What formula does the race time predictor use?

It uses two independent models. The Riegel (1981) formula is T2 = T1 x (D2/D1)^1.06, where T1 is your known time, D1 the known distance, D2 the target distance and 1.06 is the empirical fatigue exponent. The Daniels VDOT model derives your aerobic fitness index from the race and inverts the VO2/velocity relationship to predict each other distance.

Which model is more accurate — Riegel or Daniels?

Neither is universally better. Riegel tends to be more accurate for mid-distance comparisons (e.g. 5K to half marathon) and is easy to understand. The Daniels VDOT model captures physiology more directly and is especially useful for producing training zones alongside the predictions. Comparing both gives a confidence interval: if they agree closely, the prediction is more reliable.

What is a good Riegel exponent for my running profile?

The classic Riegel value of 1.06 fits well-trained runners who balance speed and endurance. Runners who specialise in shorter distances or have more fast-twitch muscle tend to fade more at long distances — try 1.08 to 1.10. Ultramarathon runners who are very efficient at slow sustained effort may fit closer to 1.03 to 1.05.

Why do the Riegel and Daniels predictions sometimes differ by several minutes?

Riegel is a purely empirical power law — it says nothing about physiology. Daniels is grounded in VO2max and assumes your aerobic capacity stays constant across distances, which breaks down at very short sprints (400 m) and very long ultras (100 km). The gap also widens if your training is highly specialised for one distance.

How do altitude and heat affect predicted race times?

The calculator applies +2% per 1000 m of elevation gain (based on IAAF altitude guidelines) and +0.3% per degree Celsius above 15 C (based on ACSM heat-stress guidance). A race at 2000 m altitude on a 25 C day carries roughly a 7% combined penalty — about 13 minutes on a 3-hour marathon.

Can I use a 5K time to predict a marathon finish?

Yes, but with wider uncertainty. The further apart the two distances are, the more training specificity matters. A well-trained marathoner will typically beat the Riegel prediction from a 5K by several minutes, while an untrained runner who only does parkruns may fall short. Use the prediction as a starting target and stress-test it with a half marathon tune-up race first.

Race Time Predictor — Gera Tools

A race time predictor translates one finish time into predicted times for every standard distance — from 400 m track efforts all the way to 100 km ultras. It runs two respected scientific models in parallel so you can see where they agree (high confidence) and where they diverge (worth digging deeper before you commit to a goal time).

How it works

The calculator combines two well-established models.

Riegel endurance exponent model

Peter Riegel published his fatigue curve in American Scientist (1981) after analysing world-record progressions across track and road distances. His formula is:

T₂ = T₁ × (D₂ / D₁)^e

where T₁ is your known time, D₁ the known distance, D₂ the target distance and e = 1.06 is the empirical fatigue exponent for trained runners. The exponent captures the fact that running speed does not scale linearly with distance — every doubling of distance costs more than twice the time because of glycogen depletion, muscle damage and cardiovascular drift.

The slider lets you tune e between 1.03 and 1.15. A lower exponent suits sprinters or runners whose short-course speed is disproportionately strong; a higher exponent reflects the heavy fade typical of ultra-marathon specialists or those who have trained overwhelmingly at long, slow distances.

Jack Daniels VDOT model

Jack Daniels (with Jimmy Gilbert) published the VDOT fitness index in their 1979 book Oxygen Power and updated it in Daniels’ Running Formula (2004). The model estimates your effective aerobic capacity from a race result using:

VDOT = VO₂(v) / %VO₂max(t)

where v is your race velocity in m/min, VO₂(v) = −4.60 + 0.182258v + 0.000104v² is the oxygen cost at that velocity and %VO₂max(t) = 0.8 + 0.1894393e^(−0.012778t) + 0.2989558e^(−0.1932695t) is the fraction of VO₂max you can sustain for a race of duration t minutes. Once VDOT is known, the calculation is inverted (via bisection) to find the time at which any other distance would be run at the same aerobic intensity.

VDOT also drives the training pace zone tab, giving you precise targets for Easy, Marathon, Threshold, Interval and Repetition workouts.

Environmental corrections

Real races happen above sea level and in warm weather. The calculator optionally applies two evidence-based corrections:

Altitude: +2% per 1 000 m (IAAF Athletics technical regulations, altitude performance tables).
Heat: +0.3% per °C above 15 °C (ACSM Position Stand on heat/fluid replacement, 2007).

Both corrections are multiplicative and stack — a 2 000 m mountain race on a 25 °C day carries roughly +7% combined.

Worked example

A runner finishes a 10 km race in 45:30 at sea level, 12 °C. Enter those numbers and the tool shows:

Distance	Riegel	Daniels
5 km	21:57	22:04
Half marathon	1:42:11	1:43:28
Marathon	3:33:28	3:37:05

VDOT = 47.2. The Riegel and Daniels marathon predictions differ by less than 4 minutes — both agree the runner should target 3:33–3:37 for a flat-course debut.

Now apply heat (race day reaches 28 °C) and altitude (900 m): the combined penalty is +3.9%, pushing the marathon prediction to 3:41–3:45.

The formula note

The Riegel exponent of 1.06 is often quoted as universal, but Riegel himself noted it was derived from world-record data, which skews toward elite runners with near-perfect pacing. For recreational runners, studies by Dugan and Sato (2014) found exponents ranging from 1.04 to 1.12 depending on weekly mileage and event specialisation. The slider in this calculator lets you dial in your personal curve once you have two or more race results to calibrate against.