Race Time Prediction: Where Riegel Holds and Where It Breaks

Where Riegel is accurate

The formula performs best when three conditions hold:

1. The input race was run near-maximally. A 5k you jogged at 80% effort gives you a misleadingly optimistic 10k prediction.
2. The target distance is within roughly 4× the input distance. 5k → 10k, 10k → half-marathon work well; 5k → marathon does not.
3. The runner is trained enough to sustain the predicted pace at the target distance. Training status matters independently of the race time.

Typical accurate applications:

Input                     Predicted                 Typical error
────────────────────────────────────────────────────────────────
5k:    22:00              10k:   45:52              ±1–2%
10k:   45:00              Half:  1:40:05            ±1–3%
Half:  1:40:00            Marathon: 3:29:28         ±2–7%   (see below)
1500m: 5:30               5k:    19:21              ±2–4%

Where Riegel breaks badly

Extrapolating to the marathon from a 5k or 10k

A 10k → marathon extrapolation with 1.06 assumes the runner has the aerobic base, muscular durability, and fuelling strategy to sustain near-lactate-threshold pace for 42 km. For recreational runners with less than 40 km/week of training, this assumption is usually false.^[2] The Riegel prediction may be 15–30 minutes optimistic against the marathon time actually achieved.

Practical correction: for marathon prediction from a sub-marathon race, use an exponent of 1.10–1.15 unless you have specific marathon-distance training volume behind you. The Race Time Predictor exposes the exponent as an input so you can adjust for your training status rather than accept a single default.

Predicting the 5k from a marathon

Riegel also fails in the opposite direction. A 3:30 marathon runner won't necessarily run a 20:00 5k — their training has been aerobic-base-biased and their speed at 5k pace is under-developed. Riegel's model assumes a balanced runner; a marathon specialist often has a 5k that's slower than the formula predicts, a half-marathon specialist often has one that's faster.

Ultra distances (above 50 km)

Fatigue exponent clearly rises above 1.06 past the marathon, and physiological factors Riegel didn't model (thermoregulation, GI tolerance, muscular damage accumulation) dominate the outcome. Do not use Riegel to predict a 100 km or a 100-mile time from a marathon PB. It will be dangerously optimistic.

What the exponent really encodes

The fatigue exponent is effectively the population average of fraction of VO2 max sustainable at different durations^[4][5]. A 5k is raced at roughly 95% VO2 max; a 10k around 90%; a half-marathon around 85%; a marathon around 75–80%. Riegel's 1.06 is the curve that matches that decay for a typical trained runner.

Elite runners have flatter decay — their lactate threshold sits at a higher fraction of VO2 max, so the gap between their 5k and marathon paces is smaller than the gap between a recreational runner's. That is why the elite-fitted exponent is below 1.06 and the recreational-fitted exponent is above.

Reverse-engineering your own exponent

If you have two recent race results at near-max effort, you can solve for your fatigue exponent:

exponent = ln(T2 / T1) / ln(D2 / D1)

Example:
  5k  in 20:00  (1200 s)
  10k in 42:30  (2550 s)

  ln(2550/1200) = 0.752
  ln(10/5)      = 0.693

  exponent     = 0.752 / 0.693 = 1.085

For this runner, using 1.085 rather than 1.06 will produce more accurate marathon predictions. This is the kind of personalisation that the baseline Riegel under-fits for.

Race-distance specific adjustments

The underlying fatigue exponent is not uniformly 1.06 across every distance pair. Based on analysing pools of race results, practically useful sub-exponents:

From → To                Typical exponent    Notes
────────────────────────────────────────────────────────────────
1500m → 5k               1.04                Elites closer to 1.02
5k → 10k                 1.06                Most reliable pair
10k → Half-marathon      1.07                Riegel-accurate
Half → Marathon          1.10                Riegel over-predicts
5k → Marathon            1.11                Rarely useful extrapolation
Marathon → 50 km         1.15                Fatigue rises steeply
Marathon → 100 km        1.20+               Highly individual

Using distance-specific exponents rather than a universal 1.06 tightens predictions by 1–3% across the range.

Alternative models briefly

Several alternatives to Riegel exist:

• Cameron's 1998 formula introduces a time-adjusted constant but produces similar results to Riegel with a slightly different shape.
• VDOT (Jack Daniels) maps race times to a fitness index, then reads out predicted paces and training paces. More sophisticated, but under the hood it's a Riegel-style fit anchored at VO2 max.
• Critical-power models (Monod-Scherrer) predict sustainable pace as a function of duration using a two-parameter fit from multiple known race times. More accurate than Riegel with sufficient data, useless with only one data point.

