TL;DR
- For a 40:00 10K, the Riegel-based race-time predictor projects a half-marathon of 1:28:15 at a baseline pace of 4:00/km.[4]
- The VDOT engine returns VDOT 51.9 and a half-marathon equivalent of 1:28:33 — only about 18 seconds slower than the Riegel prediction.[2]
- The headline result is agreement, not disagreement. Over a 21 km race, two formulas built from completely different data land within 0.3% of each other.
- Where they diverge is the marathon, not the half. The spread grows to about 38 seconds at 42.195 km and keeps widening past it — the further you extrapolate, the less the two agree.
A 40-flat 10K is the most common "what next?" entry point in recreational running. The Riegel formula and Daniels' VDOT system both project a half-marathon time from it, and they are often assumed to disagree by a minute or more. This article runs both engines on the same input and reads the actual gap — which turns out to be far smaller than the folklore suggests.
Scenario inputs
recent_distance_km: 10
recent_time_minutes: 40
target_distance_km: 21.0975 (half marathon)Engine outputs
Race Time Predictor (Riegel)
Output (excerpted):
baselinePaceMinPerKm: 4.00
predictions:
5K: 19:11 pace 3:50/km
10K: 40:00 pace 4:00/km (input)
Half Marathon: 1:28:15 pace 4:11/km
Marathon: 3:04:00 pace 4:22/kmRiegel's T2 = T1 × (D2/D1)^1.06: 40 × (21.0975/10)^1.06 ≈ 88.26 minutes (1:28:15).[1]
Run Training Paces (VDOT)
vdot: 51.9
inputRaceDistanceMeters: 10000
inputRaceTimeSeconds: 2400
inputPacePerKmSeconds: 240
zones (mid-band pace per km):
E (Easy / Long Run): 5:08/km
M (Marathon): 4:30/km
T (Threshold): 4:12/km
I (Interval): 3:48/km
R (Reps): 3:26/km
equivalent half-marathon: 1:28:33 (5313 s)
equivalent marathon: 3:04:38 (11078 s)A 40:00 10K maps to VDOT 51.9, whose Daniels-table half-marathon equivalent is 1:28:33.[2]
Reading the 18-second gap
The interesting result is how close these two engines land. Riegel projects 1:28:15; VDOT projects 1:28:33. The spread is 18 seconds over a 21.1 km race — roughly 0.3% of the total time. Two models built from entirely different source data (Riegel from world-record times across distances, Daniels from trained club and collegiate runners) converge almost exactly at the half-marathon distance for a runner in this fitness band.
That convergence is not an accident. The half-marathon sits close to the 10K input on a logarithmic distance scale, so both engines are doing a short, well-conditioned extrapolation. Riegel's 1.06 exponent and Daniels' VDOT tables were both calibrated against trained-runner data in exactly this range, so they agree where the underlying physiology is best characterised.[3]
Where the spread actually grows: the marathon
Extend the same input to 42.195 km and the agreement loosens. Riegel projects 3:04:00; VDOT projects 3:04:38. The spread widens from 18 seconds at the half to about 38 seconds at the full marathon. The pattern is consistent: the further past the input distance you extrapolate, the more the two models diverge, with VDOT trending slightly slower (more conservative) at long distances.
Distance Riegel VDOT Spread
──────────────────────────────────────────────
5K 19:11 19:18 +7 s (VDOT slower)
10K (input) 40:00 40:00 0 s
Half Marathon 1:28:15 1:28:33 +18 s
Marathon 3:04:00 3:04:38 +38 sThis is the honest reading of the two engines: they agree closely near the input distance and drift apart as you extrapolate further. At the half-marathon — the most common target off a 10K — the practical difference is negligible, well inside the noise of race-day pacing, weather, and course profile.
When the small gap still matters
Eighteen seconds is inside the margin where the runner, not the formula, decides the outcome. Use the two predictions as a tight bracket rather than rival forecasts:
- VDOT (1:28:33) as the conservative anchor. Slightly slower, which makes it the safer pacing target for a first half-marathon attempt.
- Riegel (1:28:15) as the stretch target. For a well-trained 10K runner with consistent half-marathon mileage, the slightly faster figure is reachable on a good day.
