How this instrument works
Riegel's formula predicts a runner's finish time at one distance from a known finish time at another, using the relationship t2 = t1 x (d2/d1)^1.06. Pete Riegel, an American engineer and marathoner, derived the 1.06 exponent empirically from a large set of world-class endurance performances across running, walking, and swimming, and published it in Runner's World magazine in 1977 before expanding on it in a 1981 American Scientist article.
The exponent is the whole idea: if pace held perfectly steady regardless of distance, the exponent would be exactly 1 and doubling the distance would exactly double the time. Real endurance performance degrades a little faster than that as distance grows — fatigue, glycogen depletion, and heat accumulation all take a toll — so Riegel set the exponent slightly above 1, at 1.06, meaning doubling the distance is predicted to cost a bit more than double the time.
The formula is best treated as a fitness-based estimate for a well-trained endurance performance, not a guarantee. Riegel himself scoped it to efforts lasting roughly 3.5 to 230 minutes — from mid-distance track events out to the marathon — and it assumes reasonably specific training for the target distance; a 5K specialist's predicted marathon time from this formula usually overstates what they'd actually run without marathon-specific endurance work, and vice versa for a marathoner predicting a 5K.
- Enter Known time (minutes) — your recent finish time at a distance you've actually raced.
- Enter Known distance — the distance of that recent race, in any consistent unit.
- Enter Target distance (same unit as known distance) — the distance you want a predicted time for.
- Read Predicted time (minutes) — Riegel's estimate for the target distance, based on your known performance.
- Use a recent, well-rested race result as the known time — a workout or a poorly-paced race will predict poorly too.
Worked example — predicting a 10K from a 25:00 5K
Enter a known time of 25 minutes over a known distance of 5, with a target distance of 10 — a 25:00 5K predicting a 10K. Predicted time = 25 x (10/5)^1.06 = 25 x 2^1.06 = 52.123 minutes, about 52:07 — noticeably more than double the 5K time, because the formula predicts pace slows slightly as distance doubles.
Questions
Why is the exponent 1.06 and not exactly 1?
An exponent of exactly 1 would mean pace never slows as distance grows — doubling the distance would exactly double the time. Real endurance performances slow down a bit more than that as fatigue and glycogen depletion accumulate, and Pete Riegel found 1.06 fit a large set of world-class race results best, meaning the predicted time for double the distance comes out a little over double, not exactly double.
How accurate is Riegel's formula for predicting a marathon from a 5K?
Reasonably accurate for well-trained runners doing distance-appropriate training, but it tends to overstate marathon readiness for someone who only trains for 5Ks, since the marathon punishes a lack of long-run endurance in a way the formula can't see. It works best over a moderate distance jump — predicting a 10K from a 5K, or a half-marathon from a 10K — and gets less reliable the further apart the known and target distances are.
Can I predict a shorter distance from a longer one, not just longer from shorter?
Yes — the formula works in both directions. Enter a longer known distance and a shorter target distance and the same t2 = t1 x (d2/d1)^1.06 applies, predicting a faster time at the shorter distance. It tends to be a bit less reliable in this direction for marathon-to-5K predictions specifically, since marathon fitness and 5K speed draw on different training.
Where did Riegel's formula come from?
Pete Riegel, an American engineer and long-time competitive runner, published the formula in Runner's World magazine in 1977 and expanded on the underlying analysis in a 1981 American Scientist article titled 'Athletic Records and Human Endurance.' The 1.06 exponent was derived empirically from world-record and elite-performance data across running, race walking, and swimming, not assumed from theory.
Does this replace the site's marathon-pace or race-time-improvement calculators?
No — they answer different questions. Race-predictor estimates a finish time at a new distance from a known result; marathon-pace converts a chosen finish time directly into a steady per-mile pace; race-time-improvement measures the percentage gain between two times at the same distance. Use race-predictor first to set a realistic goal, then marathon-pace to turn it into a pacing plan.