Marathon Time Predictor: How the Riegel Formula Estimates Race Times from Training Pace

Last reviewed: 2026-05-08 — ScoutMyTool Editorial

A 35-year-old runner posts a 21-minute 5K and wants to know what marathon time they could realistically target. Plugging into a typical race-time predictor returns "3:24:30 marathon." Six months of training later, they run 3:38:15 — a 14-minute miss. The formula wasn't broken; the prediction assumed they would maintain the same fatigue characteristics over 26.2 miles that they showed at 5K, plus they'd train at marathon-specific volume. Most amateur runners do neither. The Riegel formula — the underlying math behind nearly every "marathon time predictor" — uses a fatigue exponent that empirically captures the average runner's slowdown over longer distances. The original is Riegel 1981 American Scientist "Athletic records and human endurance" (which extended his earlier 1977 Runner's World analysis). It's an excellent baseline; it's not a guarantee, and the gap between Riegel-predicted and actual times typically runs 5–15 minutes for amateurs per the Vickers & Vertosick 2016 PeerJ analysis of marathon predictions.

This guide explains the Riegel formula, the 1.06 fatigue exponent, when predictions are reliable, and how to use the race time predictor for planning.

The Riegel Formula

Pete Riegel's 1977 / 1981 American Scientist formula:

T₂ = T₁ × (D₂ / D₁)^1.06

Where:

• T₁, D₁ = known race time and distance
• T₂, D₂ = predicted time and target distance
• 1.06 = empirical "fatigue exponent" from data analysis

For a 21:00 (1260 seconds) 5K (5,000m) predicting a marathon (42,195m): T₂ = 1260 × (42195/5000)^1.06 = 1260 × 8.439^1.06 ≈ 1260 × 9.78 ≈ 12,323 seconds ≈ 3:25:23

The 1.06 exponent reflects the empirical observation that race times scale slightly faster than linearly with distance. A doubling of distance produces roughly 2.08× the time (2^1.06 = 2.085) for the average competitive runner. The Vickers & Vertosick 2016 paper re-analyzed 2,303 amateur marathoners and found a population-average exponent closer to 1.07–1.10 — meaning Riegel's 1.06 systematically underpredicts marathon time for amateurs.

When the Formula Is Reliable (and When It Isn't)

The formula works best:

• Same fitness and form: prediction assumes the runner's fitness doesn't change between input race and target race
• Adequate distance training: the formula assumes the runner has trained for the target distance. A 5K-only-trained runner predicting marathon time will significantly miss because they haven't built the aerobic base for 26.2 miles per the Daniels & Gilbert Daniels' Running Formula (3rd ed.) VDOT methodology
• Similar conditions: weather, terrain, course profile must be comparable
• Mid-range distances: most accurate from 1500m to half-marathon. Predictions for shorter (sprints) or much longer (ultramarathons) distances are less reliable

The formula breaks down:

• From very short races (e.g., predicting marathon from mile time): the runner's anaerobic capacity dominates short-race time but is irrelevant for marathon. Massive over-prediction of marathon ability.
• From untrained athletes: a runner with great 5K but no long-run training will significantly underperform marathon prediction
• In adverse conditions: heat, hills, headwind all slow marathon times beyond what 5K reveals — see the Ely et al. 2007 Med Sci Sports Exerc analysis of marathon performance and weather
• For elite vs amateur runners: elite runners typically meet or exceed Riegel predictions; amateurs often miss by 5–15 minutes per Vickers & Vertosick 2016

The Vickers & Vertosick analysis shows Riegel's predictions are typically within 1–2% of actual elite marathon times but 4–8% optimistic for average amateur marathon times.

How the Race Time Predictor Calculator Works

The race time predictor takes a known race time + distance, target distance, returns predicted time using Riegel's formula. Some advanced calculators allow exponent adjustment (1.06 default; some recommend 1.07–1.10 for amateurs targeting marathon).

Pair with:

• Running pace converter for min/km ↔ min/mi
• Finish time from pace for race-day execution
• VDOT calculator for VO2max-based race-equivalent times (Daniels' Running Formula method)
• McMillan pace equivalents for an alternative race-time prediction methodology
• Our VO2 max improvement deep dive for the aerobic-engine training that determines whether you can actually hit the predicted time

Worked Examples

Example 1 — Marathon from 10K time. Runner with 45:00 10K. Marathon prediction at k=1.06: 2700 × (42195/10000)^1.06 = 2700 × 4.624 = 12,485 seconds = 3:28:05. For a runner who has trained marathon volume, this is a reasonable target. For someone who only trains 10K-distance runs, they should expect to miss this by 10–20+ minutes — a k=1.10 estimate predicts 3:39:39, closer to amateur reality per Vickers 2016.

Example 2 — Half-marathon from 5K. Runner with 22:00 5K. Half prediction: 1320 × (21097/5000)^1.06 = 1320 × 4.624 = 6,103 seconds = 1:41:43. Half-marathon prediction from 5K is typically more reliable than full marathon prediction because the distance ratio is smaller.

