Marathon in 3:30:00
- Solve for
- Pace
- Distance
- 42.195 km
- Finish time
- 3:30:00
- Pace and splits per
- Kilometre
- Pace per km
- 4 min 58 s
- Pace per mile
- 8 min
- Speed
- 12.06 km/h
Checked against: 12600 s ÷ 42.195 km; 12600 ÷ (42195/1609.344) mi; 42.195 ÷ 3.5 h
Running pace calculator
Running pace per km or mile from distance and time, or finish time or distance from pace, with even splits and Riegel race predictions.
By AdminDrafted with AI writing toolsUpdated Checked examples: 6
Pace per km
5 minper km
Pace per km: 5 min per km
- Pace per mile
- 8 min 2 sper mile
- Finish time
- 50 min
- Distance
- 10km
- Distance in miles
- 6.214mi
- Speed
- 12.00km/h
- Speed in miles per hour
- 7.46mph
- Predicted 5K
- 23 min 58 s
- Predicted 10K
- 50 min
- Predicted half marathon
- 1 h 50 min 19 s
- Predicted marathon
- 3 h 50 min
Race predictions assume training for the target distance; marathon times predicted from short races are usually optimistic.
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.
Riegel race predictions
Equal-effort pace by distance
Even splits per km
| 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 |
How it's calculated S
Pace per km
Speed
Riegel prediction (marathon)
Times are shown truncated to the second.
About the running pace calculator
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.
How to calculate running pace
Divide finish time by distance. A 10 km run in 50:00 is 5:00 per kilometer, which is 8:03 per mile and a speed of 12 km/h. Multiply pace by distance to get a finish time. This works for any steady run; predicting a different race distance needs the Riegel formula below.
Pace per kilometer and pace per mile
A mile is exactly 1.609344 km (NIST SP 811), so multiply a per-kilometer pace by 1.609344 to get pace per mile. 5:00 per km is 300 s × 1.609344 = 482.8 s, which rounds to 8:03 per mile.
Speed is the inverse of pace: km/h = 3,600 ÷ seconds per km. At 5:00 per km that is 3,600 ÷ 300 = 12 km/h, or 7.46 mph.
Mixing the two units is the usual slip. An 8:00 mile pace held for 5 km takes 24:51, because 5 km is 3.107 miles. At 8:00 per kilometer the same 5 km takes 40:00, so set the pace unit to miles before entering a per-mile pace.
Pace for common race goals
A half marathon is 21.0975 km and a marathon 42.195 km, the World Athletics road distances. The pace that finishes exactly on each goal time, to the nearest tenth of a second:
- 25:00 5K or 50:00 10K: 5:00.0 per km, 8:02.8 per mile
- 2:00:00 half marathon or 4:00:00 marathon: 5:41.3 per km, 9:09.2 per mile
- 3:30:00 marathon: 4:58.6 per km, 8:00.6 per mile
- 3:00:00 marathon: 4:16.0 per km, 6:51.9 per mile
The half and the full marathon share a pace because the half is exactly half the distance.
To beat a goal, round the pace down. The exact 3:00:00 pace is 4:15.95 per km, so a steady 4:16 finishes in 3:00:02, while 4:15 gives 2:59:20.
Finish time and distance from a pace
Finish time is pace × distance. At 5:00 per km a half marathon takes 300 s × 21.0975 = 6,329 s, or 1:45:29.
Distance is time ÷ pace. Running for 1:45:00 at 5:00 per km covers 6,300 ÷ 300 = 21 km, or 13.05 miles.
How the Riegel race predictor works
Peter Riegel's 1981 formula scales one race result to another distance: T₂ = T₁ × (D₂ ÷ D₁)^1.06 (Riegel 1981).
From 10 km in 50:00, a marathon is 3,000 s × 4.2195^1.06 = 3,000 × 4.600 = 13,801 s, about 3:50:00. The same 10K predicts a 1:50:19 half marathon.
The exponent above 1 builds in slowing. The predicted marathon works out at 5:27 per km against 5:00 for the 10K, while holding 10K pace all the way would give about 3 h 31 min.
Riegel fitted his exponent to world-record performances lasting roughly 3.5 to 230 minutes, so predictions from very short or very long efforts are less reliable.
Among 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.
Treat a marathon time predicted from a 5K or 10K as a best case that assumes training for the full distance.
Three worked cases
- Default: 10 km in 50:00.
- Marathon example: 42.195 km in 3:30:00.
- Mile pace to 5K: 5 km at 8:00 per mile.
Clock times are cut to whole seconds, and the last column is the Riegel marathon prediction from each run.
| Scenario | Pace per km | Reference finish time | Predicted marathon |
|---|---|---|---|
| Default | 5:00 | 50:00 | 3:50:00 |
| Marathon example | 4:58 | 3:30:00 | 3:30:00 |
| Mile pace to 5K | 4:58 | 24:51 | 3:58:23 |
A marathon predicts itself: the formula returns the reference time when the two distances match.
The 5K at 4:58 per km predicts a slower marathon than the 10K at 5:00 per km, because holding nearly the same pace for twice the distance is the stronger result.
Mistakes that change the answer
- Typing a decimal for seconds. A decimal is read as minutes, so 5.30 is 5 minutes 18 seconds. Enter 5:30 for five and a half minutes, and 3:30:00 for three and a half hours.
- Treating a displayed pace as exact. Each second per km is 42.2 seconds over a marathon. The 4:58 above for a 3:30:00 marathon is 4:58.6 cut to whole seconds; a true 4:58 pace finishes in 3:29:34.
- Reading a prediction as a pacing plan. Running a marathon at your 10K pace is a different, much harder target than the Riegel time.
Related calculators
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- Heart-rate zone calculator: training intensities
- Calories burned calculator: the energy a run uses
Worked examples
5K at 8:00 per mile
- Solve for
- Finish time
- Distance
- 5 km
- Pace and splits per
- Mile
- I know my
- Pace
- Pace
- 8:00
- Finish time
- 24 min 51 s
- Pace per km
- 4 min 58 s
Checked against: 480 s × 5000/1609.344 = 1491.2909 s
Distance from 1:45:00 at 5:00 per km
- Solve for
- Distance
- Finish time
- 1:45:00
- Pace and splits per
- Kilometre
- I know my
- Pace
- Pace
- 5:00
- Distance
- 21 km
- Distance in miles
- 13.049 mi
Checked against: 6300 s ÷ 300 s/km = 21 km = 13.04880 mi
Riegel predictions from 10 km in 50:00
- Solve for
- Pace
- Distance
- 10 km
- Finish time
- 50:00
- Pace and splits per
- Kilometre
- Predicted 5K
- 23 min 58 s
- Predicted 10K
- 50 min
- Predicted half marathon
- 1 h 50 min 19 s
- Predicted marathon
- 3 h 50 min
Checked against: 3000 × (D₂/10000)^1.06 for 5000, 21097.5 and 42195 m
Questions
How do you calculate running pace?
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.
What pace do you need for a sub-4-hour marathon?
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.
Are Riegel race time predictions reliable?
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.
How long is a marathon and a half marathon?
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.
About this calculator
Sources
- 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
For information only, not medical advice. These formulas describe populations, not you; talk to a clinician before acting on a result.
Checked against references
This calculator includes 6 worked examples with independently sourced answers. They run in the test suite, and you can run them here too.