Riegel Race Time Formula
Riegel's formula predicts a race time at a new distance from a known race time. The 1.06 exponent reflects the empirical observation that pace drops at longer distances — humans don't hold 5K pace through a marathon. The formula is well-calibrated for 5K-half marathon predictions; marathon predictions tend to be optimistic by 1-3 minutes for fit recreational runners.
Formula
Copy the exact expression or work through it step by step below.
T2 = T1 × (D2 / D1)^1.06 Variables
T2
Predicted time for new distance
Time to complete distance D2, in the same units as T1 (typically seconds or minutes). The formula does not adjust for course profile, weather, or training specificity.
T1
Known race time
Time for a recent race at distance D1. Use a race ≤8 weeks old to capture current fitness. Time trials work but rate-perceived effort tends to undercut race-day performance.
D2
Target distance
Distance you want to predict. Same units as D1 (km or mi). Riegel's data is most reliable for 5K, 10K, half marathon; marathon predictions need correction for endurance-specific training.
D1
Known distance
Distance of the reference race. Ideally close to D2 — predicting marathon from a 5K time is less reliable than predicting half from 10K.
Step By Step
- 1
Get a recent race time in seconds. Convert if needed.
Recent 10K in 42:30 = 2,550 seconds.
- 2
Divide target distance by known distance.
Predicting half marathon (21.0975 km) from 10K: 21.0975 / 10 = 2.10975.
- 3
Raise the ratio to the power 1.06.
2.10975^1.06 ≈ 2.2273.
- 4
Multiply by your known race time.
2,550 × 2.2273 = 5,680 seconds = 1:34:40 half marathon prediction.
- 5
For marathon predictions from shorter races, add 2-3 minutes as a known-bias correction — Riegel underestimates the endurance penalty.
Marathon prediction from 10K: apply formula, then add 2-3 minutes to be realistic.
Worked Example
Recreational runner with 42:30 10K wants half marathon prediction
Known time (T1)
42:30 (2,550 seconds)
Known distance (D1)
10 km
Target distance (D2)
21.0975 km (half marathon)
T2 = 2,550 × (21.0975 / 10)^1.06 = 2,550 × 2.2273 = 5,680 seconds
1:34:40 predicted half marathon. Real-world adjustment: subtract ~30s if you've trained specifically for the half distance; add 30-60s if all your training is 10K-focused.
Common Variations
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Sources & References
- Athletic Records and Human Endurance (Riegel, 1981) — American Scientist — original publication of the exponent 1.06
- Cameron, D.B. (1998). Predicting marathon times. — Archived analysis of Cameron's variant of Riegel's formula
- Daniels' Running Formula (3rd ed., 2014) — Human Kinetics — VDOT methodology and race-pace tables