endurance Formula

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.

4 VARIABLESPublished May 14, 2026Live Content

By AI Fit Hub · AI Fit Hub Team

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Race Time Predictor

Race Time predictor: predict finish times across 5K, 10K, half marathon, and marathon from any known race result using Riegel's formula.

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On This Page

Formula 4 variables Worked example Variations

Education · Not medical advice. Output is deterministic math from your inputs.Editorial standards Sponsor disclosure Corrections

Formula

Copy the exact expression or work through it step by step below.

T2 = T1 × (D2 / D1)^1.06

Variables

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.

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.

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.

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

Cameron formula (1998): T2 = T1 × (D2 / D1)^1.066. Slightly steeper exponent — better for longer races. Use for marathon prediction from half marathon.

Pete Riegel re-fit (2010): exponent 1.07 for marathon-and-beyond when D2 ≥ 30K. Acknowledges Riegel's marathon underestimation bias.

Daniel's VDOT tables: empirical lookup table from race times to training paces. More accurate than Riegel for race prediction because it explicitly models lactate threshold and VO2 max.

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FAQ

Questions people ask next

The short answers readers usually want after the first pass.

What is the Riegel race time formula?

Riegel's formula predicts a race time at a new distance from a known race time: T2 = T1 x (D2 / D1)^1.06. The 1.06 exponent reflects the empirical observation that pace drops at longer distances, since runners cannot hold 5K pace through a marathon.

How do I predict my half marathon time from a 10K?

Convert your 10K time to seconds, divide 21.0975 km by 10 to get 2.10975, raise it to the power 1.06 (about 2.2273), then multiply by your time. A 42:30 (2,550 s) 10K gives 2,550 x 2.2273 = 5,680 seconds, or a 1:34:40 half marathon prediction.

Is the Riegel formula accurate for the marathon?

It is well calibrated for 5K to half marathon predictions but tends to be optimistic for the marathon, by about 1-3 minutes for fit recreational runners. The page recommends adding 2-3 minutes as a known-bias correction when predicting a marathon from shorter races, because Riegel underestimates the endurance penalty.

What race should I use as the input for the prediction?

Use a recent race no more than about 8 weeks old to capture current fitness, and pick a distance close to your target, since predicting a marathon from a 5K is less reliable than predicting a half from a 10K. The formula does not adjust for course profile, weather, or training specificity.

Are there alternatives to the Riegel formula?

Yes. The Cameron formula uses a slightly steeper 1.066 exponent that fits longer races better, and a Pete Riegel re-fit uses 1.07 for distances of 30K and beyond. Daniels' VDOT tables are an empirical lookup that is more accurate for race prediction because they explicitly model lactate threshold and VO2 max.

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