Running Fatigue Factor Calculator
Enter two recent all-out race results to calculate the fatigue factor that best describes how your pace changed with distance. Use it to predict a third distance and compare that estimate with the usual 1.06 Riegel exponent.
Personal fatigue factor1.057
- Pace slowdown when distance doubles
- 4%
- Personalized target time
- 01:54:26
- Personalized target pace
- 5:25/km, 8:44/mi
- Standard 1.06 target time
- 01:54:44
- Personal versus standard difference
- -00:00:18
Uses the Riegel distance-time relationship and assumes both entered races were comparable all-out efforts.
The target is far outside the two race distances, so this prediction is an extrapolation.
How to use this calculator
- Enter the shorter race distance and its full finish time.
- Enter a longer race from a similar fitness period, effort level, and type of course.
- Enter the target distance you want to predict.
- Read the personal factor, pace slowdown, and the personalized and standard predictions together.
How the running fatigue factor is calculated
The Riegel relationship estimates how an all-out race time changes with distance. It writes the longer time as a multiple of the shorter time: Tlong / Tshort = (Dlong / Dshort)^k. In that equation, T is finish time in seconds, D is distance in kilometers, and k is the fatigue factor. A larger factor means pace is expected to slow more as distance increases.
This calculator reverses that relationship using your two race results:
k = ln(Tlong / Tshort) / ln(Dlong / Dshort)
It then applies your factor to the longer result: Ttarget = Tlong × (Dtarget / Dlong)^k. The standard comparison uses the same calculation with k = 1.06. The pace-slowdown result is 100 × (2^(k − 1) − 1), which expresses how much average pace changes when the race distance doubles.
Choosing useful race results
The two results should be genuine hard efforts from roughly the same training cycle. A 5 km and 10 km, or a 10 km and half marathon, give the calculation a more useful spread than two nearly identical distances. Use certified or reliably measured distances when possible, and enter complete elapsed time rather than a watch's moving time.
Conditions can move the factor as much as endurance does. Hills, trail surface, heat, wind, altitude, a crowded start, poor pacing, and a tactical rather than all-out effort all change finish time. Comparing a fast road 5 km with a hilly trail half marathon can produce a precise number that does not describe a stable personal trait.
How to read the prediction
A factor near the standard value means this two-race pattern is close to the common fixed-exponent model. A lower factor means less modeled pace fade; a factor at or below 1.00 means the longer result had equal or faster average pace and is usually a prompt to recheck comparability. A notably high result can reflect endurance limits, but it can also reflect different courses, weather, fitness, or effort.
The calculation leaves out preparation for the target event. It does not model fueling, heat acclimation, hills, injury, tapering, pacing strategy, or day-to-day fitness. Treat a target well beyond the two entered distances with extra caution: published research found fixed Riegel predictions reasonably calibrated through the half marathon but often too optimistic for recreational runners at the marathon.
Worked example
A runner has a 5 km result of 25:00 and a 10 km result of 52:00. The time ratio is 3,120 ÷ 1,500 = 2.08 and the distance ratio is 10 ÷ 5 = 2, so k = ln(2.08) ÷ ln(2) = 1.057. The pace slowdown per doubling is 4.00% because the average 10 km pace is 4% slower than the 5 km pace.
For a 21.0975 km target, the personalized calculation gives about 01:54:26, at about 5:25 per km or 8:44 per mile. Using the standard 1.06 factor gives about 01:54:44, so this runner's two-race factor predicts a result 00:00:18 faster.
Common questions
What is a running fatigue factor or Riegel exponent?
A Riegel exponent is the number that describes how race time increases as distance increases in the Riegel distance-time relationship. It is often called a fatigue factor because a higher value represents more modeled slowing of average pace over longer races. It is a performance-model parameter, not a direct measurement of physiology.
What is considered a good Riegel fatigue factor?
Lower is more favorable within a pair of genuinely comparable all-out races because it predicts less pace fade. The commonly used fixed value is 1.06, while Riegel cited values around 1.05 to 1.08 for specific groups. A personal result is most useful as a description of comparable race results, not as a ranking by itself.
Why use two race results instead of the standard 1.06 exponent?
Two results allow the formula to estimate the exponent implied by your own pace change rather than assuming the same pace fade for everyone. That can make the prediction more relevant when the races were comparable. It cannot correct for different weather, courses, fitness, or effort between the two events.
How far apart should the two race distances be?
Choose distances far enough apart that ordinary timing and distance error do not dominate the calculation, such as 5 km and 10 km or 10 km and a half marathon. The longer result still needs to represent a similar all-out effort. A target outside the two distances is an extrapolation, especially when it is much longer than the longer race.
Can I compare track, trail, and road race results?
You can calculate a number, but it may not isolate endurance. Surface, elevation change, turns, weather, and distance accuracy can change time independently of fitness. Use results from similar courses and conditions when you want a prediction for a road race.
What does pace slowdown per doubling mean?
It is the modeled percentage increase in average time per kilometer or mile when distance doubles. For example, 4% means a runner averaging 5:00 per km over one distance would model to about 5:12 per km over twice that distance. It summarizes the exponent, but it is not a promise that every doubling will produce exactly that change.