Your 5K, 10K, half and marathon times
One recent race and your time: your times and paces for all four distances, plus four dots racing side by side so you can watch the pace slow down.
On race day, you hold your pace with split times: write them on a pace band and keep it on your wrist.
Your four paces, fast-forward
How it's calculated
- Riegel's law: your predicted time at a distance D2 equals your time T1 for your reference race D1, multiplied by (D2 ÷ D1) to the power of 1.06. Peter S. Riegel, "Athletic Records and Human Endurance", American Scientist, vol. 69, no. 3, 1981, pp. 285–290: across several endurance sports, time grows a little faster than distance. 1.06 is the exponent the Cadevia app uses, the same for all its pace conversions; Riegel cited 1.08 for elite runners and 1.05 to 1.06 for recreational runners aged 40 to 70 (per Vickers and Vertosick, 2016, below).
- The distances are the official road race distances: 5 km, 10 km, half marathon 21.0975 km, marathon 42.195 km (World Athletics technical rules). In miles: 1 mile = 1.609344 km exactly (the 1959 international yard and pound agreement). Your reference race uses the same distance, so predicting your own race gives you back your own time. Another distance can be 3 to 50 km (1.9 to 31 mi): a Cadevia setting, to stay within the family of road races this page connects.
- The rounding is the app's, to the digit: the predicted time is cut to the second, and the pace is that time divided by the distance, rounded to the nearest second per kilometer. Per mile, that pace is multiplied by 1.609344 and rounded again. Speed is distance divided by time, to one decimal.
- What the prediction assumes: that you train for the distance you're targeting. Your 10K doesn't give you a marathoner's endurance: without long runs, your time will be slower.
- The least certain (marked "~"): the distance furthest from your reference race, as a ratio of distances (a marathon is 4.2 times a 10K, a 5K is 4.2 times shorter than a half). The bigger the gap, the less certain the prediction: that's a Cadevia setting.
- The marathon: among 2,303 recreational runners, Riegel's law was on target up to the half marathon, but predicted the marathon too fast: by 10 minutes or more for half of them, and by more than 20 minutes for nearly a quarter (A. J. Vickers, E. A. Vertosick, "An empirical study of race times in recreational endurance runners", BMC Sports Science, Medicine and Rehabilitation, 2016). They used an exponent of 1.07; with 1.06, a marathon predicted from a shorter race comes out a little faster still.
- The safety check: under 2:34 per kilometer (4:08 per mile), the page warns you. That's faster than the 5K road world record (12:49, Berihu Aregawi, 2021, ratified by World Athletics), the shortest distance on this page.
- The four lanes: each dot runs one mile (or one kilometer) at the pace predicted for its race, and they all start together. The clock runs in fast-forward; each dot stops on its time for that mile or kilometer, which is its pace. With this law, the gap between the dots doesn't depend on your level: your marathon pace is always 13.7% slower than your 5K pace ((42.195 ÷ 5) to the power of 0.06), so when your 5K dot finishes, your marathon dot is always about 12% of the way behind: roughly 210 yards over a mile, 120 m over a kilometer.
Frequently asked questions
How do I predict my half marathon time?
With Riegel's formula: your 10K time multiplied by (21.0975 ÷ 10) to the power of 1.06, about 2.21. A 50:00 10K gives a 1:50:19 half marathon, at 8:25 per mile, if you train for the distance.
What marathon time does a 50-minute 10K predict?
3:50:00 by Riegel's formula, at 8:46 per mile. It's the least certain prediction: for half of the recreational runners studied, the marathon took 10 minutes longer than predicted, or more (Vickers and Vertosick, 2016).
How do I calculate my running pace?
Divide your time by the distance. 50 minutes for 10 km is 3,000 seconds ÷ 10 = 300 seconds: 5:00 per km, or 8:03 per mile (12.0 km/h, 7.5 mph).
How accurate is the Riegel formula?
Fairly accurate up to the half marathon, too optimistic for the marathon: 10 minutes or more too fast for half of the 2,303 recreational runners in one study (Vickers and Vertosick, 2016). It assumes you train for the distance.