For a single known race time, Riegel is the right tool. For multiple known race times across a wide distance range, a critical-power fit is slightly more accurate at the cost of complexity.

Using Riegel on meet day

The single most useful application of Riegel is pacing. If you know your 10k PB is 42:30, Riegel says your half-marathon is roughly 1:34:19. That means:

• Your half-marathon target pace is about 4:28/km.
• If you go through 10k in 42:00 (faster than your all-out 10k PB), you are racing a 10k, not a half-marathon.
• If you go through 10k in 45:00, you are on track.

The Running Pace Calculator converts predicted times into kilometre and mile splits so you can build a pacing strip. Combined with the Race Time Predictor, you can sanity-check your target pace before committing to it.

Hedge

Summary

• Riegel is a single-equation model for race-time extrapolation. Default exponent 1.06.
• Accurate for mid-distance extrapolation (5k ↔ 21k) in trained runners.
• Too optimistic for under-trained marathoners; raise exponent to 1.10–1.15.
• Unreliable for ultra distances and for specialists extrapolating away from their discipline.
• Use it for pacing, not for training-status assessment.

Tools: Race Time Predictor, Running Pace Calculator.

Population boundaries of the original fit

Riegel's 1981 regression was fit on world-record performances across distances from 400 m to the marathon^[1]. That sampling choice has three consequences most users ignore:

• Elite bias. World-record holders have near-flat pace-vs-duration curves. The 1.06 exponent is closer to what the median trained masters/recreational runner produces than what Riegel's original dataset did — later re-fits on amateur race databases typically produce 1.06–1.08.
• Male bias. Record pools in 1981 were predominantly male. Women's physiology produces slightly different lactate-threshold-to-VO2-max ratios and slightly different glycogen-depletion dynamics over long distances^[5]. Modern re-fits on mixed-gender data still produce values near 1.06–1.08; the effect is small but the original fit didn't probe it.
• Flat-course, controlled-weather bias. World records are set on optimised courses. Real-world races include hills, heat, crosswinds, and crowded starts — all of which degrade pacing independently of any fatigue exponent. A Riegel-predicted marathon time is the time on a flat course in ideal conditions; add 3–8% for hilly courses, 4–10% for hot-weather races (24°C+ with humidity).
• No ultra-distance data. Riegel's dataset topped out at the marathon. The smooth extrapolation to 50 km and beyond has no empirical support in the original paper and, as the distance-specific exponent table above shows, fails in practice.
• No sub-400m data. Riegel is useless for sprint predictions — the physiological constraints (alactic capacity, maximum velocity) are discontinuous with aerobic endurance and require a separate model.

Alternative-view framing: VDOT vs Riegel vs critical power

Riegel is not the only endurance-performance model. The honest comparison across three widely used frameworks:

Model                     Inputs needed                 Strengths                    Limits
─────────────────────────────────────────────────────────────────────────────────────────────────────
Riegel (1 race time)       One race time + exponent      Cheap, ±3% for mid-distance  Single data point,
                                                                                       fixed exponent
VDOT / Daniels (1 race)    Race time + VO2 tables        Gives training paces too     Same single-point
                                                                                       weakness as Riegel
Critical-power (Monod)     Two or more race times        ±1–2% fit, handles curves    Needs multiple
                                                                                       near-max races
Tanaka time-area model     Weekly volume + race time     Captures training context    Unvalidated at
                                                                                       recreational scale

Saunders et al.'s review of running economy^[4] documents the degree to which economy (ml/kg/km) dominates long-distance performance independently of VO2 max itself. Models that bake in economy implicitly (VDOT) outperform models that don't (Riegel) at the individual level — but only if you have accurate VO2-max and economy inputs, which most recreational runners don't. The practical ranking for a single known race time is: Riegel with a personalised exponent > default-1.06 Riegel > VDOT with a population VO2 estimate. With two or more known near-max race times, critical-power fits beat everything.

Worked example: marathon prediction with personalised exponent

A recreational runner has two recent near-max results: 10k in 44:30 and half-marathon in 1:39:20. Compute their personal fatigue exponent, then project a marathon time and compare against default Riegel.

