Race Time Predictor — Riegel Formula

A race time predictor turns one result you already own into an estimate for a distance you have not raced yet. The arithmetic behind almost every one of them is Pete Riegel’s, published for runners in 1977 and formalized in American Scientist in 1981. Enter the race you have, pick the distance you want:

The equation, and what the exponent is doing

T₂ = T₁ × (D₂ ÷ D₁)^1.06

T₁ and D₁ are the time and distance you already ran; T₂ is the predicted time over D₂. Everything interesting is in that exponent. If it were exactly 1, doubling the distance would double the time and your pace would never change. Riegel fitted it to records across endurance events and got a number slightly above 1 — a fatigue factor, in his words. At 1.06, doubling the distance multiplies your time by 2^1.06 = 2.085, not 2.

The value is not carved in stone. Riegel reported roughly 1.08 for elite runners and 1.05 to 1.06 for recreational men aged 40 to 70; the Runner’s World calculator settled on 1.06, and the 2016 study that tested the formula on 2,303 recreational runners chose 1.07 as a compromise. This calculator uses 1.06, which is the friendlier end of that range — worth remembering when you read the output.

Worked example: 5K to 10K

A runner who covers 5K in 25:00 is holding 5:00/km (8:03/mile). Predicted 10K:

T₂ = 25:00 × (10 ÷ 5)^1.06 = 25:00 × 2.0849 = 52:07

That is 5:13/km, or 8:23/mile — thirteen seconds per kilometer slower than the 5K pace. The gap is the whole point of the exponent, and it matches what runners see on the road: nobody holds their 5K pace for twice the distance.

The four common jumps

Each has its own page, because the reliability is very different at each step:

• 10K time from a 5K — the safest extrapolation of the set
• Half marathon time from a 10K
• Marathon time from a half marathon — the riskiest
• Race time equivalency calculator, which prints 5K, 10K, half and full from a single result

Where the prediction stops being trustworthy

The formula was fitted to record performances, so it silently assumes you are equally well trained for both distances. That holds up better than you would expect at short range and falls apart at the marathon. In the 2016 survey of recreational runners, Riegel predictions were well calibrated for 10K and half marathon but at least ten minutes too fast for half of all marathoners, and more than twenty minutes too fast for about a quarter of them. A 2024 study benchmarking prediction models on ultra-distance races put Riegel’s accuracy at 80%, behind purpose-built models.

Two practical rules follow. Use the shortest jump you can — predict the half from your 10K, not from your 5K. And treat the marathon line as an optimistic floor, not a goal. The accuracy page has the residuals in full, and the VO2 max calculator covers the other common way of estimating what you are capable of.