- Either, for training zones. The difference is too small to change session prescription. Use VDOT's pace bands because it returns them directly.
How the two models differ in structure
The numbers agree, but the engines are built differently — worth knowing for cases where they don't:
- Continuous function vs table. Riegel is one scalable exponent (1.06), applicable to any distance. VDOT is a piecewise table-driven mapping. Inside the well-fitted range they track each other; far outside it they can drift apart.
- Pace zones vs single race time. VDOT returns training zones (Easy / Marathon / Threshold / Interval / Reps) plus race equivalents, which is more useful for actual training. Riegel returns equivalent times only.
- Extrapolation behaviour. Riegel's flat exponent applies the same fatigue assumption at every distance. VDOT's table bends slightly more at long distances, which is why the spread widens toward the marathon rather than the half.
When to use which
Practical guidance:
- For a half-marathon goal pace off a 10K personal best, treat the two outputs as one answer — they agree to within 18 seconds. Pick VDOT as the conservative pacing number and run.
- For setting training zones, use VDOT directly — the pace bands map cleanly onto session intensities. The Run Training Paces Calculator exposes them.
- For predicting a marathon from a 10K, expect the engines to start disagreeing (about 38 seconds here) and both to lose accuracy. Verify with a marathon-paced training block, not a 4× distance extrapolation.
- For hilly courses, neither tool handles elevation; pair them with the Marathon Pace Elevation tool which adds the slope correction.
The runner the engines were built for
Both models were derived from competitive-runner data: Riegel from world-record times across distances, VDOT from a population of trained club and collegiate runners. The 40-minute 10K runner (VDOT 51.9) sits in the heart of the cohort both models were fit to, which is exactly why they agree so closely here. For runners well outside that range — beginners over 60 minutes, sub-elites under 32 minutes — both engines lose precision in different directions, and the half-marathon spread can open up well beyond 18 seconds.[2]
The Race Time Predictor exposes the Riegel exponent as a tunable parameter (default 1.06). For under-trained runners, raising the exponent to 1.10–1.12 makes Riegel more conservative at the half-marathon distance, pushing it past the VDOT prediction.
Cross-checking against other content
Deeper reads: Race Time Prediction: Riegel Limits for the formula failure modes, VDOT vs Riegel Failure Modes for where the two disagree, and How To Train For A 5K for the volume-vs-intensity framing that determines which engine wins on race day.
The Running Pace Calculator is the right tool for converting goal times back into per-kilometre paces; useful for the final goal-setting step after picking between Riegel and VDOT.
FAQ
Which prediction should I aim for on race day?
For the half-marathon the two are 18 seconds apart, so it barely matters. Aim for the VDOT figure (1:28:33) as the conservative target; if the race goes well you'll naturally drift toward the Riegel time (1:28:15). The gap is smaller than the swing a single hill or a warm afternoon will cause.
What's the right Riegel exponent for me?
The default 1.06 fits trained runners well and produces a half-marathon prediction within 18 seconds of VDOT for a 40:00 10K. For lower training volume (under 50 km/week), raise it to 1.08–1.10 to make the prediction more conservative; for low-mileage runners (under 35 km/week), 1.12 is reasonable.[3]
Does heat change which engine wins?
Neither engine adjusts for heat — both were calibrated on temperate-condition races. Above 20°C, both over-predict by roughly 2–5%. A common pacing rule is to add about 1% to the predicted time per 5°C above 15°C, applied to whichever engine you picked.
Why does VDOT include training paces but Riegel doesn't?
Daniels designed VDOT explicitly as a training-prescription system; Riegel designed his formula as a race-time extrapolation tool. The difference reflects intent, not theoretical depth. Use VDOT when the next step is a training block, use Riegel when the next step is a goal time on the race calendar.
References
- 1 Athletic records and human endurance (Riegel) — American Scientist (PubMed PMID 7235349) (1981)
- 2 Daniels' Running Formula and the VDOT system: a critical review — Sports Medicine (2003)
- 3 Modelling endurance performance from race time data (Vandewalle et al.) — European Journal of Applied Physiology (2016)
- 4 Methodology notes for the Race Time Predictor — AI Fit Hub (2026)