Example 3 — 5K time from marathon time. A 3:30:00 marathoner predicting their 5K. 12600 × (5000/42195)^1.06 = 12600 × 0.1078 = 1359 seconds = 22:39. Reverse-direction predictions are typically reliable; if you ran 3:30 marathon trained, your 5K should be around 22-23 minutes.

Example 4 — When prediction misleads. Recreational runner with 19:00 5K but only training 25-30 mpw (miles per week). Riegel predicts marathon at 3:08:00. Reality: with under-trained marathon volume — typical "good marathon training" is 50–70 mpw at this pace per the Daniels training pyramid — they're likely to run 3:30–3:45. The formula doesn't know about training volume; it only knows the input time. Over-prediction of marathon ability by 25+ minutes is common for under-trained runners.

Common Pitfalls

The biggest pitfall is treating Riegel predictions as precise targets. The formula is a baseline; actual performance depends heavily on training volume, recent fitness changes, weather, course profile, and pacing strategy.

The second is using sprint times (mile or shorter) to predict marathon. The energy systems differ too much. Use 10K or half-marathon as the input race for marathon prediction; mile predictions of marathon are unreliable.

The third is ignoring training volume. A "20:00 5K" runner training 15 mpw and a "20:00 5K" runner training 60 mpw will run dramatically different marathon times. Volume matters more than the input speed for endurance events per Foster et al. 2008 Sports Med training-load review.

The fourth is using the prediction to set goal pace. Goal-paced training works backward from the predicted time, but if the prediction is wrong (typically too fast for amateurs), training at predicted goal pace becomes too aggressive. Better practice: use Riegel as a ceiling; train at slightly slower pace.

The fifth is forgetting course-specific factors. Boston has 90 feet of net descent; Big Sur has 1,800 feet of net climbing per the respective USATF course-certification database. The same marathon-trained athlete will run very different times. Riegel doesn't know about course profiles.

Frequently Asked Questions

Q: What is the Riegel formula? A: T₂ = T₁ × (D₂/D₁)^1.06, where 1.06 is the empirical fatigue exponent. Predicts race time at a target distance based on a known race time at a different distance. Per Pete Riegel's 1981 American Scientist paper "Athletic records and human endurance".

Q: How accurate is marathon time prediction from a 5K? A: Reasonable for marathon-trained runners (within 5–10 min) per Vickers 2016. Often unreliable for under-trained runners (can miss by 20+ min). Better predictions come from longer input distances (10K or half-marathon).

Q: What's the difference between Riegel and VDOT predictions? A: Riegel is empirical fatigue-exponent math. VDOT (Jack Daniels) uses VO2max-based race-pace equivalents per Daniels' Running Formula. Both produce similar predictions for typical scenarios; VDOT is more accurate at trained-athlete level. The VDOT calculator provides the alternative.

Q: Why do amateurs miss Riegel predictions? A: Insufficient marathon-specific training volume. The formula assumes adequate aerobic base; amateurs often have peak speed (5K) without endurance volume. The Vickers & Vertosick 2016 paper found amateur fatigue exponents cluster at 1.08–1.10 rather than 1.06.

Q: Should I train at the predicted goal pace? A: Use predicted pace as a ceiling. Most experienced coaches recommend training at slightly slower than predicted goal pace to build durability without breaking down. McMillan and Daniels have specific training-pace recommendations.

Q: How do hot conditions affect marathon prediction? A: Significantly. The Ely et al. 2007 study of 7 major US marathons found marathon times slow approximately 1.5–3% per 10°F above ~50°F (10°C) optimal — that's 3–6 minutes slower for a 3:30 marathoner running in 70°F. Adjust your race-day target accordingly.

Q: Does altitude affect race time prediction? A: Yes. Altitude above 3,000 ft (900 m) reduces race performance roughly 1–2% per 1,000 ft per USATF altitude-correction tables and the Peronnet & Thibault 1989 Eur J Appl Physiol model. Riegel doesn't include altitude — adjust manually for races above sea level.

Wrapping Up

Riegel's formula (T₂ = T₁ × (D₂/D₁)^1.06) gives a good baseline for race-time prediction but assumes the runner has trained for the target distance. Use the race time predictor as a planning starting point, not an absolute target. Pair with the running pace converter, VDOT calculator, and finish time from pace calculator for full race-planning analysis. The 1977/1981 Riegel formula remains widely used in running science 50 years later because the 1.06 exponent captures real fatigue patterns at the elite level — but amateurs typically need an exponent of 1.08–1.10 for accurate marathon predictions per the Vickers 2016 re-analysis. This article is general fitness information, not medical advice; consult a clinician before starting a new high-volume training program.

Sources & References

• Riegel 1981 — Athletic records and human endurance (American Scientist)
• Vickers & Vertosick 2016 — An empirical study of race times in recreational marathon runners (PeerJ)
• Daniels & Gilbert — Daniels' Running Formula (Human Kinetics, 3rd ed.)
• Ely et al. 2007 — Impact of weather on marathon-running performance (Med Sci Sports Exerc)
• Peronnet & Thibault 1989 — Mathematical analysis of running performance and world running records (Eur J Appl Physiol)
• Foster et al. 2008 — Athletic performance in relation to training load (Sports Med)
• USATF — Course certification and search