The Riegel Formula: How Race Time Prediction Actually Works

Last updated: May 2026

When you run a 25-minute 5K and wonder what marathon you’re capable of, the Riegel formula is what most coaches and prediction tools use to find out. Developed in 1977 by Peter Riegel — an American research engineer and competitive runner — and published in Runner’s World magazine, this equation has become the standard model for race time prediction across virtually every running distance.

The Formula

T₂ = T₁ × (D₂ ÷ D₁)^1.06

Where:

• T₁ = your known race time
• D₁ = the distance of that race
• D₂ = the target distance you want to predict
• T₂ = the predicted finish time
• 1.06 = the fatigue exponent

The exponent 1.06 is the key element. It captures the fact that running pace slows in a consistent, predictable pattern as distance increases. Without the exponent — if you simply multiplied your 5K pace by the ratio of distances — the prediction would be unrealistically optimistic. The 1.06 factor accounts for the reality that longer efforts consume and deplete energy at an accelerating rate.

Worked Example

You ran a 5K in 25:00 (1,500 seconds). How fast should you be able to run a marathon (42.195 km vs. 5 km)?

T₂ = 1,500 × (42.195 ÷ 5)^1.06

T₂ = 1,500 × (8.439)^1.06

T₂ = 1,500 × 9.22

T₂ = 13,830 seconds ≈ 3:50:30

The key step is that exponent. If you used 1.0 instead of 1.06, you would get 1,500 × 8.439 = 12,659 seconds ≈ 3:31 — an overestimate by nearly 20 minutes. That difference grows substantially at longer distances and is why simple pace-doubling methods consistently overpredict performance.

Prediction Table: 5K Starting Times

Accuracy and Limitations

Riegel’s formula is the most widely validated prediction model in distance running, but it carries important assumptions:

Training must be specific to the distance. The formula predicts what your fitness allows, not what your endurance training can sustain. A runner with a 25:00 5K who has never run beyond 10 miles will not run a 4:00 marathon — the aerobic base and long-run adaptation haven’t been built. The formula assumes you’ve done the training for the target distance.

Use a genuine race effort. The input time must represent a real all-out race effort, not a training run or a paced workout. Plugging in a comfortable long run time will produce an overestimate.

Most accurate between similar distances. Predicting a 10K from a 5K is highly reliable. Predicting a marathon from a 1K is not — the further apart the input and target distances, the more other factors (endurance training, fuelling, mental strategy) dominate the result.

Less accurate at extremes. The formula becomes less reliable for times under approximately 3:30 (sprinting territory) and over 4 hours, where additional variables related to ultra-endurance physiology come into play.

No course or weather adjustment. Hills, heat, wind, and altitude are not accounted for. A hilly course prediction based on a flat road 5K will overestimate performance.

Why the Exponent Is 1.06

Riegel derived the 1.06 figure empirically from analysis of world record times across multiple distances and sports. It represents the average rate of pace degradation per doubling of distance for competitive athletes. Research has since validated this value across a broad population of recreational and competitive runners, though elite athletes with exceptional aerobic economy may see slightly less degradation (closer to 1.04–1.05), and newer runners may see more (1.07–1.08).

The practical result: your pace slows by roughly 4–5% every time distance doubles. A runner who can hold 8:00/mile for a 5K will be unable to hold that pace for a 10K, and considerably slower for a marathon.