How to use it
- Under Calculate, choose what you want to find: Pace, Time, Distance, or From treadmill speed.
- Enter the Distance and pick km or mi, or tap 5K, 10K, Half marathon or Marathon.
- Type the Time as h:mm:ss, or the Pace as min:sec and choose per km or per mi.
- For a treadmill, pick From treadmill speed and type the Treadmill speed in km/h or mph.
- Read pace per km and per mile, speed, the race table (same pace and Riegel estimate), the splits and the treadmill chart. They update as you type.
How the calculation works
Pace is time divided by distance: pace = time ÷ distance. Speed is the reverse: speed = distance ÷ time. One mile is exactly 1.609344 km, the factor NIST lists for the international mile, so pace per mile is pace per km × 1.609344.
The quick buttons use the official race lengths. World Athletics gives the marathon as 42.195 km (26 miles 385 yards) and the half marathon as exactly half of it, 21.0975 km.
Race time estimates use Peter Riegel's endurance formula: T2 = T1 × (D2 ÷ D1)^1.06. T1 and D1 are the time and distance you entered; D2 is the race you want an estimate for.
| Result | Value |
|---|---|
| Pace | 5:00 per km · 8:03 per mi |
| Speed | 12.0 km/h · 7.5 mph |
| 5K estimate | 23:59 |
| Half marathon estimate (21.0975 km) | 1:50:19 |
| Marathon estimate (42.195 km) | 3:50:01 |
How accurate is this?
Pace, time, distance, speed and the treadmill chart are exact arithmetic: 60 minutes divided by the speed gives the pace. A treadmill's own speed display can be off, and the chart does not adjust for incline.
The race table shows two columns. "At the same pace" just multiplies your pace by each distance. The Riegel estimate adds the slowing that Riegel found in world-record performances. Vickers and Vertosick (2016) found that for recreational runners the marathon came out slower than Riegel predicts, so treat long-range estimates as optimistic.
Pace for common goal times
Even pace needed for popular half marathon and marathon goals. A marathon in 3:30 needs exactly the same pace as a half marathon in 1:45, because the distance is double.
| Goal | Pace per km | Pace per mile |
|---|---|---|
| Half marathon in 1:30:00 | 4:16 /km | 6:52 /mi |
| Half marathon in 1:45:00 | 4:59 /km | 8:01 /mi |
| Half marathon in 2:00:00 | 5:41 /km | 9:09 /mi |
| Half marathon in 2:15:00 | 6:24 /km | 10:18 /mi |
| Half marathon in 2:30:00 | 7:07 /km | 11:27 /mi |
| Marathon in 3:00:00 | 4:16 /km | 6:52 /mi |
| Marathon in 3:30:00 | 4:59 /km | 8:01 /mi |
| Marathon in 4:00:00 | 5:41 /km | 9:09 /mi |
| Marathon in 4:30:00 | 6:24 /km | 10:18 /mi |
| Marathon in 5:00:00 | 7:07 /km | 11:27 /mi |
How well does Riegel's formula do at the very top? The race predictions vs world records page checks it against the current world records.
Where the 1.06 exponent comes from
Riegel described the time–distance rule as t = a × x^b in "Athletic Records and Human Endurance" (American Scientist, 1981). He called the exponent b the "fatigue factor": how much slower you get as the distance grows.
For world running records, that article fitted about 1.08 (1.077 for men, 1.083 for women). For masters age groups, the values were lower, about 1.05 to 1.06. The calculator uses 1.06; Vickers and Vertosick (2016) note that the Runner's World online calculator uses the same constant.
The exponent matters more the farther you project. From the same 10 km in 50:00, an exponent of 1.08 gives a half marathon of 1:51:59 and a marathon of 3:56:44.
Limits of race time estimates
Riegel's article says the pattern holds from about 3.5 to 230 minutes of running. Outside that range, the estimates lose their footing.
A 2016 study by Vickers and Vertosick in recreational runners found the formula reasonably accurate up to the half marathon. For the marathon, it gave times at least 10 minutes too fast for half of the runners.
An estimate also assumes similar training for each distance, a similar course and similar weather. Treat it as a reference point, not a forecast.
Using the split table
The split table lists the running time at each kilometer or mile at an even pace. At 5:00 per km, you pass 1 km at 5:00, 5 km at 25:00 and 10 km at 50:00. In miles, the same run passes mile 1 at 8:03 and covers 6.21 mi in total.
Running by heart rate instead of pace? The heart rate zone calculator turns your age and resting rate into five zones.
Questions
- How do I convert pace per km to pace per mile?
- Multiply by 1.609344. A pace of 5:00 per km is 300 seconds × 1.609344 = 483 seconds, or 8:03 per mile.
- How long is a half marathon exactly?
- 21.0975 km, or about 13.11 miles. It is half of the 42.195 km marathon, the distance World Athletics uses.
- Why does the marathon estimate look fast?
- The formula uses one fixed fatigue factor. In a 2016 study of recreational runners, it predicted marathon times at least 10 minutes too fast for half of them. A small change in the exponent also moves a long projection by several minutes.
- Which race should I enter for the best estimate?
- The closer the two distances, the less the exponent matters. Doubling a half marathon to a marathon is a smaller jump than multiplying a 5K by more than eight.
- Can I enter pace and get distance?
- Yes. Set Calculate to Distance, then enter a Time and a Pace.
- How do I convert treadmill speed to pace?
- Divide 60 by the speed. At 10 km/h, 60 ÷ 10 = 6 minutes per km; at 6 mph, 60 ÷ 6 = 10 minutes per mile. Choose From treadmill speed to do it here, or open the treadmill chart under any result.