Calculator
Choose what to work out (pace, finish time or distance), enter the other two in kilometres or miles, and the calculator gives your pace per km and per mile, your speed and your splits. Or switch to "Predict a race", enter a recent race you ran as hard as you could, and it predicts your 5K, 10K, 10-mile, half marathon and marathon times with Riegel's formula, the one most race predictors use. For the marathon, add your weekly running distance: Riegel's formula tends to run fast over 42.2 km, and a model that uses your mileage did better. Treat every prediction as a starting point, because hills, heat and training change it, and run easy days by the talk test, not a pace.
Choose what to work out and enter the other two values, in km or miles; "25:00" counts as minutes and seconds. To predict a race, enter one you ran as hard as you could in the last 6 months, and add your weekly running distance, or a second race, for a better marathon prediction.
5:00per km
5:00 per km, 8:03 per mile; 12 km/h or 7.46 mph; 50:00 for 10 km.
| Km | Time |
|---|---|
| 1 | 5:00 |
| 2 | 10:00 |
| 3 | 15:00 |
| 4 | 20:00 |
| 5 | 25:00 |
| 6 | 30:00 |
| 7 | 35:00 |
| 8 | 40:00 |
| 9 | 45:00 |
| 10 | 50:00 |
Easy runs: go by the talk test, not a pace. If you can talk comfortably in full sentences, you're at an easy pace. Zone 2 training
50 minutes for 10 km is 5:00 per km. A mile is exactly 1.609344 km, so pace per mile is pace per km × 1.609344: 8:03 per mile here (our arithmetic). A marathon is 42.195 km, and a half marathon is exactly half, 21.0975 km.
Predicted time = your time × (new distance ÷ your distance)^1.06, with an exponent taken from world records. Each time the distance doubles, the predicted pace slows by about 4% (our arithmetic).
In 2,303 recreational runners, Riegel's formula was right on average for the 10K and half marathon, but for the marathon it was 10 minutes or more too fast for half of them. For one runner, a prediction of any distance is often 5 to 10% out (our reading).
A model that adds your typical weekly mileage to one or two recent races cut the marathon errors, and halved the share of runners predicted 10 minutes or more too fast. The calculator uses it when you give your mileage.
Source 6
Recreational marathoners who start too fast are the most likely to slow sharply later, and recent marathon world records were run at an even pace. An even effort is the safe plan.
Runners slow as it gets warmer and on hills, and no formula can tell one runner by how much, so run those by effort. Easy runs go by the talk test: if you can talk in full sentences, you're at an easy pace.
The presets are World Athletics' standard road distances: the mile (1,609.344 m), 5 km, 10 km, 10 miles (16,093.44 m), the half marathon (21.0975 km, "exactly half the length of a marathon") and the marathon (42.195 km, or 26 miles 385 yards, a distance fixed in 1921). The mile is the UK's legal mile of 1,760 yards, each 0.9144 m.
Road courses are measured "along the shortest possible route that an athlete could follow" and must not be shorter than the official distance, and World Athletics recommends laying them out 0.1% long: 1,001 m for every km. Few runners hold the shortest line, so a watch usually reads a little over. The calculator uses the official distance (our choice).
Pace per km = time ÷ distance in km, and pace per mile = pace per km × 1.609344. Speed in km/h = 3,600 ÷ pace in seconds per km, and miles per hour (mph) = km/h ÷ 1.609344. Finish time = pace × distance.
Paces and times are shown to the second, and speeds to two decimal places (our choice). The splits table, folded under the result, gives your time at the end of each km or mile at an even pace, with the last part-km or part-mile worked out in proportion.
Examples (our arithmetic): 10 km in 50:00 is 5:00 per km, 8:03 per mile, 12 km/h and 7.46 mph. A marathon at 6:00 per km takes 4:13:10, which is 9:39 per mile, and a half marathon at 9:00 per mile takes 1:57:59, which is 5:36 per km.
