Marathon Time Predictor
Enter a recent race time and distance to predict your marathon finish time using Riegel's endurance formula. Works from a 5K, 10K, 15K, half marathon and other common race distances.
Predicted marathon finish time
3:27:01
- Predicted pace per km
- 04:54 / km
- Predicted pace per mile
- 07:54 / mi
- Predicted half-marathon time
- 1:39:17
- Input race pace per km
- 04:30 / km
- Marathon pace vs race pace
- +9.0% slower per km
Predicted marathon time uses Riegel's endurance model: T2 = T1 × (D2 / D1)^1.06 (Pete Riegel, "Athletic Records and Human Endurance", American Scientist 1981). The 1.06 exponent captures the fatigue cost of going further — doubling distance more than doubles time. The model assumes you're trained for both distances and works best when the input race is within 0.5×–3× the marathon (so a 10K or half-marathon prediction is more reliable than a mile prediction). Marathon distance is 42.195 km exactly (World Athletics TR4.3). Mile ↔ km uses the NIST exact factor 1 mile = 1.609344 km.
How to use this calculator
Pick the distance of a recent race you ran flat-out — 5K, 10K, half marathon and a handful of less common road and track distances are all in the dropdown. Enter the finish time in hours, minutes and seconds. The headline answer is your predicted marathon finish time. The breakdown adds the pace per kilometre and per mile you would need to average, your projected half-marathon time from the same fitness, the pace of the input race for comparison, and a "+x% slower per km" figure that shows how much you slow down per km as you stretch from the short race to the marathon. The predictor assumes you are trained for both distances — if you have only done short races, the marathon number will likely be optimistic, and you should add 5-10 minutes for the wall.
How the calculation works
The maths is Pete Riegel's endurance model from his 1981 American Scientist paper "Athletic Records and Human Endurance": T2 = T1 × (D2 / D1)^1.06. T1 is your race time, D1 the race distance, D2 the marathon distance (42.195 km, World Athletics TR4.3), and the exponent 1.06 captures the fatigue cost of going further. The exponent is not a guess — Riegel fit it to thousands of track and road records from 800 m up through the marathon, and it is reproduced near-exactly in every later dataset. A 1.0 exponent would mean perfect even pace across all distances (impossible); 1.06 says that for every doubling of distance you lose about 4 % to fatigue. The model is symmetric — you can use it in reverse to predict a 5K from a marathon — but it works best when the input race is within roughly 0.5× to 3× the target. Riegel himself recommended at least 1500 m as the lower bound; below 3.5 km the exponent drifts because anaerobic capacity dominates over endurance. Half-marathon-to-marathon predictions are the most accurate in practice because aerobic fitness and pacing experience transfer cleanly. Mile ↔ km uses the NIST exact factor of 1 international mile = 1.609344 km.
Worked example
Recent race: 10K in 45:00. Convert to seconds: T1 = 2,700 s. D1 = 10 km, D2 = 42.195 km. Ratio D2/D1 = 4.2195. Apply Riegel: 4.2195^1.06 = exp(1.06 × ln(4.2195)) = exp(1.06 × 1.4395) = exp(1.5259) = 4.5988. Predicted marathon time T2 = 2,700 × 4.5988 = 12,416.8 s = 3:26:57. Required pace = 12,416.8 ÷ 42.195 = 294.3 s/km = 4:54 per km, or 12,416.8 ÷ 26.21876 = 473.6 s/mile = 7:54 per mile. The input race pace was 4:30 per km, so the marathon pace is about 9 % slower per km — Riegel's fatigue penalty at this distance ratio.
Frequently asked questions
How accurate is Riegel's marathon predictor?
Across large datasets the Riegel formula is accurate to within roughly ±3-5 % when the input race is within 0.5× to 3× the marathon. Half-marathon predictions are the most accurate (mean error well under 5 minutes for trained runners). Predictions from a 5K or shorter tend to be 10-20 minutes optimistic for recreational marathoners because the formula assumes equal training for both distances. The most common failure mode is "5K hero, marathon zero" — fast short-race runners who haven't trained the long runs hit the wall around 32 km and finish 15-30 minutes behind the prediction.
Why is the exponent 1.06?
Pete Riegel fit the exponent empirically in his 1981 American Scientist paper "Athletic Records and Human Endurance". He took world records from 800 m through 100 km for both men and women and found that across the running distances the relationship T = a × D^k held with k ≈ 1.06. A k of exactly 1.0 would mean even pace at all distances (which is biologically impossible — humans slow down as distances grow). Higher k values (~1.08-1.10) fit ultramarathon data better; lower k values (~1.04) fit middle-distance track data better. 1.06 is the sweet spot for everyday road running from 1500 m to the marathon.
Should I use my 5K, 10K or half marathon as the input?
Use the longest recent race you have — half marathon is best, 10K is the most common, 5K is acceptable. The closer the input distance is to the marathon, the more reliable the prediction, because the energy systems and pacing skills involved overlap more. A 5K barely taxes aerobic endurance; a half marathon is genuinely the front half of the marathon energy system. If you only have a 5K, treat the prediction as "what you could run if you actually trained for the marathon", not "what you will run next Sunday".
What other marathon predictors are out there?
Three are widely used. Riegel's formula (this calculator) is the simplest and most popular. Dave Cameron's model from 1998 uses a more elaborate two-parameter fit that handles the very short and very long ends better. Frank Horwill's "5 seconds per km" rule of thumb says each doubling of race distance adds about 20 seconds per mile to your pace — a useful sanity check. For elites the predictors all agree within a minute or two; for back-of-pack marathoners they can disagree by 20+ minutes because the underlying assumption (equal training quality across distances) breaks down.
Does Riegel work for ultramarathons?
Imperfectly. Riegel's exponent of 1.06 systematically underpredicts ultramarathon times because the formula does not capture the GI shutdown, thermoregulation collapse and pacing strategy specific to events over six hours. For 50 km or 50 miles, Riegel will be roughly within 10 %. For 100 km or 100 miles it can underpredict by 30-60 minutes. Ultra-specific formulas use exponents around 1.08-1.12 and add walk-break adjustments.
How do I convert the predicted finish time into pacing for race day?
Divide the predicted seconds by 42.195 to get pace per km, or by 26.21876 to get pace per mile. The calculator does both for you. Race day strategy: target the predicted pace for the first half, and if you feel strong at 30 km, accelerate; if you feel tight, hold. Negative splits (running the second half faster) are statistically faster on average — see the Berlin Marathon dataset (Diaz et al. 2017) — but require disciplined early pacing.
Can I use this in reverse to predict a 5K from my marathon time?
Yes. Riegel's formula is symmetric. Predict a 5K from a marathon time by reversing the ratio: T2 = T1 × (5 / 42.195)^1.06 = T1 × 0.0996. So a 3:30:00 marathon (12,600 s) predicts a 5K of 12,600 × 0.0996 = 1,255 s = 20:55. Reverse predictions are usually conservative because most marathoners under-train short, fast running; if you race a 5K hard the morning after a marathon recovery cycle, you may beat the prediction by 30-60 seconds.