Predict race times at any distance using the Riegel formula. Estimate 5K, 10K, half marathon, and marathon times from a single recent race result.
The Race Predictor (Riegel) Calculator estimates your finish time at any running distance using the Riegel formula, one of the most widely used race prediction models in endurance sports. Developed by researcher Peter Riegel and originally published in 1977, the formula uses a fatigue exponent to account for the natural slowing that occurs as race distance increases.
Simply enter a recent race time and the calculator will predict your equivalent performance at distances from 1 mile through 100 miles. The calculator supports both standard road distances and custom ultra-marathon distances, with modified exponents for events beyond marathon distance where fatigue compounds non-linearly.
Whether you're targeting a PR at a new distance, planning pacing for an upcoming race, or comparing performances across different distances, this tool provides data-driven predictions based on decades of validated research. Whether you are a beginner or experienced professional, this free online tool provides instant, reliable results without manual computation.
Choosing the right race goal is critical for pacing strategy. Overly optimistic time goals lead to hitting the wall, while conservative goals leave potential on the table. The Riegel formula provides an objective, research-validated baseline prediction that helps you set realistic targets. It also lets you compare performances across distances — is your 10K PR better than your half marathon time?
Riegel Formula: T₂ = T₁ × (D₂ / D₁) ^ e Where: • T₁ = known race time (seconds) • D₁ = known race distance • T₂ = predicted time at target distance • D₂ = target race distance • e = fatigue exponent (default 1.06 for road races) Modified Exponents: • Road racing (5K–Marathon): e = 1.06 • 50K–50 Mile: e = 1.07 • 100K: e = 1.08 • 100 Mile: e = 1.10
Result: Predicted marathon: 3:16:18 | Pace: 7:29/mi (4:39/km)
A 10K time of 42:00 (2520 seconds) is used in the Riegel formula: T₂ = 2520 × (42.195/10)^1.06 = 2520 × 4.2195^1.06 ≈ 11,778 seconds = 3:16:18. This assumes equivalent fitness and training volume for the marathon distance. In practice, marathon predictions from shorter races tend to be optimistic unless marathon-specific training (long runs, fueling) has been done.
As race distance increases, average pace necessarily slows. This isn't simply a matter of running out of energy — it reflects the interaction of glycogen depletion, neuromuscular fatigue, thermoregulation demands, and metabolic substrate shifting from carbohydrate to fat oxidation. The Riegel exponent captures this relationship in a single parameter. A value of 1.06 means that doubling the distance increases the time by a factor of 2^1.06 ≈ 2.085, or about 4.2% more than a pure linear scaling.
Race prediction is most useful for pacing strategy. If the calculator predicts a 1:35 half marathon, you know to target ~7:15/mile pace from the start rather than going out at your 10K pace of 6:45/mile. For ultra-marathons, predictions help with crew and aid station timing, nutrition scheduling, and cutoff planning. For coaches, comparing actual race times to Riegel predictions reveals whether an athlete is better suited to short or long distances.
The Riegel formula assumes a well-trained, healthy runner on a flat, temperature-neutral course at sea level. Real-world factors that cause deviations include: course elevation profile, weather conditions, altitude, nutrition and hydration, race-day pacing errors, and training specificity. For the most reliable predictions, use recent race data from conditions similar to your target race.
The Riegel formula is accurate to within 2–4% for most recreational and competitive runners when predicting between road distances of 5K to marathon. It is best when the known and predicted distances are within 2–4× of each other (e.g., 10K to half marathon). Larger jumps (mile to marathon) carry greater uncertainty. Elite runners may beat predictions, while undertrained runners may fall short.
The fatigue exponent (e) models how much pace slows as distance increases. A higher exponent means more fatigue. The standard value of 1.06 fits road distances well. For ultra distances, glycogen depletion, sleep deprivation, terrain, and nutrition issues cause disproportionate slowing, requiring higher exponents (1.07–1.10). Some coaches use 1.04–1.05 for highly trained athletes who fatigue less.
Yes, the formula works bidirectionally. You can predict 5K time from a marathon result and vice versa. However, going from long to short tends to underestimate speed because the formula doesn't capture neuromuscular speed and anaerobic capacity that help in shorter races. A 3:10 marathoner might run a sub-19:00 5K, not the ~19:30 the formula predicts.
Use your most recent race from the past 6–8 weeks. An all-time PR from years ago may not reflect current fitness. If your recent race was in poor conditions (extreme heat, hills, altitude), your PR might be more representative. Use judgment and consider running a time trial for accurate input data.
Marathon performance depends heavily on marathon-specific preparation: long runs, fueling practice, pacing discipline, and accumulated mileage. A runner who trains mostly 5K/10K distances may be aerobically fit but lack the endurance adaptations needed for 26.2 miles. The Riegel prediction assumes equivalent training; if you haven't done the marathon-specific work, you'll likely run slower than predicted.
Jack Daniels' VDOT tables are based on similar principles but use empirical data tables rather than a single exponent. VDOT tends to be slightly more conservative for marathons and slightly more generous for shorter distances. Both are validated tools; the Riegel formula is simpler (one equation) while VDOT provides additional training pace recommendations.