How race-time prediction actually works
Every race-time predictor on the internet is doing one of two things. Either it is fitting a power law to your input (Pete Riegel's 1981 method), or it is running you through a physiology model that estimates the fraction of VO2max you can sustain for a given duration (Jack Daniels' 1979 method). Both approaches converge on similar answers for trained runners across moderate distance jumps. Both quietly fail in predictable ways at the marathon.
This page runs both methods on your input simultaneously, so you can see the spread. When they agree, the prediction is solid. When they disagree by more than 2-3%, that itself is a useful signal about how confident to be.
Method 1: Pete Riegel's endurance formula (1981)
Pete Riegel was a mechanical engineer and a competitive distance runner who, in American Scientist in 1981, fit a simple power law to world-record performances across distances from 1500m to the marathon. He found that finish time scales with distance to a small power greater than 1:
The exponent 1.06 captures the fact that you cannot hold a given pace forever. As distance doubles, time slightly more than doubles. Riegel found the exponent was relatively stable across distances from 800m to the marathon for elite athletes.
The formula's strength is its simplicity. It needs no physiology, no oxygen costs, no training context. The weakness is that the exponent 1.06 was fit to world records. For recreational runners, the effective exponent at marathon distance is closer to 1.07 to 1.10, which is why Riegel predictions tend to flatter amateur marathon performance.
Method 2: Daniels and Gilbert's VDOT model (1979)
Two years before Riegel, exercise physiologist Jack Daniels and mathematician Jimmy Gilbert published a different approach in Oxygen Power: Performance Tables for Distance Runners. They built a two-equation system that goes through physiology rather than around it.
The first equation gives the oxygen cost of running at a given velocity:
The second gives the fraction of maximum aerobic capacity sustainable for a race of duration t:
From your input race, the system derives a fitness score (VDOT). To predict a time at another distance, it finds the duration at which oxygen cost equals VDOT times the sustainable fraction. The model has a physiological story for every number.
If you want the full background, see our VDOT explainer and the dedicated VDOT calculator, which exposes the underlying VDOT score and adds training paces.
Why both methods overestimate amateur marathons
The cleanest evidence comes from Vickers and Vertosick (2016), who collected 2,303 race performances from 304 recreational endurance runners and tested how well 5K, 10K, and half-marathon times predict marathon times. Their finding: marathon times were systematically slower than Riegel's prediction by an average of 4-5%, with much wider scatter than predictions at shorter distances. The longer the prediction jump, the worse the fit.
This is not a flaw in either formula. It reflects something real:
- A 5K tests aerobic ceiling and lactate clearance. A marathon tests fat oxidation, glycogen capacity, fluid replacement, heat tolerance, and pacing discipline. The 5K does not load any of these.
- The %VO2max-versus-duration curve was fit to runners who completed those durations well-trained for them. A 20-minute 5K runner who has never run more than 12 km in their life is well outside the curve's training context.
- Riegel's exponent 1.06 came from world records. The athletes setting world records at the marathon have done the marathon training. Amateurs predicting from a 5K usually have not.
The honest takeaway: a race-time predictor tells you what is possible if you train. It does not tell you what you will run on race day. The gap between the two is closed by consistent marathon-specific training - typically 16-22 weeks, 50-70 km per week, long runs progressing to 28-32 km, with marathon-pace and threshold work in the final block. See our guides on how long marathon training takes and Pfitzinger vs Daniels vs Canova for what that actually looks like.
When to trust the prediction
The prediction is most reliable when:
- You are predicting between similar distances (5K → 10K, 10K → half).
- Your input race was a true maximal effort in similar conditions to your goal race.
- You are already training for the target distance (long runs, marathon-pace work, appropriate weekly volume).
The prediction is least reliable when:
- You are predicting marathon time from a 5K or shorter.
- Your input race was on a hilly course, in heat, or at altitude.
- Your goal race is in conditions very different from the input race.
- You have not yet done the long-run mileage needed to back the prediction up.
Practical use
Use the prediction as a planning target, not a guarantee:
- Setting a goal pace: Use the prediction as an upper bound. Many coaches recommend setting your race-day goal 1-3% slower than the prediction to leave room for the conditions you cannot control.
- Choosing a pacing group: Pick the group closest to (and slightly slower than) your prediction. The downside of pacing too fast in a marathon is non-linear and brutal.
- Tracking fitness over a build: Run the same input race format every 4-6 weeks and watch the predictions move. The trend is usually more useful than the absolute prediction.
- Picking the right race: If your half-marathon prediction is significantly faster than your marathon prediction, you are short on endurance. If the reverse, you are short on speed.
Frequently asked
How is this different from the VDOT calculator?
The VDOT calculator focuses on training paces (Easy, Marathon, Threshold, Interval, Repetition) derived from your fitness score. This page focuses on cross-distance race predictions and shows two methods side by side. The underlying Daniels math is identical; the framing and outputs differ.
Why does my marathon prediction differ between sites?
Almost every site uses one of three approaches: Riegel with exponent 1.06, Riegel with a tweaked exponent (often 1.08 for marathon predictions), or a Daniels-style VDOT model. Some calculators (McMillan, RunSMART) tune their tables on top of these formulas. Across calculators, expect ±3-5% spread on marathon predictions from the same 5K input.
Can I use this predictor for ultras?
No, neither model is reliable past the marathon. Ultra performance depends on factors (terrain, climbing, nutrition, sleep, fuelling strategy) that road race predictors do not model. Use ultra-specific calculators or coach guidance.
What if my input race was on a hilly course?
Subtract roughly 1-2% from your finish time for every 100m of climb on the course before plugging it in. Or trust the result and mentally add 2-3% back to the marathon prediction. The model assumes flat conditions.
How do I improve my predicted time?
The predictor is downstream of fitness, not the cause of it. To move the prediction, raise VDOT - which means consistent volume at Easy pace plus targeted weekly Threshold and Interval work. See what VDOT is and how training load drives fitness.
References
- Riegel, P. S. (1981). "Athletic Records and Human Endurance." American Scientist, 69(3), 285-290. The original power-law formulation.
- Daniels, J. & Gilbert, J. (1979). Oxygen Power: Performance Tables for Distance Runners. Tafnews Press. The VDOT physiology model.
- Daniels, J. (2021). Daniels' Running Formula (4th ed.). Human Kinetics. The modern canonical reference.
- 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. Empirical evidence on Riegel marathon overestimation in recreational runners.