Inputs
  10k  D1 = 10 km    T1 = 2670 s (44:30)
  Half D2 = 21.1 km  T2 = 5960 s (1:39:20)

Personal exponent
  exponent = ln(T2/T1) / ln(D2/D1)
           = ln(5960/2670) / ln(21.1/10)
           = ln(2.232)    / ln(2.11)
           = 0.803        / 0.747
           = 1.075

Marathon prediction (42.195 km)
  Default 1.06 from half-marathon        3:28:57
  Personal 1.075 from half-marathon       3:33:18  (+4:21)
  Default 1.06 from 10k                   3:24:05
  Personal 1.075 from 10k                 3:30:42
  Honestly expected (under-40 km/wk       3:35–3:45
    training, first marathon)

The personal exponent (1.075) correctly identifies this runner as slightly endurance-weak relative to the Riegel population, and produces a marathon estimate 4–6 minutes slower than default-1.06 Riegel. The "under-trained marathoner" correction (raise to 1.10–1.15) would shift it further to ~3:40, which matches observed results for first-time marathoners with modest weekly volume. The three numbers — default Riegel, personalised Riegel, and training-adjusted Riegel — bracket the realistic range the runner should pace against.

Common failure modes

• Using a tempo-run time as "race time." The input race has to be near-maximal. A 10k tempo at RPE 8 with 2 km to spare produces a Riegel output that's 3–5% optimistic because the input wasn't the true race performance.
• Extrapolating across a 10x distance ratio. 1500 m → marathon or mile → ultra crosses too many physiological systems for any single-equation model^[2]. Limit to roughly 4x distance ratio.
• Using race-day Riegel ignoring heat/hills. A flat-course 1:39 half predicts 3:29 on flat roads. A Boston-style rolling marathon in 22°C routinely runs 3:40+ for the same fitness. Pace against the course and conditions, not just the model number.
• Treating elite exponents as applicable to amateurs. Sub-1.05 exponents appear in elite samples^[3] because their LT-to-VO2max ratios are tighter. A recreational runner applying an elite exponent over-predicts own marathon time by 5–10 minutes.
• Ignoring the specificity term. A 5k specialist who has never run beyond 15 km has an empirical marathon equivalent far slower than Riegel suggests. The model predicts what a balanced runner of that fitness could do; specificity gaps fall outside the model entirely.
• Running two maximal efforts in one week to "calibrate" the exponent. Back-to-back near-max races compromise recovery and produce a second-race time that reflects accumulated fatigue more than the athlete's true performance state. Space personal-exponent calibration efforts by 3+ weeks.
• Treating the predicted marathon time as a pacing target without executing the aerobic-base training. Riegel says what you could run at full fitness for the distance; if you haven't trained the distance, the prediction is unreachable on race day regardless of how good the input 10k was. Execute the training volume the prediction implicitly assumes before pacing for the predicted time.

Cross-modality Riegel

Riegel was developed on running but has been applied with mixed results to cycling and swimming. The exponent shifts because drag and efficiency curves differ across modalities:

• Cycling. Exponent typically fits closer to 1.04 for recreational cyclists and 1.02 for trained cyclists — air resistance dominates at higher speeds and the fraction of VO2 max sustainable over longer durations is flatter than in running. A 40k TT PB predicts a 100k TT PB fairly well at 1.04; applying 1.06 overstates the 100k time by 2–4%.
• Swimming. Exponent typically near 1.07–1.08 for pool swimming, slightly higher than running. Drag and technique degrade faster than in running as duration extends.
• Triathlon. Riegel fails cleanly for sport-to-sport extrapolation because the physiology is different. Use discipline-specific Riegel fits for each of swim, bike, run; don't try to cross-extrapolate.

The Race Time Predictor exposes the exponent as a user input for exactly these cross-modality and personalised applications — the default 1.06 is a starting point, not a universal law.

Historical-total rescoring and era comparisons

Using Riegel to compare performances across eras requires two adjustments most amateur comparisons skip: shoe technology and course certification standards. Both have shifted meaningfully and both affect the "same distance" assumption.

• Super-shoe era effect (2017+). Nike Vaporfly and successor shoes with carbon plates and advanced foams are documented to improve running economy by 4% in trained runners. A 3:00 marathon in 2024 in a super-shoe is roughly comparable to 3:08 in a 2016 racing flat at the same fitness. Riegel predictions transferred across this era transition over-predict or under-predict by the technology gap.
• Course certification. World Athletics-certified courses are measured with a specific accurate-to-within-0.1% protocol. Non-certified community races can be short by 1–3% (common) or long by 1–2% (less common). A 10k PB on an uncertified course is not directly comparable to the same time on a certified course for Riegel extrapolation.
• Altitude. World-record attempts at altitudes above ~1,500 m are meaningfully affected by oxygen availability. The physiological model of Lemaitre et al. 2015^[3] provides altitude corrections; rule-of-thumb adjustments are roughly 30–50 seconds per 1,000 m of altitude for a marathon.

These adjustments matter for era comparison and for travel-race planning. A runner who built fitness at sea level and races Boulder's 1,650 m altitude should derate Riegel-predicted times by 2–3% for the altitude cost alone.