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Enter the distance and finish time of a race you ran recently, plus the distance you want to predict. The calculator converts your finish time to total seconds and applies the Riegel formula, T2 = T1 × (D2 / D1)¹.06, to estimate your equivalent finish time at the new distance. It also divides the predicted time by the target distance to show the average pace per kilometre you would need to hold.
The Riegel formula was developed by research engineer and marathoner Peter Riegel and published in Runner's World in 1977. It states that your finish time scales with distance according to a power law: T2 = T1 × (D2 / D1)¹.06, where T1 is your known finish time, D1 is the distance you ran, D2 is the distance you want to predict, and T2 is the predicted time. The exponent 1.06 captures a well-documented fact: pace slows by roughly 6 percent every time the race distance doubles. Doubling the distance multiplies your time by 2¹.06, about 2.085, so a 50-minute 10K predicts a half marathon of roughly 50 × 2.085 × 1.06-adjusted minutes. Halving the distance multiplies your time by 0.5¹.06, about 0.48, so a 45:00 10K predicts a 5K of about 21:35. Because the formula uses a ratio, it works in any distance unit as long as both distances use the same one.
Enter your recent running race distance in kilometres (use 1.609 for a mile, 21.0975 for a half marathon, 42.195 for a marathon), your finish time in minutes and seconds, and the target distance. For the best prediction, use a race from the last 8 to 12 weeks run at near-maximal effort, similar to how you would race the target distance. The calculator instantly shows your predicted finish time in seconds and the average pace per kilometre required. If your predicted pace feels too aggressive, treat it as an upper bound and set an A/B/C goal structure around it.
A 10K finished in 45:00 is 2,700 seconds over 10 km. Predicting a 5K: 2,700 × (5 / 10)¹.06 = 2,700 × 0.4796 = 1,295 seconds, or 21:35, at 4:19 per km. Predicting a half marathon: 2,700 × (21.0975 / 10)¹.06 = 2,700 × 2.2057 = 5,955 seconds, or 1:39:15, at 4:42 per km. Predicting a marathon: 2,700 × (42.195 / 10)¹.06 = 2,700 × 4.6561 = 12,571 seconds, or 3:29:31. A 5K in 25:00 (1,500 seconds) predicts a 10K of 1,500 × 2¹.06 = 1,500 × 2.0849 = 3,127 seconds, or 52:07. These are equivalent-performance estimates, so each assumes similar conditions and appropriate training for the target distance.
A race prediction estimates an equivalent performance, not a guaranteed result. Studies and coaching experience suggest conventional predictors are right for roughly 4 out of 5 runners when the input is recent and the training matches. Predictions are most reliable within a 2 to 4 times distance gap, for example 5K to 10K or 10K to half marathon. Stretching from a 5K all the way to a marathon introduces more uncertainty, because the formula cannot see your long-run durability, fueling practice, or heat tolerance. Weather, hills, altitude, and course measurement all move the real result. Use the number as a planning target for goal setting and pacing, then refine it with threshold workouts and your own race history. Estimates vary with training and conditions, so treat the output as a guide, not a promise.
Predicting a longer race from a shorter one assumes you have built the endurance base the new distance demands. A 5K specialist who has never run over 10 miles will usually run slower than the marathon prediction until long-run training catches up. Conversely, predicting a shorter race from a longer one assumes speed: a marathon runner predicting a 5K may fall short without interval work and leg turnover. The safest predictions sit close together in distance, and the best single input is the race nearest your target that you ran all-out recently.
A prediction becomes useful when it feeds your training. Pair it with a pace calculator to split the predicted time into kilometre or mile splits for race day. Many runners anchor training paces to the predicted fitness: easy runs well below the predicted marathon pace, tempo runs near the predicted 10K-to-half-marathon pace, and intervals near the predicted 5K pace. After every significant race or time trial, recalculate with the new result so every pace stays tied to your current fitness rather than where it was months ago.
The most common mistake is treating the prediction as a guarantee and going out too fast on race day. Others include using an old personal best from years ago instead of a recent result, entering a trail race or heat-affected effort as if it were a flat road race, and using an easy training run time that underrepresents fitness by 1 to 3 percent. Do not predict a marathon from a 5K without marathon-specific long runs, and do not use the output as medical or coaching advice. It is a mathematical estimate of equivalent performance, and your body still has to do the work.
The Riegel formula is T2 = T1 × (D2 / D1)¹.06. It predicts your finish time (T2) at a new distance (D2) from a known finish time (T1) at a known distance (D1). The 1.06 exponent reflects that pace slows by roughly 6 percent each time the distance doubles. It was developed by Peter Riegel and published in 1977, and it remains the most widely used race time model.
It is a strong estimate for well-trained runners when the input race is recent (last 8 to 12 weeks) and run at near-maximal effort, but it is not a guarantee. Accuracy is best within a 2 to 4 times distance gap, and it drops for big jumps like 5K to marathon, or when course, weather, altitude, or training differ. Estimates vary with training and conditions.
Any distance from a fast mile up to an ultramarathon, as long as you enter distances in the same unit. The formula is most reliable for efforts lasting roughly 3.5 minutes to about 4 hours, which covers the mile through the marathon for most recreational runners.
Yes, but adjust for conditions. Training runs without a taper or race-day adrenaline typically underperform by 1 to 3 percent, so add that buffer before predicting. A recent time trial run at full effort works better than a casual easy run.
Different calculators use different models: Riegel's power law, McMillan's empirical tables, or Jack Daniels' VDOT system. For the same input they can differ by several minutes at the marathon, because no formula captures individual physiology, genetics, or training history. Use the prediction as a range, not an exact number.
The 1.06 exponent is the default fatigue factor: it assumes your pace decays at the average rate as distance grows. Speed-oriented runners sometimes fit better with 1.03 to 1.05, while endurance specialists or ultra runners may fit 1.07 to 1.10. Compare past predictions against your actual results to find the value that matches your own pattern.
After every significant race or time trial. Recent performances give the best snapshot of current fitness and keep predictions anchored in reality. Do not keep using a personal best from a previous season once your fitness has changed.
It can calculate one, but treat it cautiously. The formula assumes you have done the long-run training, fueling practice, and durability work a marathon demands. Without marathon-specific preparation, your actual marathon will likely be slower than the prediction, so use it as a long-term goal rather than a race-day target.
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