Race Time Predictor
Type a recent race and time, pick the race you are aiming for and get your predicted finish time and pace, worked out with Riegel's formula.
Predicted times for every race
| Race | Riegel Cameron | Pace | Trust |
|---|
“Good” means within about twice your race distance, “Fair” up to about 4.5 times, “Rough” beyond that. Longer races also need the training behind them.
How your race time is worked out
Compare the two distances, add a little extra for tiring over the longer race, then scale your time.
- 1
Distance ratio
21.0975 ÷ 10= 2.1098
- 2
Add fatigue
2.1098 ^ 1.06= 2.2064
- 3
Scale your time
50:00 × 2.2064= 1:50:19
- 4
Your pace
1:50:19 ÷ 21.0975= 5:14 /km8:25 /mi
Read more: the formulas, a worked example and how far to trust a prediction
A race time predictor takes one race you have run all-out and estimates what you could run at another distance with the same fitness. You slow down a little as races get longer, so the time does not simply scale with distance: a fatigue exponent a bit above 1 adds that extra. These are estimates from published models, not a promise; your training, the course and the weather on the day all count.
The formula
Riegel (1977, 1981): predicted time = your time × (new distance ÷ your distance) ^ 1.06
Your own exponent from two races: k = ln(time 2 ÷ time 1) ÷ ln(distance 2 ÷ distance 1)
Cameron model: predicted time = your time ÷ your distance × new distance × a(your distance) ÷ a(new distance), where a(d) = 13.49681 − 0.000030363 × d + 835.7114 ÷ d^0.7905 and d is in metres
Pace = predicted time ÷ new distance
Worked example
You ran a 10K in 50:00 (3,000 seconds) and want a half marathon (21.0975 km) time.
- Distance ratio: 21.0975 ÷ 10 = 2.10975.
- Add fatigue: 2.10975^1.06 = e^(1.06 × ln 2.10975) = e^(1.06 × 0.746569) = 2.206403.
- Scale your time: 3,000 × 2.206403 = 6,619.21 seconds = 1 hour, 50 minutes, 19.2 seconds, so about 1:50:19.
- Pace: 6,619.21 ÷ 21.0975 = 313.74 s per km = 5:14 per km; per mile, 6,619.21 ÷ 13.1094 = 504.92 s = 8:25 per mile.
The Cameron model gives a(10,000) = 13.768695 and a(21,097.5) = 13.175198, so 3,000 ÷ 10,000 × 21,097.5 × 13.768695 ÷ 13.175198 = 6,614.36 s, about 1:50:14: almost the same. For the marathon the two part ways: Riegel says 3,000 × 4.2195^1.06 = 13,800.6 s (3:50:01) and Cameron says 14,055.7 s (3:54:16).
With a second race, say a 5K in 24:00 (1,440 s), your own exponent is ln(3,000 ÷ 1,440) ÷ ln(10,000 ÷ 5,000) = 0.733969 ÷ 0.693147 = 1.0589, a touch below the standard 1.06.
Predictions from a 50:00 10K
| Race | Riegel time | Pace /km |
|---|---|---|
| 1 mile | 7:13 | 4:29 |
| 5K | 23:59 | 4:48 |
| 10K | 50:00 | 5:00 |
| 15K | 1:16:51 | 5:07 |
| 10 miles | 1:22:48 | 5:09 |
| Half marathon | 1:50:19 | 5:14 |
| Marathon | 3:50:01 | 5:27 |
How far to trust a prediction
- Nearby distances work best. 5K to 10K or 10K to half marathon are usually within a minute or two for a trained runner.
- Big jumps are rough. A 5K time only shows your speed. Running a marathon at the predicted pace needs endurance: months of long runs and steady weekly mileage. Without that, expect to be slower than the prediction, sometimes by 10–20 minutes or more.
- Use a real race. An all-out effort on a flat, accurately measured course works best. A training run or a hilly or hot race gives a slower base time.
- Two races beat one. Your own exponent from two recent races captures whether you are more of a speed or an endurance runner.
- Very short races. Below about 1 mile, sprint speed plays a bigger part and the formulas fit less well.
Riegel's formula was published by Pete Riegel in 1977 (Runner's World) and in more detail in 1981 (American Scientist). The Cameron model is credited to Dave Cameron. This tool follows the formulas as they are commonly written; it is general information, not coaching or medical advice.
Common questions
How do I predict my marathon time from a 10K?
Use Riegel's formula: marathon time = 10K time × (42.195 ÷ 10)^1.06. A 50:00 10K gives 3,000 s × 4.2195^1.06 = 13,800.6 s, about 3:50:01. It assumes you have done the long runs and weekly mileage a marathon needs, so many runners finish slower than this.
What is Riegel's formula?
T2 = T1 × (D2 ÷ D1)^1.06. T1 is your time over distance D1, and T2 is the predicted time over D2. Pete Riegel published it in 1977 and expanded on it in 1981. The 1.06 is a fatigue exponent: it makes you a little slower per km as the distance grows.
What is the Cameron model?
Dave Cameron's model is another race predictor. It scales your pace by a factor a(d) = 13.49681 − 0.000030363 × d + 835.7114 ÷ d^0.7905 (d in metres) worked out for both distances. For long jumps such as 10K to marathon it usually predicts a slower time than Riegel, which many runners find closer to real life.
How do I find my own fatigue exponent?
Take two recent all-out races at different distances. Your exponent k = ln(T2 ÷ T1) ÷ ln(D2 ÷ D1). For a 24:00 5K and a 50:00 10K, k = ln(3,000 ÷ 1,440) ÷ ln 2 = 1.059. A lower number means you hold your speed well over longer races.
How accurate are race time predictions?
They are best between nearby distances, like 5K to 10K or 10K to half marathon. The further you stretch, the less reliable they get. From a 5K to a marathon the formula assumes you have the endurance for 42 km, which needs specific long-run training. Hills, heat, wind and pacing on the day also matter.
Does this work for walking or cycling?
Riegel's formula was made for running (and some other endurance sports like swimming and walking races). The default exponent of 1.06 fits running best. For cycling, a speed-based calculator is a better guide.
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