Source 1
Predicted time = your race time × (new distance ÷ your race distance)^1.06. It goes back to Riegel's 1977 article in Runner's World magazine, and fixes the exponent at 1.06, "derived from world-record performances". By another study's account, Riegel's 1981 paper gave about 1.08 for elite runners and 1.05 to 1.06 for male recreational runners aged 40 to 70. We couldn't open either of Riegel's own papers, so these details come from the two studies cited here.
Doubling the distance multiplies the time by 2^1.06, about 2.085, so the predicted pace slows by about 4% each time the distance doubles (our arithmetic). The calculator predicts the 5K, 10K, 10 miles, half marathon and marathon, leaving out the race or races you entered.
Add your typical weekly running distance, from a race between 5K and the half marathon (the distances the models were built from), and the calculator uses Vickers and Vertosick's models, built in 2,303 recreational runners. Distances go in as metres, times as seconds and mileage as miles a week (the calculator converts km), and the marathon time comes out in minutes. With one race, model 1:
Source 6
With two recent races between 5K and the half marathon, a shorter and a longer one, the calculator uses model 2, which works out how much you slowed between them:
Source 6
Without your weekly distance, or from a race outside 5K to the half marathon, the calculator shows Riegel's marathon time, labelled likely too fast: in one large study it was 10 minutes or more too fast for half of recreational runners. Vickers and Vertosick's models can also adjust a race run on a difficult or fast course; the calculator assumes an average course and doesn't use those adjustments.
Source 6
Predicted times under an hour are shown to the second, and longer ones rounded to the minute, as the calculator shows them.
Most calculators use Riegel's exponent of 1.06. Vickers and Vertosick tested 1.07, which was well calibrated up to the half marathon in their runners; up to that distance the two give times within about 1% of each other (our arithmetic), so the calculator keeps the published 1.06. Daniels' VDOT tables are a different system, built from his own equations; we couldn't check the printed tables, so this calculator doesn't use them.
In UK law a mile is 1,760 yards and a yard is 0.9144 m, so a mile is 1,609.344 m, the length World Athletics gives its road mile. World Athletics lists the marathon as 42.195 km and describes the half marathon as exactly half, 21.0975 km or 13.1094 miles.
In the formula as practitioners use it, the exponent is fixed at 1.06, "derived from world-record performances". One study reports that Riegel's 1981 paper analysed world records across several endurance sports, and gave about 1.08 for elite runners and 1.05 to 1.06 for male recreational runners aged 40 to 70. His own papers couldn't be checked.
In 2,303 recreational runners (39% women, median age 35, typically running 30 miles a week), the formula with an exponent of 1.07 was well calibrated for the 10K and the half marathon. For the marathon it gave times "at least 10 min too fast for half of runners", and more than 20 minutes too fast for nearly a quarter. In a model fitted to 164,746 British club runners, the typical runner slowed with distance more than world-record holders do (an exponent of about 1.12).
The recreational runners reported their own times, and were younger and faster than a typical big-city marathon field.
Tested on races it hadn't seen, Riegel's formula had a typical error of about 10% of the time in British club runners, or about 7% in the fastest quarter of them (our arithmetic from the published errors). In 7,663 runners who ran a half marathon and then a marathon in Valencia, a simple model using the half-marathon time and sex was out by 5.7% on average. A review of 114 marathon prediction equations found no single best one, with standard errors from 0.27 to 27.4 minutes, and many ignored hills, sex and weather.
In the 156 runners used to test them, Vickers and Vertosick's models had mean squared errors of 228 and 208 against 381 for Riegel's formula, typical errors of about 15 and 14 minutes against 19.5 (our arithmetic), and the share predicted 10 minutes or more too fast fell from about half to about a quarter. For the middle half of runners, model 1 ranged from about 10 minutes too fast to 6.5 minutes too slow.
Other training-based models did well in the runners they were built on and less well elsewhere: one equation from weekly distance and training pace had a standard error of 4 minutes in its own 46 runners and about 17 in another group, and critical speed worked out from logged training was about 7.7% out.
