Marathon Time Predictor Explained

What a marathon time predictor actually predicts

A marathon time predictor takes a race you have already run — typically a 5K, 10K or half marathon — and projects what you would run over 42.195 km on a similar day, similarly trained. It is not a crystal ball. It is a relationship that has held across millions of recorded race results for a century: aerobic running times scale with distance to a fixed power, and once you know one time you can convert it into any other distance with one line of arithmetic. The marathon time predictor on Calc Dragon implements Pete Riegel's 1981 formula, which is the version every running coach, race-result database and pacing app builds on top of.

The thing to understand up front is that “predict” in this context means “what an equivalently trained athlete would run.” Plug in a 20-minute 5K and the predictor returns a 3:08 marathon. That is the time you would run if your marathon training matched the quality of your 5K training. If you race fast 5Ks but only run 25 km a week, the marathon number is aspirational rather than predictive. That single caveat decides whether the formula works for you or doesn't, and the rest of this article is about getting it right.

The Riegel formula in one paragraph

Pete Riegel, an American engineer who certified marathon courses for USA Track & Field, published the formula in “Athletic Records and Human Endurance” (American Scientist, May–June 1981, pp. 285–290). It says:

T2 = T1 × (D2 / D1)^1.06

T1 is your known race time, D1 the known race distance, D2 the distance you want to predict, and T2 the predicted time. The exponent of 1.06 is the whole reason the formula is interesting. A 1.0 exponent would mean even pace at every distance — impossible, because the body cannot sustain 5K pace for 42 km. A 2.0 exponent would mean each doubling of distance doubles the per-kilometre cost — also wrong, because we are not that bad at endurance. Riegel fit the exponent against world records from 800 m up through 100 km, separately for men and for women, and got 1.06 ± 0.01 in every dataset. Later re-analyses by Vandewalle (2018) and the Strava data science team have reproduced it to two decimal places on modern populations. It is one of the most robust empirical relationships in sport science.

Worked example: predicting a marathon from a 10K

Suppose you ran a 10K last weekend in 45:00 flat. You are eyeing a spring marathon and want a target time. Open the marathon time predictor and the math runs as follows.

Step 1. Convert the input time to seconds. 45 minutes = 45 × 60 = 2,700 s. So T1 = 2,700 and D1 = 10 km.

Step 2. Compute the distance ratio. D2 / D1 = 42.195 / 10 = 4.2195.

Step 3. Apply the exponent. 4.2195^1.06= exp(1.06 × ln(4.2195)) = exp(1.06 × 1.4395) = exp(1.5259) = 4.5988.

Step 4. Multiply by T1. T2 = 2,700 × 4.5988 = 12,416.8 s.

Step 5. Convert to hours:minutes:seconds. 12,416.8 s ÷ 3,600 = 3.449 h = 3 h 26 min 57 s, written 3:26:57.

Divide that by 42.195 km to get the required pace — 12,416.8 ÷ 42.195 = 294.3 s/km, or 4:54 per km. Per mile it is 12,416.8 ÷ 26.21876 = 473.6 s/mile, or 7:54 per mile. The input race was run at 4:30 per km, so marathon pace is about 9% slower per km — Riegel's fatigue penalty for the distance ratio you are stretching across. The predictor prints all of these in one go so you don't need to run the long division by hand. The Calc Dragon marathon pace calculator is the inverse problem — given a target time, what pace do you need to hold — and the two tools are designed to be used together.

Factors that move the prediction up or down

Distance of the input race

The closer the input distance is to the marathon, the more accurate the prediction. A half marathon is the gold standard because it stresses the same aerobic energy system, the same fuel availability and the same thermoregulatory window as the marathon — the difference is mostly duration, not mechanism. A 10K is the most common input and is reliable for trained runners. A 5K is acceptable but tends to over-predict by 10–20 minutes because anaerobic capacity inflates short-race performance relative to long-race performance. A 1500 m time is the lower bound where Riegel still behaves; below that the exponent drifts because the race is dominated by VO2 max and lactate clearance rather than fat-oxidation endurance.

