Running Pace Converter (min/km, min/mile, km/h, mph)
Running Pace Converter (min/km, min/mile, km/h, mph)
Convert between minutes per kilometre, minutes per mile, km/h and mph in every direction, get finish times for the mile, 5K, 10K, half and full marathon, work backwards from a goal time, and see an equivalent performance from Riegel’s published model with its stated range of validity computed for your own pace.
Pace, speed and race times
5:00 per kilometre, with a 5K as the base and the marathon as the target
Exact arithmetic for the units, a named model for the rest
- 1.609344
- kilometres in a mile, exactly, from the 1959 international yard of 0.9144 m
- b
- Riegel’s endurance exponent. 1.06 for running; he gave 1.05 to 1.06 for recreational men aged 40 to 70 and 1.08 for elite runners
- range
- Riegel stated the model for efforts lasting 3.5 to 230 minutes. In distance that depends on your pace, which is why the page computes it
- 42.195 km
- the marathon. The half is 21.0975 km and the mile 1 609.344 m
Worked example
5:00 per kilometre, with a 5K as the base and the marathon as the target
5 minutes 0 seconds is 300 s per kilometre, which is 5.000 min/km
Per mile that is 300 × 1.609344 = 482.80 s, which is 8:2.8 — and the speed is 3 600 / 300 = 12.0 km/h, 7.456 mph
Held flat, that is 25.00 minutes for 5 km, 3.516 hours for the marathon
Riegel takes the 5K time of 25:00 and scales it: 1 500 × (42 195 / 5 000)^1.06 = 14,387 s, which is 3:59:46 — 28.8 minutes more than flat 5:00 pace would give
At 5:00 per kilometre, Riegel's 3.5-to-230-minute window runs from 0.70 km to 46.0 km, so the marathon is just inside it — and Vickers and Vertosick would still read that 3:59:46 as at least ten minutes optimistic
The pace and speed identities, which are the easy part
| min/km | min/mile | km/h | mph | m/s | 5K | 10K | Half | Marathon |
|---|---|---|---|---|---|---|---|---|
| 3:00 | 4:49 | 20.00 | 12.43 | 5.556 | 15:00 | 30:00 | 1:03:17 | 2:06:35 |
| 3:30 | 5:37 | 17.14 | 10.65 | 4.762 | 17:30 | 35:00 | 1:13:50 | 2:27:40 |
| 4:00 | 6:26 | 15.00 | 9.32 | 4.167 | 20:00 | 40:00 | 1:24:23 | 2:48:46 |
| 4:30 | 7:14 | 13.33 | 8.28 | 3.704 | 22:30 | 45:00 | 1:34:56 | 3:09:52 |
| 5:00 | 8:02 | 12.00 | 7.46 | 3.333 | 25:00 | 50:00 | 1:45:29 | 3:30:58 |
| 5:30 | 8:51 | 10.91 | 6.78 | 3.030 | 27:30 | 55:00 | 1:56:02 | 3:52:04 |
| 6:00 | 9:39 | 10.00 | 6.21 | 2.778 | 30:00 | 60:00 | 2:06:35 | 4:13:10 |
| 7:00 | 11:15 | 8.57 | 5.33 | 2.381 | 35:00 | 70:00 | 2:27:40 | 4:55:21 |
| 8:00 | 12:52 | 7.50 | 4.66 | 2.083 | 40:00 | 80:00 | 2:48:46 | 5:37:33 |
| 9:00 | 14:29 | 6.67 | 4.14 | 1.852 | 45:00 | 90:00 | 3:09:52 | 6:19:45 |
Equivalent performances from a 25:00 5K, at Riegel’s 1.06
| Distance | km | Riegel prediction | Pace, min/km | At a flat 5:00/km for comparison | Riegel adds, minutes | Inside Riegel’s 3.5 to 230 minute range? |
|---|---|---|---|---|---|---|
| The mile (1,609.344 m) | 1.6093 | 0:07:31 | 4:40 | 0:08:02 | -0.5 | inside |
| 5 km | 5.0000 | 0:25:00 | 5:00 | 0:25:00 | 0.0 | inside |
| 10 km | 10.0000 | 0:52:07 | 5:12 | 0:50:00 | 2.1 | inside |
| Half marathon (21.0975 km) | 21.0975 | 1:55:00 | 5:27 | 1:45:29 | 9.5 | inside |
| Marathon (42.195 km) | 42.1950 | 3:59:46 | 5:40 | 3:30:58 | 28.8 | OUTSIDE |
Riegel’s range of validity is a DURATION range, so it is a different distance range for every runner
| Your pace | 3.5 minutes is | 230 minutes is | Is the marathon inside it? |
|---|---|---|---|
| 3:00 per km — a fast club runner | 1.17 km | 76.7 km | Yes |
| 4:00 per km | 0.88 km | 57.5 km | Yes |
| 5:00 per km | 0.70 km | 46.0 km | Yes |
| 6:00 per km | 0.58 km | 38.3 km | No — beyond the range, and the prediction is extrapolation |
| 7:30 per km | 0.47 km | 30.7 km | No — beyond the range, and the prediction is extrapolation |
| 9:00 per km — a walk-run pace | 0.39 km | 25.6 km | No — beyond the range, and the prediction is extrapolation |
The arithmetic, and then the model with its limits stated
The unit conversions on this page are trivial and are not why it exists. A pace per mile is a pace per kilometre times 1.609344, which is exact; a speed is 3 600 divided by a pace in seconds per kilometre. What is worth having is the second half: what a pace means at other distances, according to a named model, with the model’s own limits stated instead of quietly ignored.
