Half Marathon Time Predictor

A 50-minute 10K points to a half marathon of about 1:51; a 25-minute 5K, about 1:57

If you ran a recent 10K in 50:00, your predicted half marathon time (21.0975 km, or 13.1094 miles) is 1:51:09, an average of 8:29 per mile. A 5K in 25:00 gives 1:56:40, or 8:54 per mile. Both figures come from Riegel's formula with an exponent of 1.07, the average value that a study of the race times of 2,303 recreational runners chose for the formula. Moving the exponent between 1.06 and 1.08 shifts the 10K-based prediction between 1:50:19 and 1:51:59, and the 5K-based one between 1:55:00 and 1:58:22. The closer the source distance is to the half marathon, the narrower that spread gets.

The calculator above takes up to three recent times, shows the half marathon prediction from each one at the end of its row, and builds the main prediction and range from the time closest to the half. Set a goal such as sub-2 and it works backward to the 5K and 10K times you need, then shows how far a goal pacer would be from you at the finish line, with a drawing and a checkpoint table. Enter your usual weekly mileage and it also predicts a marathon with the adjusted formula from the research. If all you need is one time converted to several distances, the Running Pace Calculator is simpler.

Why predict your half marathon time in advance

A half marathon is more than twice as long as a 10K. Start at your 10K pace and you will probably fade badly in the second half; start too slowly and you cross the line with energy left over. Knowing the predicted time from your current fitness helps you choose a starting pace, and it shows in minutes and seconds how far a goal is from where you are now.

• Before signing up for a first half marathon: use your 5K and 10K times to estimate a finishing time and compare it with the race's time limit.
• When chasing sub-2 (under 2 hours): pick the sub-2 goal chip and you will see that you need a 10K in 53:58 or faster, or a 5K in 25:42 or faster.
• Checking progress mid-training: enter new 5K and 10K times every few weeks and see how much the half marathon prediction has dropped.
• Thinking about a marathon after a half: enter your half time and weekly mileage to see how far the marathon prediction lands above double your half time.

How to use the calculator

1. Enter recent times: choose a distance and enter the time in hours, minutes and seconds. If you leave the hours box empty, minutes can go above 59 (for example, 53 minutes = 53). The "Add a time" button lets you enter up to three.
2. Check the anchor time: among the times that are not a half marathon, the one with the longest distance is marked "Anchor", and the big number is the half marathon prediction from that time. Each row also shows the half marathon prediction from its own time.
3. Enter weekly distance (marathon): enter how far you usually run in a week and the marathon prediction switches to the adjusted formula from the research. Leave it empty and you only get the Riegel value.
4. Set a goal: enter a goal half marathon time or tap a chip to see the 5K and 10K times that fit it, plus the goal pace. Goals are always treated as "under this time".
5. Watch the finish line: you and the goal pacer each run at an even pace, and you see checkpoint times and the gap at the finish. "Make a pace plan from this time" opens the Marathon Pace Calculator with the same time, where you can build a split plan and a wrist pace band.

How it works: Riegel's formula and the 1.07 exponent

Half marathon time = time × (21.0975 ÷ distance of that time)^1.07

In a 1981 paper, Riegel showed that endurance records from about 3.5 to 230 minutes follow a power-law relationship between distance and time. The exponents he calculated from running world records were 1.07732 for men and 1.08283 for women, and 1.05 to 1.06 for men aged 40 to 70. An exponent above 1 means that when the distance doubles, the time more than doubles; with 1.07, doubling the distance multiplies the time by 2^1.07, about 2.10.

This calculator uses 1.07. Vickers and Vertosick (2016) did not measure 1.07 from their data: they chose it as an average value between the 1.08 Riegel gave for elite runners and the 1.05 to 1.06 he gave for recreational men aged 40 to 70. They then tested Riegel's formula on the race times of 2,303 recreational runners collected in an online survey, checking the sensitivity at 1.06 and 1.08. The formula predicted 10K and half marathon times well, but for the marathon it was 10 minutes or more too fast for half of the runners. So the half marathon uses Riegel's formula, and the marathon uses the adjusted formula described below.