Daniels' VDOT tables predicted the Valencia marathon from the half marathon to within about 1 to 2% for runners finishing in under 3 hours, but 10 to 18% out for those taking 5 to 6 hours, and 7.9% on average. The VDOT score blends VO2 max (the most oxygen your body can use in all-out exercise) with running economy, and in 20 runners it read lower than their lab-measured VO2 max.
A review suggests that in events longer than about 2 minutes, a more even pace may improve times, and recent marathon world records were run at a very even pace. In big-city marathons, men slowed more than women and slower runners slowed most, and runners who ran the first half faster than about 94% of their critical speed were more likely to slow by more than 25%. Pacing a race, below, has the detail.
Marathon times slowed step by step as the weather warmed, more for slower runners, and more runners dropped out in the heat. On an undulating course, experienced runners went 23% slower uphill and about 14% faster downhill. Neither effect can be predicted for one runner, so the calculator assumes a flat course on a cool day.
The point where speech first gets harder matches your first breathing threshold, it follows that threshold as your fitness changes, and in 16 active volunteers it set the pace of 30-minute runs on its own. A pace formula can't track any of that.
The splits table shows even splits. These notes say why.
In 32 men's 5,000 m and 34 men's 10,000 m world records, the first and last km were faster than the middle ones, "resulting in an overall even pace with an end spurt". Recent marathon world records were evenly paced, while championship marathons were run faster in the first half than the second. Across 50 years of marathon records, the authors concluded that very little change of speed "may be the way to go".
In 319 runners on a looped course in cold weather, older runners, women and faster runners paced more evenly. In 91,929 finishes in 14 US marathons, men slowed by 15.6% in the second half and women by 11.7%, and slower finishers slowed more. In 1.9 million race records, 28% of men and 17% of women "hit the wall", slowing by 25% or more for at least 5 km, at a cost of about half an hour against their recent best. Runners who ran the first half too fast for their fitness were the most likely to slow sharply.
In 11 moderately trained women, running the first 1.63 km of a 5 km time trial 3% or 6% faster than their average pace didn't change the finish time significantly (21:11 for the even start, 20:52 and 20:39 for the faster ones), and 8 of the 11 ran their fastest with the 6% start. One small treadmill study isn't enough to recommend a fast start.
Source 28
Aim for an even effort. In a marathon, start at your goal pace or a little slower and don't try to bank time; a slightly faster second half is fine. A review of elite racing advises runners with modest goals to start at a realistic pace and stay with a group. Over 5K, a first km a little quicker than goal pace is unlikely to cost you, on the limited evidence.
In seven marathons over up to 36 years, the leading men were 1.7% slower than the course record on the coolest race days and 4.5% slower on the warmest (wet bulb globe temperatures, a heat index that also counts humidity and sun, of 5 to 10°C against 20 to 25°C), and slower runners were "more negatively affected". In 1,791,972 finishes at six big marathons, average speeds were highest at air temperatures of about 4 to 10°C, and more runners dropped out as it got warmer. In 1,258 elite races, each degree of heat outside the best range cost 0.3 to 0.4%.
The UK's National Health Service (NHS) lists people who "spend a lot of time outside, particularly if they're physically active, such as runners, cyclists and walkers" among those more at risk in a heatwave. Its advice: "Keep out of the heat if you can. If you have to go outside, stay in the shade especially between 11am and 3pm", "avoid exercise or activity that makes you hotter", and drink extra fluids. To prevent heat exhaustion, it suggests more cold drinks "especially if you're active or exercising", light, loose clothing and avoiding extreme exercise.
The NHS lists the signs of heat exhaustion: tiredness, dizziness, headache, feeling or being sick, heavy sweating with pale, clammy skin, cramps in the arms, legs and stomach, a high temperature, being very thirsty and feeling irritable. Move to a cool place, take off unnecessary clothing, drink water or a sports drink and cool your skin; you should start to feel better within 30 minutes.
