From a 40-Minute 10K to a Half Marathon: A Riegel Walkthrough

A 40-minute 10K is a recognizable benchmark — roughly the line between recreational and serious club-level training. The Riegel formula scales it to other distances in a single equation. This is the worked-example entry in our race-prediction series: it runs one concrete benchmark through the engine end to end. The numbers are correct under the model's assumptions; the assumptions are worth checking before using a prediction to choose a race goal.

The scenario

A trained runner with a recent track 10K time of 40:00 flat (4:00/km, 6:26/mile). The runner wants two derived numbers: a realistic half marathon goal time for an upcoming race, and a "stretch" marathon projection for planning purposes.

What the calculator returns

Running the inputs through the Race Time Predictor:

# 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

Half marathon 88.26 minutes = 1:28:15. Marathon 184.01 minutes = 3:04:00. The "difficulty delta" column shows how much pace decay the model expects: roughly 4.6% for the half, 9.0% for the marathon, both measured from the 10K baseline pace.

Reading the numbers

The Riegel formula^[1]:

T2 = T1 × (D2 / D1)^1.06

For the half marathon:
  T2 = 40 × (21.0975 / 10)^1.06
     = 40 × 2.10975^1.06
     = 40 × 2.2064
     = 88.26 minutes

For the marathon:
  T2 = 40 × (42.195 / 10)^1.06
     = 40 × 4.2195^1.06
     = 40 × 4.6002
     = 184.01 minutes

The 5K back-projection (19.19 min) is also useful as a calibration check. If the runner can run 5K in 19:10 to 19:20 fresh, the 40:00 10K is "well-calibrated" — meaning the input reflects current fitness rather than a great day or a bad day. If 5K efforts in training land at 19:45+ with similar effort, the 10K time is a positive outlier and the half/marathon projections will over-promise.

Where the formula breaks

Riegel's 1.06 exponent was fitted at a population scale across many distances. Three failure modes show up at the individual level.

Insufficient endurance volume. Riegel does not know how much running the athlete does. In 2,303 recreational runners, weekly mileage and interval training were associated with race speed at every distance,^[2] so two runners with the same 40:00 10K can have very different marathons. The half marathon depends on that less than the marathon does.

The marathon end is where the fit fails. A survey of 2,303 recreational endurance runners found Riegel well calibrated for races up to the half marathon, then dramatically optimistic at the marathon — at least 10 minutes too fast for half the sample^[2]. The 1:28:15 half is the number to plan around; the 3:04 marathon is a ceiling, not a target.

Heat, course, and event variance. The model assumes a flat course in cool, still conditions. Heat, hills and wind all slow a race independently of fitness, so Riegel returns the time attainable under good conditions, not the time a given race day will allow.

Calibration against training paces

A predicted half time only carries information if it lines up with what the runner can hold in workouts. The Jack Daniels VDOT system encodes a similar projection with different math; the Run Training Paces Calculator puts the same 40:00 10K at a 1:28:33 half, 18 seconds from Riegel.

For a 40:00 10K (VDOT 51.9)
  Easy pace (E)         5:08/km     (range 4:45 – 5:41)
  Marathon pace (M)     4:23/km     (Riegel: 4:22/km, 1 s apart)
  Threshold (T)         4:07/km
  Interval (I)          3:43/km
  Repetition (R)        3:26/km

If the runner cannot hold 4:23/km for a 90-minute marathon-paced workout 4 to 6 weeks out, the 3:04 marathon prediction is not yet earned. The half marathon prediction is more forgiving — a runner who can sustain marathon pace for 60 minutes is usually within range of the 1:28:15 target.

A simple practical check: run a 30-minute threshold tempo three weeks out and a 90-minute marathon-paced run two weeks before peak week. If the marathon-paced effort breaks down well before 90 minutes, the marathon prediction is not yet earned; the half prediction asks less of the runner.

Related tools and follow-ups

• Race Time Predictor — the Riegel-based engine used in this walkthrough.
• Running Pace Calculator — converts between pace, time, and distance for arbitrary intervals.
• VO2 Max Estimator — separate physiological cross-check on aerobic ceiling.

Related in this series

• Race Time Predictor — the prediction pillar: source paper and failure modes.
• Riegel vs VDOT: Half-Marathon From a 10K — head-to-head on this same input.
• 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 walks through the build-up for the shorter end of the distance.

FAQ

What half marathon time predicts from a 40-minute 10K? Roughly 1:28:15. The Riegel formula T2 = T1 × (D2/D1)^1.06 with T1 = 40 min, D1 = 10 km, D2 = 21.0975 km returns 88.26 minutes — equivalent to 4:11/km or 6:43/mile.

Why does Riegel use the 1.06 exponent? Riegel fit a power law to athletic records in his 1981 American Scientist paper, and 1.06 is the exponent used for runner race prediction. The largest test in recreational runners found it well calibrated up to the half marathon and too fast at the marathon for half of them.

When is Riegel too optimistic about the marathon? Mostly at the marathon. A 40:00 10K predicts a 3:04 marathon under Riegel, but in 2,303 recreational runners the formula gave marathon times at least 10 minutes too fast for half of them, and training volume was one of the factors associated with race speed.