Every runner has wondered: "If I can run a 5K in 25 minutes, what time can I expect for a marathon?" The Riegel formula provides a mathematical answer to this question, and it's the formula used in the race time predictor on this site.

The Formula

Published by B. Riegel in 1981 in Medicine and Science in Sports and Exercise, the formula is:

T₂ = T₁ × (D₂ / D₁)^1.06

Where:

T₁ = Your known race time (in any unit)
D₁ = Your known race distance (in the same unit)
D₂ = Your target race distance
T₂ = Predicted race time for D₂
1.06 = The fatigue exponent (constant)

Worked Example

Let's say you ran a 10K in 50 minutes and want to predict your marathon time:

T₁ = 50 minutes

D₁ = 10 km

D₂ = 42.195 km (marathon)

T₂ = 50 × (42.195 / 10)^1.06

T₂ = 50 × 4.2195^1.06

T₂ = 50 × 4.56

T₂ ≈ 228 minutes ≈ 3:48:00

Why 1.06?

The fatigue exponent of 1.06 represents how endurance decreases with distance. If the exponent were 1.0, doubling the distance would exactly double the time. The 1.06 value means that as distance increases, you slow down slightly more than linearly. Research has shown this value works well for distances from 5K to ultra-marathons.

Accuracy and Limitations

The Riegel formula is most accurate when:

The target distance is within 2x the input distance
You used maximum effort in the reference race
Race conditions (weather, terrain, altitude) are similar
Your fitness level is stable (no major training changes)

The formula becomes less accurate for larger gaps between distances (e.g., predicting a marathon from a 5K) because it cannot account for the unique endurance demands of longer races.

Try It Yourself

Use the race time predictor to see your equivalent race times across all distances. Enter one recent result and get instant predictions for 5K, 10K, half marathon, and marathon.