Race Time Predictor

The Riegel formula — the field’s standard predictor

Pete Riegel published “Time predicting” in Runner’s World magazine in August 1977 and later formalized the method in his 1981 paper “Athletic records and human endurance” in American Scientist. He had collected race results across distances and fit a power-law curve to the data:

T2 = T1 × (D2 ÷ D1)^1.06

Where T1 is the known race time, D1 is the known race distance, T2 is the predicted time for the target distance, and D2 is the target distance.

The 1.06 exponent (sometimes called the “fatigue factor”) captures the empirical observation that as distance doubles, time slightly more than doubles. You can’t quite hold the same pace as distance grows because fatigue compounds.

Worked example: you ran a 5K in 22:00. Predicted marathon time:

• T1 = 1320 seconds (22:00)
• D1 = 5000m
• D2 = 42195m (marathon)
• T2 = 1320 × (42195 ÷ 5000)^1.06
• T2 = 1320 × 8.439^1.06
• T2 = 1320 × 9.71
• T2 = 12,817 seconds = 3:33:37

That’s the Riegel prediction. The reality is usually slower (more on this below).

Where Riegel works best

The formula is most accurate when:

1. Adjacent distances: 5K → 10K is reliable. 10K → half-marathon is reliable.
2. Recent races: T1 should be within the last 6 weeks. Older results may not reflect current fitness.
3. Appropriate training: predictions assume you’ve trained for the target distance, not just the known distance.
4. Similar conditions: race conditions (heat, wind, course) should be comparable.
5. Trained runner: the formula was calibrated on serious runners; beginners may see larger errors.

Where Riegel fails

Riegel himself warned against extrapolating too far. The formula consistently underestimates marathon times for runners whose only known race is a 5K, because:

• A marathon stresses systems (glycogen depletion, muscle damage, thermal regulation) that 5K races barely touch
• Marathon-specific training (long runs, fueling practice) matters enormously
• A runner who hasn’t trained for marathon distance simply can’t perform at Riegel-predicted level
• Mental and pacing experience for marathons is a separate skill

The empirical adjustment: add 5-10% for non-marathon-trained runners

Coaches commonly add 5-10% to Riegel marathon predictions for runners without dedicated marathon training. So our 5K-to-marathon example (3:33:37 Riegel prediction) becomes 3:45-3:55 in reality.

Alternative predictors

Several other formulas exist:

Cameron formula (1998): similar power-law approach with different coefficient: T2 = T1 × (D2 ÷ D1)^1.0641

Cameron used a slightly higher exponent. Predicts slower marathon times than Riegel from short-distance results.

VDOT system (Jack Daniels, 1998): based on physiology, not pure data fitting. Each runner has a “VDOT” value derived from race performance. VDOT-equivalent times are listed in tables, and the system accounts for race distance more nuancedly.

McMillan calculator: similar to Riegel but with adjustments for different runner types (speed-oriented vs endurance-oriented).

Tanda formula: specifically for marathon prediction from training data (not race times). More accurate for marathon prediction if you have weekly mileage data.

Different formulas give slightly different predictions. Riegel remains the most widely cited because it’s simple and reasonably accurate for adjacent distances.

Race time predictions across common distances

Here’s what Riegel predicts for various 5K times:

For marathon predictions from 5K, add 5-10% for realistic expectations.

The “VO2max equivalent” interpretation

The Riegel formula implicitly assumes a runner’s VO2max (maximum oxygen uptake) is the limiting factor and that fatigue follows a predictable pattern. Both are approximately true but with significant individual variation:

• Some runners are “speed-biased”: exceptionally fast 5K relative to marathon performance
• Some are “endurance-biased”: exceptionally strong marathon relative to 5K
• Genetic factors (slow-twitch vs fast-twitch muscle ratio) explain some of this
• Training emphasis (intervals vs long runs) explains more

If your races consistently don’t match Riegel predictions across distances, you may have a natural bias one way or another.

The “5-mile/8K predictor advantage”

Many running coaches consider an 8K (4.97 mile) race to be the single best predictor of marathon performance — better than 5K or 10K. The 8K distance:

• Long enough to stress aerobic systems
• Short enough that training for it doesn’t conflict with marathon prep
• More resistant to short-distance speed bias

Unfortunately 8K races are rare in the US. The 10K serves as a close substitute.

How recent should the known race be?

Race times degrade quickly after peak fitness. As a rough guide:

• Within 2 weeks: highly predictive
• 2-6 weeks: still reasonably predictive
• 6-12 weeks: predictions get loose
• 3+ months: probably unreliable; current fitness has shifted
• 6+ months: you need a new benchmark

If your last race was 6 months ago and you’ve been training inconsistently since, predictions from that race are essentially fiction.

Real-world prediction limits

In practice, expect Riegel predictions to be:

• Within 1-2% accurate for adjacent distance predictions (5K→10K, 10K→HM)
• Within 3-5% accurate for 1-step extrapolations (5K→HM, 10K→Marathon) for trained runners
• 5-15% optimistic for 2-step extrapolations (5K→Marathon) for trained runners
• 15-30% optimistic for 5K→Marathon if untrained for marathon distance

Common race-prediction mistakes

1. Extrapolating from old PRs: yesterday’s 5K time doesn’t predict today’s marathon
2. Ignoring marathon-specific training: you can’t run a Riegel-predicted marathon without doing the long-run work
3. Assuming flat-course conditions: hilly courses run 30-90 sec/mi slower
4. Underweighting heat: every 5°F above 60°F adds 1-2% to marathon time
5. Ignoring sleep and recovery: bad sleep night before adds 1-3 minutes per hour of racing
6. Not pacing strategically: even-pace running beats positive splits

Bottom line

The Riegel formula (T2 = T1 × (D2/D1)^1.06) is the standard race-time predictor and remains useful nearly 50 years after publication. It works best for adjacent distance predictions with recent races by trained runners. For 5K-to-marathon extrapolations, add 5-10% to predictions to account for marathon-specific demands the formula doesn’t capture. For real race-prediction work, use VDOT, McMillan, or Tanda formulas as alternatives, especially for marathon prediction. Most importantly: race-day execution (pacing, fueling, conditions) determines whether you hit predicted times.