What the calculator does
You enter a distance (1 km to marathon, or a custom distance) and your time. The calculator turns that result into predictions for 1.5 km, 1 mile, 3 km, 5 km, 10 km, 15 km, half marathon, 30 km and marathon, once using Riegel and once using VDOT. Next to each prediction you see the pace per kilometre, so you know straight away how the target effort should feel.
The two methods diverge most over large distance jumps. A 10k runner often gets two different marathon times, which is not an error but shows the limits of any formula.
The Riegel formula
Peter Riegel published the formula T₂ = T₁ · (D₂/D₁)b in the journal American Scientist in 1981. T₁ is your known time over distance D₁, T₂ the time you want over D₂. Riegel's default exponent b is 1.06 and describes how much pace fades as distance increases.
You can change the exponent in the calculator. A study by Vickers and Vertosick on recreational runners (2016, BMC Sports Science, Medicine and Rehabilitation) found that the default value of 1.06 underestimates marathon time for many recreational runners, and that an exponent between 1.07 and 1.08 often fits this group better, because they fade more over the marathon than highly trained runners. If you run low weekly mileage, plan with 1.07 or 1.08 rather than the default.
The VDOT method after Daniels
Jack Daniels and Jimmy Gilbert published a model in Oxygen Power in 1979 that turns a race result into a VDOT value, a measure of the oxygen uptake used during the race. From that VDOT value you can derive the time for any other distance, because the model assumes runners can sustain a typical share of their VO2max for each race duration. The VDOT calculator gives you the matching training paces.
Limits of the prediction
Both methods use averages from large datasets. They assume your training matches the target distance: a marathon prediction from a 5k result only holds if you have also built long runs and endurance volume. Without that volume you will run slower than either prediction, because pace is not your limiter, endurance is.
Example: a runner with a 45:00 10k gets a marathon prediction of 3:27:01 with a Riegel exponent of 1.06, 3:30:01 with 1.07 and 3:33:03 with 1.08. The VDOT method for the same runner (VDOT 45.3) gives about 3:27:15. Which figure applies depends heavily on prior marathon training.
Frequently asked questions
Which distances can I enter?
Any distance from 1 km to marathon, plus a custom distance. The output always shows the same nine target distances from 1.5 km to marathon.
Why do Riegel and VDOT give different results?
Riegel uses a fixed exponent on distance, VDOT uses a physiological model of oxygen uptake. Over short distance jumps they are close; over the jump from 10k to marathon they can differ by several minutes.
Which Riegel exponent is right for me?
The default of 1.06 suits well-trained runners with high mileage. According to Vickers and Vertosick (2016), recreational runners with fewer weekly sessions often do better with 1.07 to 1.08, because their marathon time fades more than the 1.06 formula assumes.
Is one 5k test enough to know my marathon time?
Only as a rough guide. A prediction from a 5k says nothing about your endurance at kilometre 30. Without long runs in training you will likely run slower in the marathon than either prediction here.
Can I plan my target time directly from the prediction?
The prediction is a starting point for a target time, not a promise. Use the split calculator to plan race-day splits, and the VDOT calculator for training paces.
Sources and method
- Riegel, P. S. (1981): Athletic Records and Human Endurance, American Scientist 69(3)
- Daniels, J. & Gilbert, J. (1979): Oxygen Power: Performance Tables for Distance Runners
- Vickers, A. J. & Vertosick, E. A. (2016): An empirical study of race times in recreational endurance runners, BMC Sports Science, Medicine and Rehabilitation 8:26