Health & Medicine · Fitness · Cardio & Endurance
Marathon Time Predictor
Predicts your marathon finish time based on a recent race performance using the Riegel endurance formula.
Calculator
Formula
T_2 is the predicted finish time for the target race distance D_2. T_1 is your known finish time for a recent race of distance D_1. The exponent 1.06 is Riegel's fatigue factor, which accounts for the non-linear relationship between race distance and performance — longer races slow proportionally more than shorter ones.
Source: Riegel, P.S. (1981). Athletic Records and Human Endurance. American Scientist, 69(3), 285–290.
How it works
The foundation of this calculator is the Riegel formula, published by exercise scientist Peter Riegel in 1981. Riegel analyzed athletic performance records across a wide range of distances and found that human endurance follows a consistent power-law relationship: as race distance increases, performance degrades predictably. The key insight is that this degradation is not linear — longer races slow you down proportionally more than simply doubling the distance would suggest.
The formula is expressed as T₂ = T₁ × (D₂ / D₁)^1.06, where T₁ is your known finishing time at a known distance D₁, D₂ is your target race distance, and T₂ is the predicted finishing time. The exponent 1.06 is Riegel's empirically derived fatigue factor. A value of 1.0 would imply perfectly linear scaling (pace stays constant regardless of distance), while 1.06 captures the physiological reality that aerobic capacity, glycogen depletion, and muscular fatigue all compound over longer efforts. For example, if you could hold your 10 km pace forever, a marathon would take exactly 4.2195× as long — but due to fatigue, it actually takes longer, and the 1.06 exponent quantifies this.
In practice, coaches and runners use this formula for several purposes: setting a realistic marathon goal time from a recent half marathon result, calibrating training paces across different workout distances, evaluating whether a current fitness level supports a target finishing time, and planning negative splits or even pacing strategies. The prediction is most accurate when the known race was run at a genuine race effort (not a training run), was completed in similar conditions (flat course, good weather), and the target distance is within roughly 2–4× the known distance. Using a 5 km time to predict a marathon introduces more error than using a half marathon time.
Worked example
Consider a runner who recently completed a half marathon (21.0975 km) in 1 hour, 45 minutes (6,300 seconds) and wants to predict their marathon time.
Step 1 — Identify known values:
T₁ = 6,300 seconds, D₁ = 21.0975 km, D₂ = 42.195 km
Step 2 — Compute the distance ratio:
D₂ / D₁ = 42.195 / 21.0975 = 2.0000
Step 3 — Apply the Riegel exponent:
2.0000^1.06 = 2.0^1.06 ≈ 2.0845
Step 4 — Multiply by known time:
T₂ = 6,300 × 2.0845 ≈ 13,132 seconds
Step 5 — Convert to hours, minutes, seconds:
13,132 ÷ 3600 = 3 hours, 38 minutes, 52 seconds
Predicted Marathon Time: 3:38:52
Step 6 — Predicted pace:
13,132 ÷ 42.195 ≈ 311.2 seconds per km = 5:11 per km
This result shows that even though the marathon is exactly twice the half marathon distance, the predicted time is not simply twice the half marathon time (which would be 3:30:00) — it is approximately 8 minutes and 52 seconds slower, reflecting the physiological cost of the additional distance. This runner should target a starting pace of around 5:05–5:10 per km and expect to work harder in the final 10 km.
Limitations & notes
The Riegel formula is a statistical model derived from population-level data and carries several important limitations. First, it assumes that both races are run at a similar level of maximum effort under comparable conditions — a training run or a race in extreme heat will produce an inaccurate baseline. Second, the 1.06 fatigue factor is an average across a large population; elite runners often have a fatigue factor closer to 1.04–1.05, while less trained runners may have a factor of 1.07–1.10, meaning the formula may slightly overestimate performance for beginners and slightly underestimate it for highly trained athletes. Third, course profile matters significantly — predicting a marathon on a hilly course from a flat half marathon time will overestimate performance. Fourth, the formula becomes less reliable when the distance ratio (D₂/D₁) is very large; using a 5 km time to predict a marathon (a ratio of ~8.4×) introduces substantially more error than using a half marathon result (ratio of 2×). Fifth, individual factors such as nutrition strategy, altitude, heat acclimatization, and race-day psychological state are not captured by the formula. Users should treat the output as a starting point for planning, not a guaranteed outcome. Always consult a qualified running coach when setting goal times for major races.
Frequently asked questions
What is the most accurate input distance to use for predicting marathon time?
A half marathon (21.0975 km) run at race effort is widely considered the most accurate input for predicting marathon time using the Riegel formula. The closer the known distance is to the target distance, the smaller the extrapolation error. A 10 km time can also work well, but using distances shorter than 5 km significantly reduces accuracy.
Does the Riegel formula work for distances other than the marathon?
Yes. The Riegel formula is general-purpose and can predict performance at any target distance given any known race result. It is commonly used to predict 10 km times from 5 km results, half marathon times from 10 km results, and ultra-marathon estimates from marathon performances, though accuracy decreases as the distance ratio grows.
Why is the fatigue exponent 1.06 and not 1.0?
An exponent of 1.0 would mean race pace is perfectly constant regardless of distance, which is physiologically unrealistic. Riegel's analysis of competitive race records showed that performance degrades at a rate consistent with an exponent of approximately 1.06, reflecting the compounding effects of glycogen depletion, muscular fatigue, and cardiovascular drift over longer efforts.
My actual marathon time was slower than predicted — is the formula wrong?
Not necessarily. The Riegel formula provides a theoretical best-case prediction assuming optimal training, pacing, nutrition, and race conditions. Common reasons for slower-than-predicted times include inadequate long-run training (the formula does not account for training volume), going out too fast and hitting the wall, heat and humidity, or the known race being run on a faster course than the marathon.
Can I use this calculator to predict a pace strategy for race day?
Yes. Once you have a predicted finish time, divide the total seconds by the race distance in kilometers to get your target pace per kilometer. Many runners aim for a slight negative split — running the second half marginally faster than the first — so consider using the predicted pace as your average target and starting about 5–10 seconds per kilometer slower than that pace for the first 10 km.
Last updated: 2025-01-15 · Formula verified against primary sources.