mileage runner.
Units: Metric (km, kg) or US units (miles, pounds). Race distances convert between kilometres and miles when you switch; times stay as typed.

Race Time formula

T₂ = T₁ × (D₂ ÷ D₁)^1.06 · T₁ and D₁ are the race you ran, D₂ the distance to predict · pace = T ÷ D

T_2 = T_1 \left(\frac{D_2}{D_1}\right)^{1.06}

Nobody holds their 5K pace for a marathon. Riegel found that record times at every distance follow one curve: time grows with distance to the power 1.06, so doubling the distance takes 2^1.06 = 2.085 times as long, not twice — about 4% slower per kilometre for every doubling. Feed in a recent race and the formula predicts any other distance at the same fitness. It is a fitness comparison, not a promise: the marathon prediction assumes the training to go the distance, and runners who have not built the mileage typically miss it by several minutes as they slow in the last 10 km. The page shows the substitution, the predicted pace in both units, the slowdown against the race you entered, and the equivalent times for every standard distance.

Race Time worked example

A half marathon in 1:45:00 (4:59/km). The marathon is 42.195 ÷ 21.1 = 2.0 times the distance, and 2.0^1.06 = 2.084, so the predicted marathon is 1:45 × 2.084 = 3:38:53 — 5:11/km, about 4% slower than the half. The same runner's equivalents: 10K in 47:35 (4:45/km) and 5K in 22:49 (4:34/km).

More Race Time examples

A 25:00 5K predicts the 10K: 25:00 × 2^1.06 = 25:00 × 2.0849 = 52:07, a pace of 5:13/km — 4.2% slower per kilometre than the 5K.

A 2:00:00 half with the more cautious exponent 1.08: 2:00:00 × 2.114 = 4:13:41, against 4:10 at Riegel's 1.06.

Where the Race Time calculator can give the wrong answer

Riegel's exponent describes elite records across distances. For recreational runners the marathon usually comes out a little optimistic — 1.07 to 1.08 fits many better — and the exponent box lets you try it.
The prediction assumes equal preparation. A half-marathon time from peak training predicts a marathon only if the marathon training (long runs of 30 km+) has been done; otherwise expect to be slower than the figure, sometimes much slower.
Predicting up from a very short race (a 5K to a marathon, an 8× jump) compounds the formula's error. The best predictor of a marathon is a half; of a 10K, a 5K.
Course, weather and terrain are not in it. A hilly or hot marathon is slower than a flat, cool half predicts by a margin the formula cannot see.
Times are entered in hours, minutes and seconds; the distances must be in the same unit as each other, and the page converts the pace to the other unit.

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Race Time reference table

Equivalent performances by Riegel's formula (exponent 1.06)
5K	10K	Half marathon	Marathon
20:00	41:42	1:32:00	3:11:49
25:00	52:07	1:55:00	3:59:47
30:00	1:02:33	2:18:00	4:47:44
35:00	1:12:58	2:41:00	5:35:41

Source: Riegel PS, American Scientist 1981: T₂ = T₁ × (D₂ ÷ D₁)^1.06

Race Time FAQ

: Multiply the half time by 2.084 (that is 2^1.06, the Riegel adjustment for doubling the distance). A 2:00 half predicts 4:10; a 1:30 half predicts 3:08. Enter the race above and the page shows the arithmetic and the pace to run.
: Multiply the 10K time by (42.195 ÷ 10)^1.06 = 4.60. A 50:00 10K predicts 3:50:00; a 40:00 10K predicts 3:04:00. The prediction from a 10K is rougher than from a half, because the marathon is four times as far.
: T₂ = T₁ × (D₂ ÷ D₁)^1.06, published by Peter Riegel in 1981 after fitting record times from the mile to the marathon. The 1.06 says that time grows slightly faster than distance — each doubling costs about 4% in pace.
: Usually mileage. The formula assumes the same fitness expressed over a longer distance; without the long runs, glycogen runs out around 30–35 km and pace collapses. Heat, hills and a fast first half do the rest. Predict from a recent half run in similar conditions and train the distance.
: About 25:00 by Riegel's formula, which predicts 3:59:47. Most runners need a faster 5K than that, because marathons tend to come out slower than the prediction.