Quality of your long-run training

Riegel implicitly assumes equal training quality across distances. In the real world a runner who hammers track sessions twice a week but skips long runs will race 5K fast and marathon slow. The cleanest test is whether your weekly long run is at least the same duration as your predicted marathon time, in minutes. If the predictor says 3:30 and your longest run this cycle is 2:00, expect the actual finish to be 15–30 minutes slower. Coaches sometimes call this the “Riegel gap”: the gap between physiological capacity and marathon-specific readiness.

Course profile and conditions

The formula assumes the marathon will be run on a course of similar profile and in similar conditions to the input race. London, Berlin and Chicago are net-flat record-eligible courses. Boston has the Newton hills. Comrades is a road ultra with 800 m of elevation. A Riegel prediction off a flat 10K under-predicts on hilly marathons by 3–10% and over-predicts on point-to-point downhill marathons by 1–3%. Heat penalises the marathon harder than the shorter race — every 1°C above 14°C slows marathon pace by roughly 0.5%.

Pacing discipline on the day

The single most common reason runners miss their Riegel prediction is going out 10–15 s/km too fast in the first 10 km. The penalty for early over-pace is non-linear: Diaz et al. (2017), analysing 1.3 million Berlin Marathon finish times, showed that runners who went through 21 km more than 90 s ahead of their average pace lost an average of 6 minutes over the second half. Negative splits — running the second half faster than the first — are statistically the fastest pacing strategy on a flat course.

Fuelling and hydration

Riegel predicts a time, not whether your glycogen will last 42 km. Glycogen depletion (“the wall”) happens at roughly 30–35 km for a runner who has not practised in-race carbohydrate intake, and the slowdown when it hits is 30–60 s/km. The current sports-science recommendation (Burke et al. 2019, International Journal of Sport Nutrition and Exercise Metabolism) is 60–90 g of carbohydrate per hour during the marathon, achieved through gels, drinks or chews. Without that, the prediction is optimistic by exactly the wall slowdown, and the carbohydrate calculator is a useful sanity check on training-week intake.

How to use the prediction without fooling yourself

• Use the longest recent race you have. A 1:35 half marathon predicts the marathon better than a 19:00 5K. If you can race a half four to eight weeks out from the marathon, do that and let the predictor re-base off the better data point.
• Bracket the answer. Run Riegel from your 5K, your 10K and your half if you have all three. If they cluster within a 5-minute window the prediction is solid. If the 5K-based prediction is 20 minutes faster than the half-based one, the half is closer to the truth.
• Add a buffer for your first marathon. Add 5–10 minutes to the prediction for the wall, the adrenaline, the porta-loo queue and the fact that you have never paced this distance before.
• Re-predict at peak training. The prediction off a race in week 4 of a 16-week block is not the same as the prediction off a race in week 12. A tune-up race three to four weeks before the marathon is the most useful single data point for setting goal pace.
• Match daily fuel to training load. Marathon training averages 600–900 kcal/day above baseline depending on volume — use the calorie calculator and the BMR calculator to set a sensible intake. Under-fuelling for months blunts the training response and the prediction holds for a fitness level you no longer have.
• Don't race a marathon to predict another marathon. Recovery from a full marathon takes three to six weeks, and the input race won't reflect current fitness if you ran it before you fully recovered.

Common mistakes

Using a parkrun time as a marathon predictor. Parkruns are 5K, which is at the short end of the Riegel window. The number the formula returns is a ceiling, not a likely outcome, and most runners under-perform it by 15–30 minutes the first time around. Use parkruns to track fitness trends, not to set marathon goal time.

Predicting a marathon off a treadmill time. Treadmills are 1–3% easier than the road at the same displayed pace (Jones & Doust, 1996). Riegel applied to a treadmill 10K gives a marathon time you will not match outdoors. Use a road or track race as the input.

Forgetting the formula is reversible. Some runners apply Riegel to a marathon time to predict a 5K and feel disappointed when they don't hit it. Marathon-trained runners typically race short distances below Riegel because they have not done the speedwork. That is not a failure of the formula — it is a sign your training is marathon-specific.

Treating one prediction as the truth. Riegel is one of three or four widely used predictors. Dave Cameron's 1998 model uses a more elaborate two-parameter fit that handles the short and long ends better. Jack Daniels' VDOT tables are derived from a different physiological framework and tend to give slightly slower marathon predictions for fast 5K runners. Frank Horwill's rule of thumb says each doubling of distance adds about 20 s/mile. Spread your data across two or three methods and use the median.

