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Race Predictor

Fatigue is superlinear. The 1.06 exponent is why your 5K time does not double into your 10K — and why linear math ruins marathons.

Peter Riegel's formula — T₂ = T₁ × (D₂/D₁)^1.06 — has been the standard race-prediction model since 1977 because fatigue rises faster than distance. Doubling the race more than doubles the time. Most quick estimates (and most AI answers) scale pace linearly, which underestimates a marathon predicted from a 5K by twenty-plus minutes. This tool predicts every standard distance from any one result, shows pace per mile, and displays the linear error side-by-side so you can see exactly how the naive math lies.

Why people use this

Runners use it to convert any race result into realistic targets at every other distance — the 1.06 fatigue exponent instead of the linear pace math that overpromises a marathon by 20+ minutes and wrecks race plans at mile 18.

How it works

1. Riegel: T₂ = T₁ × (D₂/D₁)^1.06. The 1.06 fatigue exponent was fitted from competitive race results across distances.
2. A 20:00 5K predicts 41:42 for 10K, 1:32:00 for the half, and 3:11:49 for the marathon — linear scaling would promise 2:48:47, a 23-minute lie.
3. Predictions assume comparable training for both distances: a 5K predicts your marathon only if you actually did the long runs.
4. The model degrades beyond the marathon — in ultras, endurance economy and fueling dominate and no exponent rescues the prediction.

Common questions

I ran a 20:00 5K. What marathon time should I target?

The Riegel prediction is 3:11:49 (7:19/mile) — NOT the 2:48:47 that linear pace math gives. That 23-minute gap is exactly how runners end up walking the last 10K: they trained and raced to a pace a linear formula promised. Plan for 3:10–3:15 if your long-run volume supports it, and treat 3:11 as the ceiling, not the floor.

How accurate is the Riegel formula really?

Within a few percent for trained runners between 5K and marathon — a 4:00 marathon predicts a 1:55:07 half, matching published equivalency tables. Accuracy drops at the extremes: sprinters overperform at short distances (their 5K underpredicts their mile), endurance specialists do the opposite, and ultra distances break the model entirely. Use it as a training-supported estimate, not a guarantee.

Why does the pace slow down as distance grows?

Because the limiting system changes. Under ~3 minutes you are anaerobic; mile to 10K is VO₂max territory; the half and marathon are limited by lactate threshold, glycogen, and heat. Each limit tolerates a lower fraction of your top speed, which the 1.06 exponent compresses into one number. If your predicted long-distance times are consistently slower than your actuals, you are endurance-gifted — train your speed, and the short-distance predictions will catch up.

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