When you enter several times, the anchor is the longest one that is not a half marathon. The same paper also used the longest time other than the half marathon when it checked half marathon predictions. The closer the distance is to the half, the less a small difference in the exponent spreads into the result. Changing the exponent from 1.06 to 1.08 moves the prediction from a 25-minute 5K by 3 minutes 22 seconds, but the prediction from a 50-minute 10K by only 1 minute 40 seconds. If two times are at the same distance, the faster one is used.

All calculations are done in seconds and kilometers, and the screen rounds to the second. The band on the finish-time ruler runs between the anchor time with exponents 1.06 and 1.08, and the small dots are the other times with 1.07. The band only shows how far the result moves when the exponent changes; it is not a calculated range of probability.

Half marathon predictions by 5K and 10K time

Average pace is the predicted half marathon time divided by 13.1094 miles. A 5K in 25:00 and a 10K in 50:00 are both 5:00 per kilometer, yet their half marathon predictions differ by 5 minutes 31 seconds, because the 5:00 pace was held over different distances.

The 5K and 10K times you need for sub-2 and other goals

Sub-2 means running a half marathon in under 2 hours, that is, 1:59:59 or faster. The calculator treats every goal as "under this time", and it shows the required time as the slowest time to the second whose half marathon prediction, recalculated from that time, still falls inside the goal. For example, a 10K in 53:58 predicts 1:59:58, while one second slower, 53:59, predicts 2:00:00, which is not under 2 hours.

The goal pace follows the same rule. Dividing 7,200 seconds by 21.0975 km gives 341.27 seconds per kilometer, or 5:41.27 per kilometer, which is 9:09 per mile or faster. Running 5:41 per kilometer all the way finishes in 1:59:54, but 5:42 per kilometer gives 2:00:15, which misses sub-2. Crowded starts and time lost at aid stations are not included, so in a real race it is safer to leave some margin.

Personal exponent: how much you slow down as the distance grows

When you enter two or more times at different distances, the calculator works out a personal exponent from the shortest and the longest. The formula is ln(longer time ÷ shorter time) ÷ ln(longer distance ÷ shorter distance). A 5K in 25:00 and a 10K in 53:00 give ln(3,180 ÷ 1,500) ÷ ln 2 = 1.084, which is above 1.07, so you tend to slow down a little more as the distance grows. The two distances must differ by a factor of 1.2 or more for the calculation to run, and a value below 1.00 or above 1.30 is flagged separately, because the two times were probably not run at the same effort. This range is not a value taken from research; it is this calculator's own criterion.

It might seem that stretching your own exponent out to the half marathon would be more accurate, but the research says otherwise. Blythe and Király (2016) analyzed a large set of race records and reported a median individual exponent of 1.12 (5th to 95th percentile: 1.10 to 1.15), higher than Riegel's. Yet predictions that fit an exponent to each person (log-time RMSE 0.1033) were no better than Riegel's formula with one fixed exponent (0.0982). Two times also carry differences in weather, course and how you felt that day. So the calculator does not use the personal exponent for the half marathon prediction; it shows it as a reference and feeds it only into the marathon formula.

A marathon prediction is not double your half marathon time

In the data of Vickers and Vertosick (2016), Riegel's formula with an exponent of 1.07 predicted marathon times 10 minutes or more too fast for half of the runners, and 20 minutes or more too fast for about 25%. The median gap between prediction and actual time was 10 minutes 9 seconds. The authors built two formulas that also take usual weekly running distance into account, and on the same validation data the mean squared error fell from 380.7 for Riegel's formula to 227.6 (formula 1) and 208.3 (formula 2).

Marathon exponent = 1.4510756 − 0.23797948 × personal exponent − 0.01410023 × (weekly miles ÷ 10)

When you have two times at different distances, the calculator uses formula 2: it computes the marathon exponent above, then the longest time × (42.195 ÷ that distance)^{marathon exponent}. With only one time, or a personal exponent outside 1.00–1.30, it uses formula 1, which takes the marathon average speed v (in m/s) from Riegel's formula at 1.07, adjusts it to 0.16018617 + 0.83076202 × v + 0.06423826 × (weekly miles ÷ 10), and divides 42,195 m by that speed. If you enter weekly distance in kilometers, it is converted to miles (1 mile = 1.609344 km) before the calculation. The study's participants ran a median of 30 miles (about 48 km) a week, with an interquartile range of 20 to 42 miles, so the formulas may fit less well if you run far more than that. The calculator accepts up to 160 km (99.4 miles) a week, and when the marathon exponent comes out below 1 it uses formula 1.

