Riegel vs VDOT: Half-Marathon Time From a 40-Minute 10K

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 is the head-to-head comparison entry in our race-prediction series: it runs both engines on the same input and reads the actual gap — which turns out to be far smaller than the folklore suggests.

Engine outputs

A 40:00 10K through the Riegel-based Race Time Predictor and the Daniels Run Training Paces Calculator (VDOT):

# race-time-predictor (computed live from /engines/race-time-predictor.js)
Engine input
  known_distance_km     = 10
  known_time_minutes    = 40

Engine output
  predictions[0].label  = 5K
  predictions[0].distanceKm= 5
  predictions[0].timeMinutes= 19.185282
  predictions[0].paceMinPerKm= 3.8370565
  predictions[0].paceMinPerMile= 6.1751438
  predictions[0].difficultyDelta= 0.95926412
  predictions[1].label  = 10K
  predictions[1].distanceKm= 10
  predictions[1].timeMinutes= 40
  predictions[1].paceMinPerKm= 4
  predictions[1].paceMinPerMile= 6.437376
  predictions[1].difficultyDelta= 1
  predictions[2].label  = Half Marathon
  predictions[2].distanceKm= 21.0975
  predictions[2].timeMinutes= 88.256123
  predictions[2].paceMinPerKm= 4.1832503
  predictions[2].paceMinPerMile= 6.7322888
  predictions[2].difficultyDelta= 1.0458126
  predictions[3].label  = Marathon
  predictions[3].distanceKm= 42.195
  predictions[3].timeMinutes= 184.00797
  predictions[3].paceMinPerKm= 4.3608952
  predictions[3].paceMinPerMile= 7.0181805
  predictions[3].difficultyDelta= 1.0902238
  baselinePaceMinPerKm  = 4
  baselinePaceMinPerMile= 6.437376

# run-training-paces-calculator (computed live from /engines/run-training-paces-calculator.js)
Engine input
  distance              = 10k
  race_time_minutes     = 40
  race_time_seconds     = 0

Engine output
  vdot                  = 51.9
  inputRaceDistanceMeters= 10000
  inputRaceTimeSeconds  = 2400
  inputPacePerKmSeconds = 240
  zones[0].zone         = E
  zones[0].label        = Easy / Long Run
  zones[0].description  = Conversational pace for aerobic base and recovery. Use for most training volume.
  zones[0].pacePerKmSeconds= 308
  zones[0].pacePerMileSeconds= 496
  zones[0].effortPercent= 67
  zones[0].pacePerKmRangeSeconds[0]= 285
  zones[0].pacePerKmRangeSeconds[1]= 341
  zones[1].zone         = M
  zones[1].label        = Marathon Pace
  zones[1].description  = Your predicted marathon race pace. Race-specific runs for marathon training.
  zones[1].pacePerKmSeconds= 263
  zones[1].pacePerMileSeconds= 423
  zones[1].effortPercent= 82
  zones[1].pacePerKmRangeSeconds[0]= 263
  zones[1].pacePerKmRangeSeconds[1]= 263
  zones[2].zone         = T
  zones[2].label        = Threshold / Tempo
  zones[2].description  = Comfortably hard: about the pace you could race for an hour. Improves lactate threshold. Max 20 min continuous.
  zones[2].pacePerKmSeconds= 247
  zones[2].pacePerMileSeconds= 398
  zones[2].effortPercent= 88
  zones[2].pacePerKmRangeSeconds[0]= 247
  zones[2].pacePerKmRangeSeconds[1]= 259
  zones[3].zone         = I
  zones[3].label        = Interval / VO₂max
  zones[3].description  = Hard 3–5 min repeats near VO₂max. Builds aerobic power. Typical rep: 800m–1200m.
  zones[3].pacePerKmSeconds= 223
  zones[3].pacePerMileSeconds= 359
  zones[3].effortPercent= 100
  zones[3].pacePerKmRangeSeconds[0]= 223
  zones[3].pacePerKmRangeSeconds[1]= 227
  zones[4].zone         = R
  zones[4].label        = Repetition / Speed
  zones[4].description  = Short fast reps (200m–400m) with full recovery. Develops economy and speed.
  zones[4].pacePerKmSeconds= 206
  zones[4].pacePerMileSeconds= 332
  zones[4].effortPercent= 110
  zones[4].pacePerKmRangeSeconds[0]= 192
  zones[4].pacePerKmRangeSeconds[1]= 214
  equivalentRaceTimes[0].distance= 1,500m
  equivalentRaceTimes[0].distanceMeters= 1500
  equivalentRaceTimes[0].predictedSeconds= 313
  equivalentRaceTimes[1].distance= 1 Mile
  equivalentRaceTimes[1].distanceMeters= 1609.344
  equivalentRaceTimes[1].predictedSeconds= 338
  equivalentRaceTimes[2].distance= 5K
  equivalentRaceTimes[2].distanceMeters= 5000
  equivalentRaceTimes[2].predictedSeconds= 1158
  equivalentRaceTimes[3].distance= 10K
  equivalentRaceTimes[3].distanceMeters= 10000
  equivalentRaceTimes[3].predictedSeconds= 2400
  equivalentRaceTimes[4].distance= Half Marathon
  equivalentRaceTimes[4].distanceMeters= 21097.5
  equivalentRaceTimes[4].predictedSeconds= 5313
  equivalentRaceTimes[5].distance= Marathon
  equivalentRaceTimes[5].distanceMeters= 42195
  equivalentRaceTimes[5].predictedSeconds= 11078