Source 29
Eight experienced runners on an undulating course ran 23% slower uphill and 13.8% faster downhill than on the flat, working at about their breathing threshold on the climbs and well below it on the descents. The authors suggest that the most time is saved by getting back up to speed on the flat after a hill. On a treadmill, the energy cost of running rose more than fivefold at the steepest uphill slope tested and was lowest at a 20% downhill slope.
Every prediction assumes a flat course on a cool day, and that you've trained for the distance. There's no heat or hill correction, because nothing in the evidence tells one runner how much to slow (our reading). In very hot, humid weather, the US activity guidelines suggest exercising "in the cool of early morning" and lowering the intensity, for example "walking rather than running". On hot days and hilly courses, run by effort.
Source 31
After at least 5 minutes at a steady pace, say a couple of sentences out loud (our suggestion, as in our zone 2 guide). The point where speech first gets harder matched the first breathing threshold on treadmills and bikes, kept matching it when training raised the threshold, and in 16 active volunteers set the pace of 30-minute runs on its own:
No pace formula knows where your threshold is, and your easy pace shifts with heat, hills, sleep and tiredness, while the talk test moves with you (our reading). In 20 runners, a widely used calculator's training paces matched lab measures for some runners but not others. Our zone 2 guide covers easy running in more detail.
The NHS Couch to 5K plan starts with 1-minute runs and 90-second walks, 3 times a week, and builds to 30 minutes of running over 9 weeks or longer. Speak to a GP first if you're worried about your health, or if you haven't exercised for some time or have a medical condition.
In 874 new runners, those who raised their weekly distance by more than 30% over 2 weeks had more distance-related injuries than those who raised it by under 10%, though the result was uncertain and the study exploratory. A graded 13-week programme built on the 10% rule didn't reduce injuries in 532 new runners (20.8% against 20.3%). Build up gradually, without a fixed rule (our reading, as in our zone 2 guide).
Across 13 studies, new runners had 17.8 running injuries per 1,000 hours of running and recreational runners 7.7. Two strength sessions a week are the core of our strength training plan for runners.
Source 36
The NHS says it's not recommended to start a new vigorous activity in pregnancy, such as running, and that if you've been running you may find brisk walking more comfortable instead. After giving birth, our postnatal guide covers when and how to return to running.
Source 37
An even pace the whole way: paces and times to the second, speeds to two decimal places.
With a mile of 1.609344 km, a half marathon of 21.0975 km and a marathon of 42.195 km:
Predictions need a race you ran as hard as you could, and a training run isn't one. Start with a walk-run plan such as the NHS Couch to 5K, and use our zone 2 guide for easy pace.
Source 32
The models were built on road races from 5K to the marathon, and hills change speed a lot, so the calculator doesn't predict these. Run them by effort.
Predictions assume a cool day. In the heat, start slower and follow the NHS heat advice above.
The NHS advises against starting running in pregnancy. Our exercise in pregnancy guide covers what suits you.
Source 37
A return to running usually waits about 3 months, a rule based on expert opinion; our postnatal guide has the checks to do first.
A race time from before an injury doesn't reflect your fitness now (our reading). Our pain guides cover building back up.
The marathon models were built in adult recreational runners, so the calculator isn't for children's races.
Source 6
Riegel's exponent comes from world records. In British club runners the typical runner slowed with distance more than world-record holders do, and in recreational runners its marathon predictions were too fast for most of them.
Runners who start too fast are the most likely to slow sharply later, and hitting the wall cost recreational runners about half an hour against their recent best.
Recent marathon world records were run at an even pace, championship marathons were run faster in the first half, and in one small 5K study a quick start didn't hurt. We found no trial in recreational runners showing that a negative split beats an even pace; an even effort with a slightly faster finish is a safe plan.
It's a race-based score that blends VO2 max with running economy, and in 20 runners it read lower than their lab-measured VO2 max.