With the same half marathon time, a longer weekly distance lowers the marathon prediction. The adjusted formulas were built from survey participants in 2014, whose median marathon times were 3:28:02 for men and 3:54:36 for women, about 40 minutes faster than participants in the 2013 New York City Marathon.

Reading the finish-line scene and the checkpoint table

The finish-line scene assumes that you and the goal pacer start together and each hold an even pace from start to finish. It shows where the other runner is at the moment the first one crosses the line, so a time gap becomes a distance you could see in a race. A runner predicted at 1:57:49 is 2 minutes 11 seconds ahead of a sub-2 pacer; when you cross the finish line, the pacer is still about 0.24 mi back, at the 12.9 mi mark.

The checkpoint table lists elapsed times for you and the goal pacer, and the gap between them, every 3 miles (every 5 km in kilometer mode). For the same runner, at the 3-mile mark you are at 26:58 and the sub-2 pacer is at 27:28, so you are 30 seconds ahead. Real races rarely keep an even pace in the second half, so to plan a pace for each split, use the "Make a pace plan from this time" button to open the Marathon Pace Calculator.

Common mistakes

• Entering a jogging time or a time paced for a friend: the prediction is based on that speed, so the half marathon comes out slower than your fitness. The survey of Vickers and Vertosick also asked for races run all-out only.
• Treating the half marathon as 21 km: that drops the last 97.5 m (0.0975 km), which at 5:35 per km (8:59 per mile) is about 33 seconds. This calculator uses the official distance of 21.0975 km.
• Correcting a time by the distance on your watch: GPS watches can measure longer or shorter than the real distance, so a race time measured over the official distance is more accurate.
• Entering an old personal best: a prediction should be based on your current condition. The survey in the same study asked for times from the last 6 months where possible.
• Entering a time from a hilly course or a hot day as is: the study adjusted for hard and fast courses separately, but this calculator assumes a normal course. A time run in unusual conditions can throw the prediction off by that much.

Limits

• A predicted time is a reference value that assumes equal, adequate training; it does not guarantee that you will finish or what time you will run.
• The 1.06–1.08 band shows how far the result moves with the exponent. It is not a calculated range of probability.
• The adjusted formulas were built from self-reported times of runners in a 2014 online survey, and the 1.07 exponent is the average value that study chose between published figures. They may fit less well for runners much slower than the participants or with very different training.
• The study's times were for 5K, 5 miles, 10K, 10 miles and the half marathon, so using a 1-mile, 3K or 15K time means going outside that range, and the error can be larger.
• Riegel's relationship was checked for times of about 3.5 to 230 minutes, so a half marathon prediction above 230 minutes can carry a larger error. Only paces of 4:00 to 20:00 per mile (2:30 to 12:25 per km) are accepted.
• Course elevation, temperature, wind, aid stations and stopped time are not part of the calculation.

Reference date: 2026-10-19 · The formulas and coefficients were checked directly against the text and supplementary material of the sources below.

Sources

• 01Vickers AJ, Vertosick EA. An empirical study of race times in recreational endurance runners. BMC Sports Sci Med Rehabil. 2016;8:262,303 recreational runners, exponent 1.07 chosen as an average (sensitivity 1.06 and 1.08); Riegel's formula fits up to the half marathon but predicted the marathon 10 minutes or more too fast for half of runners
• 02Vickers AJ, Vertosick EA. Additional file 1 (Supplementary Materials)Reference times used to check the half marathon, coefficients of marathon formulas 1 and 2, median marathon times of participants
• 03Riegel PS. Athletic Records and Human Endurance. American Scientist. 1981;69(3):285-290Distance–time relationship over about 3.5 to 230 minutes; running exponents of 1.07732 for men and 1.08283 for women, and 1.05 to 1.06 for men aged 40 to 70
• 04Blythe DAJ, Király FJ. Prediction and Quantification of Individual Athletic Performance of Runners. PLoS One. 2016;11(6):e0157257Median individual exponent 1.12 (5th to 95th percentile: 1.10 to 1.15); predictions with individual exponents were no better than Riegel's formula
• 05World Athletics. Half MarathonHalf marathon distance of 21.0975 km (13.1094 miles)

Frequently asked questions

Related tools