Running pace per km or mile from distance and time, or finish time or distance from pace, with even splits and Riegel race predictions.
Covering 10 km in 50:00 is a pace of 5:00 per km (8:03 per mile), 12 km/h. The same effort predicts about 3:50:00 for a marathon.
| Split | Distance (km) | Split time | Elapsed |
|---|---|---|---|
| 1 | 1 | 5 min | 5 min |
| 2 | 2 | 5 min | 10 min |
| 3 | 3 | 5 min | 15 min |
| 4 | 4 | 5 min | 20 min |
| 5 | 5 | 5 min | 25 min |
| 6 | 6 | 5 min | 30 min |
| 7 | 7 | 5 min | 35 min |
| 8 | 8 | 5 min | 40 min |
| 9 | 9 | 5 min | 45 min |
| 10 | 10 | 5 min | 50 min |
Times are shown truncated to the second.
Pace is finish time divided by distance, shown per kilometre and per mile; enter two of distance, time and pace (or speed) to get the third. Race predictions use Peter Riegel's 1981 formula, T₂ = T₁ × (D₂ ÷ D₁)^1.06, which scales one result to the 5K, 10K, half marathon and marathon. Even splits are listed per kilometre or mile.
Runners use it to plan race pacing and training targets. The default 10 km in 50:00 is 5:00 per km, 8:03 per mile or 12 km/h, and Riegel's formula turns it into a 23:58 5K, a 1:50:19 half marathon and a 3:50:00 marathon.
Riegel predictions assume equal preparation for each distance. In a study of 2,303 recreational runners, Vickers and Vertosick (2016) found the formula well calibrated up to the half marathon but at least 10 minutes too fast at the marathon for half of them.
Checked against: Python 3.8 decimal: 12600 s ÷ 42.195 km; 12600 ÷ (42195/1609.344) mi; 42.195 ÷ 3.5 h
Checked against: Python 3.8 decimal: 480 s × 5000/1609.344 = 1491.2909 s
Checked against: Python 3.8 decimal: 6300 s ÷ 300 s/km = 21 km = 13.04880 mi
Checked against: Python 3.8 decimal: 3000 × (D₂/10000)^1.06 for 5000, 21097.5 and 42195 m
Divide finish time by distance. A 10 km run in 50 minutes is 50 ÷ 10 = 5:00 per km; the same run is 6.214 miles, so the pace is 8:03 per mile. Speed is the inverse: 60 ÷ 5 = 12 km/h. One mile is exactly 1.609344 km (NIST SP 811), the factor used to switch between per-kilometre and per-mile pace.
Faster than 5:41 per km, or 9:09 per mile, held for all 42.195 km: 14,400 s ÷ 42.195 km = 341.3 s per km. A sub-2-hour half marathon needs exactly the same pace, because 21.0975 km is half the marathon distance. Any time lost at aid stations or on a slow start has to be made up with faster running later.
Up to the half marathon, mostly. Vickers and Vertosick's 2016 study of 2,303 recreational runners found Riegel's formula well calibrated to that distance but too optimistic for the marathon, giving times at least 10 minutes too fast for half the runners. Their own models, which used training data and prior races, cut the marathon prediction error by about 40 %. Riegel fitted his 1.06 exponent to world-record performances.
A marathon is 42.195 km (26.219 miles) and a half marathon is 21.0975 km (13.109 miles), the standard road distances in World Athletics rules. At an even 5:00 per km they take about 3 h 31 min and 1 h 45 min. Use the distance presets to fill in these exact values.
Accuracy depends on your inputs and the method's assumptions. Decimal arithmetic uses 50 significant digits, but estimates, numerical methods and source data can be less precise; the displayed rounding does not remove those limits. It is checked against 6 worked examples whose answers come from independent sources; for example, “Marathon in 3:30:00” is checked against Python 3.8 decimal: 12600 s ÷ 42.195 km; 12600 ÷ (42195/1609.344) mi; 42.195 ÷ 3.5 h.
Riegel PS. Athletic records and human endurance. American Scientist 1981;69(3):285–290; World Athletics Competition Rules — standard road distances: half marathon 21.0975 km, marathon 42.195 km; NIST SP 811 — 1 mile = 1609.344 m exactly.
6 worked examples with independently sourced answers ship with this calculator. They run in the test suite; you can run them here too.
Heart rate zones from your maximum heart rate (220 − age, Tanaka, Gulati for women, or measured) by the Karvonen or percent-of-max method, with a target heart rate.
VO2 max from the Cooper 12-minute run, the Rockport 1-mile walk or the resting heart-rate ratio, rated against Cooper Institute norms for age and sex.
Calories burned by an activity from its MET value in the Compendium of Physical Activities, your body weight and the time spent.
Cycling power-to-weight (W/kg), speed and pace, or swimming pace per 100 m and 100 yd with your SWOLF score.
One-rep max (1RM) from a set of reps with the Epley, Brzycki, Lombardi and O'Conner equations, plus training loads from 50 % to 100 %.
Steps to distance in km and miles from a step length based on your height or measured, with walking time and calories from the ACSM equation.
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