The model is Riegel’s. Peter Riegel published it in American Scientist in 1981 after fitting world-record performances in running, swimming and walking: the time for a distance goes as T₂ = T₁ × (D₂/D₁) raised to the power b, and for running b = 1.06. Double the distance and the time goes up by 2^1.06, about 2.08 rather than 2 — and that small excess, applied over and over, is the entire content of the model. From a 25:00 5K it predicts 3:59:46 for the marathon.
It has a stated range of validity and almost nobody quotes it. Riegel’s analysis concerns efforts “in the endurance range, namely lasting between 3.5 and 230 minutes”. That is a range of times, not of distances, and the difference matters enormously, because the same range covers different distances for different runners. At 3:00 per kilometre the model is inside its own validated window from 1.17 km to 76.7 km. At 7:30 per kilometre it runs only from 0.47 km to 30.7 km — which puts the marathon outside it. So a four-hour-plus marathoner predicting from a 10K is extrapolating past the end of the model, and this page says so rather than printing a number and looking confident. It computes the window for your pace and tells you whether the prediction you asked for falls inside it.
And where it fails, it fails in one direction. Vickers and Vertosick looked at 2 303 recreational endurance runners in 2016 and found that Riegel “dramatically underestimated marathon time, giving times at least 10 min too fast for half of runners” — their own models cut the mean squared error from 381 to around 210. The reason is not arithmetic: it is that the exponent was fitted to records set by people whose endurance matched their speed, and a recreational runner’s usually does not. Riegel himself gave different exponents for different groups, 1.05 to 1.06 for recreational men aged 40 to 70 against 1.08 for elites, and the exponent is an input on this page for exactly that reason. Moving it across his own range changes that marathon prediction by about 16 minutes.
Read the marathon number as a floor. That is the one piece of advice the evidence actually supports. If Riegel says 3:59:46 from your 5K, a sub-four is what you would run with marathon-specific endurance to match the speed you have demonstrated over five kilometres, and the honest planning assumption for a first marathon is ten to twenty minutes slower than that. The shorter predictions — 10K from 5K, half from 10K — are much better behaved, because they are interpolations inside the fitted range rather than extrapolations past its end.
The splits. The table under the chart gives kilometre-by-kilometre cumulative times for whichever distance you choose, both at the pace you entered and at the pace the Riegel equivalent would need. An even split is a model and not a plan: almost every recreational marathon is run with the second half slower than the first, and the fact that this happens to everybody is precisely why the endurance exponent is greater than one.
For the distances themselves: the mile is 1 609.344 m exactly, the half marathon 21.0975 km and the marathon 42.195 km, which is exactly twice the half to the metre. For gradients — because a hilly course is a different question and the pace model here assumes a flat one — the slope and grade converter handles per cent grades and their published limits.
Frequently asked questions
How do I convert min/km to min/mile?
Multiply by 1.609344, which is the number of kilometres in a mile and is exact, not a rounding — it follows from the international yard of 0.9144 m agreed in 1959. So 5:00 per kilometre is 5 × 1.609344 = 8.0467 minutes per mile, which is 8 minutes and 2.8 seconds. Going the other way, divide.