Easy is a feeling. The talk test tracks your own breathing threshold, and no formula knows where that is.
Courses are measured along the shortest possible route, and World Athletics recommends adding 0.1%, so most runners cover, and their watches record, a little more than the official distance.
Source 2
A 13-week programme built on it didn't reduce injuries in 532 new runners, though very fast increases in weekly distance may add risk.
The warm-up gets your ankles, hips and calves ready before a run. The two strength sessions are the gym and home workouts from our strength training plan for runners, and the stretches are for comfort after a run.
An 8-minute dynamic warm-up for runners: ankle and hip mobility, lunges, skips and pogo hops.
8 minIntermediate8 movesA wallA 45-minute gym strength workout for runners: hops, heavy squats, Bulgarian split squats, calf raises and side planks, with sets, reps and rest.
45 minIntermediate13 movesA wall, A bench or boxA 40-minute strength workout for runners at home: hops, Bulgarian split squats, single-leg deadlifts, step-ups, calf raises and side planks.
40 minIntermediate15 movesA wall, A bench or boxSeven stretches for after a run: calves, soleus, quads, hip flexors, hamstrings and glutes.
10 minBeginner7 movesA wallDivide your time by the distance: 50 minutes for 10 km is 5:00 per km. To turn it into minutes per mile, multiply by 1.609344, which gives 8:03 per mile, and your speed is 12 km/h. Choose "My pace" in the calculator, enter your distance and time, and it shows all three with your splits.
A marathon is 42.195 km, or 26 miles 385 yards, a distance fixed in 1921. A half marathon is exactly half: 21.0975 km, or 13.1094 miles. Courses are measured along the shortest possible line, so your watch will usually read a little over.
For one runner they're often 5 to 10% out. In 2,303 recreational runners, Riegel's formula was right on average for the 10K and half marathon, but for the marathon it was 10 minutes or more too fast for half of them. That's why the calculator asks for your weekly mileage before it predicts a marathon.
Riegel's formula assumes you slow down over longer distances like a world-record holder, and most recreational runners slow more in the last 10 km. A model that adds your weekly mileage did better: from a 1:45 half marathon on 30 miles a week it predicts about 3:54, not Riegel's 3:39. Add your weekly distance to the calculator to use it.
It's predicted time = your time × (new distance ÷ your distance)^1.06, the formula most race predictors use, with an exponent taken from world records. From a 50-minute 10K it predicts a 1:50 half marathon. It's fair on average up to the half, but tends to be too fast for the marathon.
No. VDOT tables come from equations Daniels and Gilbert published in 1979, and we couldn't check the printed tables against them. In 7,663 Valencia runners, the tables predicted the marathon from the half to within about 1 to 2% for runners under 3 hours, but 10 to 18% out for those taking 5 to 6 hours.
Aim for an even effort and don't try to bank time: in big-city marathons, runners who started too fast were the most likely to slow sharply. Recent marathon world records were run at an even pace, and a slightly faster finish is fine. Over 5K, a first mile a little quicker than average pace didn't slow trained women in one small study.
There's no reliable formula for one runner, but marathon times slow steadily as it gets warmer, and slower runners slow most. Start slower and run by effort. In a heatwave the NHS advises avoiding exercise that makes you hotter, especially between 11am and 3pm, and drinking extra fluids.
In one study, experienced runners went 23% slower uphill and 14% faster downhill. Keep your effort even rather than your pace, and use the flat after a hill to get back up to speed. The calculator's predictions assume a flat course.
No formula can tell you: use the talk test. If you can talk comfortably in full sentences, you're at an easy pace, and once talking gets harder you've reached the top of it. In a study, the talk test alone set the pace of 30-minute runs.
Estimates for healthy adults, not a personal prescription or a diagnosis, and clinical review of these pages is pending. Check with a GP before hard training or testing a maximum if you have a heart condition, high blood pressure, chest pain, dizziness or breathlessness when active, and stop for sharp or increasing pain. Health disclaimer.