When the prediction stops being enough

Riegel is a paper-napkin tool, and a paper-napkin tool is the right level of precision for setting a goal time and choosing a pace group. It stops being enough in a few specific situations. If you are chasing a Boston Marathon qualifier and are within a minute of the standard, the right next step is a coached training block with weekly long-run pace targets — the formula cannot tell you how to make up that minute. If you are recovering from a running injury and the predicted time is meaningfully slower than your last marathon, a sports-medicine physician or physiotherapist is the right person to ask whether the slowdown is fitness loss or biomechanical. If you are over 60 or under 18, age-graded performance tables (World Masters Athletics for masters, World Athletics youth tables for juniors) give a fairer benchmark than Riegel alone. And if your prediction off the half marathon and your prediction off the 10K disagree by more than 15 minutes, you have a training imbalance that a coach can identify and fix faster than more racing will.

Frequently asked questions

How accurate is the marathon time predictor?

For a trained runner with a recent half marathon as input, the prediction is accurate to within 3–5% of actual marathon time on a flat course in temperate conditions. For a runner using a 5K or 10K as input, the spread widens to 10–15%. The most common failure mode is over-prediction from a fast short race — “5K hero, marathon zero.” Pair the marathon time predictor with the running pace calculator to sanity-check both ends of the question.

Why does Riegel use 1.06 and not some other number?

Pete Riegel fit the exponent against world record data from 800 m to 100 km and found that across the running distances the relationship T = a × D^k held with k ≈ 1.06. The fit has been re-validated against modern race databases and holds within ±0.01 across different eras, sexes and surfaces. A higher exponent (1.08–1.10) fits ultramarathon data better; a lower one (1.04) fits middle-distance track data better. 1.06 is the sweet spot for road running between 1500 m and the marathon.

Does the formula work for women as well as men?

Yes. Riegel fit it separately on male and female world records and found the same exponent within rounding. The Strava 2018 analysis of 14 million marathon finish times confirmed identical exponents within ±0.005 across genders. The formula is sex-neutral in the same way that relative speed loss with distance is sex-neutral.

Can I use the predictor for an ultramarathon?

Imperfectly. Riegel under-predicts ultramarathon times because the formula does not capture the GI shutdown, thermoregulation collapse and walk-break pacing specific to events over six hours. For 50 km the under-prediction is in the 5–10% range. For 100 km or 100 miles it widens to 20–40%. Ultra-specific models from Tanda (2011) and the iRunFar dataset use higher exponents and additional terms.

Should I add or subtract time for the marathon course?

Net-flat record-eligible courses (Berlin, London, Chicago, Tokyo) match the Riegel assumption. Boston is roughly 2 minutes slower for an equivalent effort because of the Newton hills, even though the course is net downhill. Big Sur and trail marathons are 10–30 minutes slower depending on elevation gain. Hot races (above 18°C at the gun) lose 30 s to 2 minutes per 5°C above threshold.

What input distance gives the most accurate prediction?

Half marathon by a clear margin, then 10 mile, then 10K, then 5K. The half marathon shares the same aerobic energy system and pacing rhythm as the marathon, which is why coaches plan a tune-up half 4–6 weeks before the goal race. If you only have a 5K, treat the predictor output as “what you could run with full marathon training,” not “what you will run next Sunday.”

Is the marathon distance really 42.195 km?

Exactly. World Athletics Technical Rule TR4.3 (Distances of Road Races) fixes the marathon at 42,195 m, codified in 1921 after the 1908 London Olympic course of 26 miles 385 yards. Every certified marathon since uses the same distance, so “marathon time” means the same thing in Berlin, Boston and Cape Town. Mile-to-kilometre conversion uses the NIST exact factor of 1 international mile = 1.609344 km (NIST SP 811:2008, Appendix B.8).

Related calculators

• Marathon Time Predictor — Riegel's formula across 12 input race distances.
• Marathon Pace Calculator — required pace and 5K splits for a target marathon finish.
• Running Pace Calculator — convert any distance and time into pace, speed and finish projections.
• Calorie Calculator — daily intake target from BMR and training load.
• BMR Calculator — basal metabolic rate at complete rest.
• Carbohydrate Calculator — daily carb target by training volume.