What pace do I need for a sub-four-hour marathon?
4 hours over 42.195 km is 5.688 minutes per kilometre — 5 minutes and 41.3 seconds — or 9.154 minutes per mile, at 10.549 km/h. Put the goal time in on this page and it gives you the pace and the kilometre splits.
How accurate is a race time predictor?
For the distance either side of the one you ran, reasonable. For a marathon predicted from a 5K, poor — and the research is specific about the direction of the error. Vickers and Vertosick studied 2,303 recreational endurance runners and found that Riegel’s formula “dramatically underestimated marathon time, giving times at least 10 min too fast for half of runners”, with their own models substantially outperforming it. The sensible way to read the marathon number on this page is as the time you would run if your endurance matched your speed, which for most people it does not.
What is Riegel’s formula?
T₂ = T₁ × (D₂/D₁)^1.06. Peter Riegel published it in American Scientist in 1981, from an analysis of world-record performances in running, swimming and walking, and 1.06 is the exponent he gave for running. It says that when you double the distance, the time rather more than doubles — by a factor of 2^1.06, about 2.08 — and that the excess is remarkably constant across distances. It is the model behind almost every race-equivalency table you will meet, usually without being named.
When does Riegel’s formula stop working?
Outside efforts of 3.5 to 230 minutes, which is the range Riegel himself stated — and the important thing about that is that it is a range of TIMES. Turned into distances it moves with the runner: at 3:00 per kilometre it covers 1.17 to 76.7 km, and at 7:30 per kilometre only 0.47 to 30.7 km, which leaves the marathon outside. This page computes your own window and says whether the prediction you asked for falls inside it. The model also assumes an athlete whose training is balanced across distances; Riegel himself gave different exponents for different groups — 1.05 to 1.06 for recreational men aged 40 to 70, 1.08 for elites — which is why the exponent is an input here.
Why does the exponent matter so much?
Because it is an exponent. Moving it across Riegel’s own published range of 1.05 to 1.08 changes a marathon predicted from a 25:00 5K by about 16 minutes. That is far larger than the difference between any two sensible pace calculators, and it is the honest reason predictions disagree: they are not using different arithmetic, they are using different exponents or a different model altogether.
What are the kilometre splits for my race?
The table under the chart on this page gives them for whichever distance you pick, at the pace you entered and at the pace your predicted equivalent needs. Worth saying plainly that an even split is a model rather than a plan: almost every recreational marathon is run with positive splits, the second half slower than the first, and the whole reason Riegel’s exponent is bigger than one is that this happens to everybody.
Related calculators
References
- Riegel PS. Athletic Records and Human Endurance: A time-vs.-distance equation describing world-record performances may be used to compare the relative endurance capabilities of various groups of people. American Scientist 1981;69(3):285–290. The source of T₂ = T₁ × (D₂/D₁)^b and of b = 1.06 for running. Riegel’s analysis concerns activities in the endurance range, namely those lasting between 3.5 and 230 minutes, and covers running, swimming and walking; he reported different exponents for different groups, including 1.05 to 1.06 for recreational men aged 40 to 70 and 1.08 for elite runners.
- Vickers AJ, Vertosick EA. An empirical study of race times in recreational endurance runners. BMC Sports Science, Medicine and Rehabilitation 2016;8:26. doi:10.1186/s13102-016-0052-y. 2,303 recreational endurance runners, split 2:1 into training and validation sets. The Riegel formula “dramatically underestimated marathon time, giving times at least 10 min too fast for half of runners”, with mean squared errors of 228 and 208 for their own models against 381 for Riegel. Also the finding that weekly training mileage and interval training had similar associations with velocity at all race distances.
- World Athletics competition rules for road-race distances: the half marathon is 21.0975 km and the marathon 42.195 km. The mile is 1 609.344 m exactly, which follows from the international yard of 0.9144 m agreed in 1959 by the national standards laboratories of the Commonwealth and the United States.
- National Institute of Standards and Technology. NIST Handbook 44, Appendix C, General Tables of Units of Measurement. The US liquid gallon is 231 cubic inches exactly and the international inch is 25.4 mm exactly; every volume on this page descends from those two definitions.
- Every identity on this page was round-tripped numerically rather than taken on trust, and Riegel’s equation was checked for composition — predicting 5K to 10K to marathon gives the same answer as 5K to marathon — and against a hand-worked example, in _c02b_proof.py.