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. 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:

Engine input
  tool                  = race_time_predictor
  known_distance_km     = 10
  known_time_minutes    = 40

Engine output
  baselinePaceMinPerKm  = 4.00
  baselinePaceMinPerMile= 6.4374

predictions[]:
  5K              19.19 min  pace 3:50/km   delta 0.959
  10K             40.00 min  pace 4:00/km   delta 1.000 (input)
  Half Marathon   88.26 min  pace 4:11/km   delta 1.046
  Marathon       184.01 min  pace 4:22/km   delta 1.090

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 per week. A runner doing 30 km/week with one weekly long run of 14 km cannot execute the predicted 3:04 marathon. The half marathon prediction degrades less because the half is reachable from a 30 to 40 km/week base; the marathon needs 60 to 80+ km/week to support the predicted pace through the back third of the race.

Sub-elite vs elite exponent drift. Refitting on contemporary distance-runner cohorts puts the exponent between 1.04 (elites) and 1.08 (recreational)^[2]. A 40:00 10K runner sits closer to 1.06 to 1.07, which means the marathon prediction may be 2 to 3 minutes optimistic before training volume is considered.

Heat, course, and event variance. The model assumes flat, dry, cool conditions. A hot half marathon (above 22°C ambient) adds 1 to 3 minutes for a sub-90-minute runner. A hilly course adds another 1 to 4 minutes. Riegel returns the physiologically attainable time under ideal conditions, not the time the runner will actually post on race day.

A practical example of the volume failure: a 30-year-old runner clocks 39:50 in a flat October 10K. Riegel projects 3:03:40 for a spring marathon. The runner averages 42 km/week through winter, peaking at 58 km in the last three weeks. Marathon day result: 3:21:45, 18 minutes off the prediction. The 10K time was honest; the marathon was running on cardiac fitness with no metabolic substrate or muscular conditioning to back it up. The half marathon, attempted three weeks before the marathon on a tune-up, came in at 1:29:05 — within 50 seconds of the Riegel target. The model called the half right and the marathon wrong, both for the same reason.

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; cross-checking against the Run Training Paces Calculator typically agrees within 30 to 60 seconds at the half marathon distance.

For a 40:00 10K (≈ VDOT 53)
  Easy pace (E)         5:01 – 5:18/km
  Marathon pace (M)     4:18/km     (Riegel: 4:22/km — agrees within 4s)
  Threshold (T)         4:01/km     (~10K race effort, calibration check)
  Interval (I)          3:43/km
  Repetition (R)        3:25/km

If the runner cannot hold 4:18/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 two-test calibration: run a 30-minute threshold tempo three weeks out and a 90-minute marathon-paced run two weeks before peak week. If both efforts land within 5 seconds per kilometer of the predicted half pace and the marathon-pace effort feels conversational, the model's projection holds. If the marathon-paced effort breaks down before 60 minutes, the prediction is one cycle of training away.

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.

For deeper analysis: Race time prediction: Riegel's limits covers the source paper and failure modes; Race time prediction: VDOT vs Riegel failure modes compares the two main models; 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 the exponent against world-record times across distances from 400 m to the marathon and found 1.06 as the best population-level value. Re-fits since have produced exponents between 1.04 and 1.08; 1.06 remains the defensible default for trained recreational runners.

When does Riegel over-predict marathon time? When the runner has insufficient endurance volume. A 40:00 10K predicts a 3:04 marathon under Riegel — but only if weekly volume sits above 60 to 80 km. Under that, the marathon prediction blows out by 15 to 25 minutes.