Riegel's T2 = T1 × (D2/D1)^1.06: 40 × (21.0975/10)^1.06 ≈ 88.26 minutes (1:28:15) for the half, 184.0 minutes (3:04:00) for the marathon, and 19.19 minutes (19:11) for the 5K.^[1]

A 40:00 10K maps to VDOT 51.9, whose Daniels-table half-marathon equivalent is 1:28:33 (5313 s) and marathon equivalent 3:04:38 (11078 s). The VDOT pace zones come back as E 5:08/km, M 4:23/km (the predicted marathon pace), T 4:07/km, I 3:43/km, R 3:26/km.^[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. When the standard running-performance models are compared head to head on elite endurance runners, the power-law and logarithmic fits extrapolate to longer distances more accurately than the asymptotic critical-speed models do^[3] — and Riegel's formula is exactly a power law.

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 s

This 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:

1. 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.
2. 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.
3. 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:

1. 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.
2. For setting training zones, use VDOT directly — the pace bands map cleanly onto session intensities. The Run Training Paces Calculator exposes them.
3. 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.
4. 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 are population models: Riegel a power law fit to athletic records, VDOT the Daniels–Gilbert oxygen-cost equations. The 40-minute 10K runner (VDOT 51.9) is a typical trained recreational runner, and here the two agree within 18 seconds at the half. A power law extrapolates cleanly over a modest distance range and loses accuracy as the gap widens,^[3] so expect the two to drift apart further from the input distance.

The Race Time Predictor uses Riegel's standard 1.06 exponent. If you have two recent race results, solving ln(T2/T1) / ln(D2/D1) gives your own exponent, which is better founded than a guessed correction.

Related in this series

• Race Time Predictor — the prediction pillar: where the formula comes from.
• Predicting a Half-Marathon From a 40-Minute 10K — worked example through the Riegel engine.
• Training Paces From a 3:15 Marathon PR — turning a predicted time into VDOT/McMillan training zones.

Beyond the series: How To Train For A 5K covers the volume-vs-intensity framing that determines which engine wins on race day, and the Running Pace Calculator converts goal times back into per-kilometre paces.

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 produces a half-marathon prediction within 18 seconds of VDOT for a 40:00 10K. A power-law fit extrapolates cleanly over a modest distance range and loses accuracy as the gap widens,^[3] so for longer extrapolations work out your own exponent from two recent races: ln(T2/T1) / ln(D2/D1). That is a fit to your own results, not a population constant.

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.