How accurate is the Riegel race predictor?

For well-trained runners predicting within 2× the known distance, accuracy is typically ±3–5%. Accuracy decreases when extrapolating far beyond your training race (e.g. using a 1500m to predict a marathon), which is why the calculator shows a confidence range.

What fatigue exponent (k) should I use?

Start with Balanced (k=1.06) — the scientifically validated default. Use Speed Biased (k=1.03) if your results consistently outperform the default at long distances. Use Endurance Biased (k=1.10) if you're a self-described 'slow-twitch' runner who finds long-distance estimates too optimistic.

Can I use any race distance as my input?

Yes. You can use any distance by selecting "Custom" in the dropdown and entering a value in km. Accuracy is best when the known and target distances are within 3× of each other.

Why do the confidence bands exist?

The published Riegel exponent varies slightly between studies (1.03–1.09). The confidence bands map this range to your specific race, showing the best-case (fastest, k=1.03) and conservative (slowest, k=1.09) interpretations of your fitness.

What's the difference between best-case and conservative?

Best-case uses k=1.03, which penalises longer distances less — suggesting you have good aerobic efficiency. Conservative uses k=1.09, which penalises longer distances more — suggesting higher fatigue accumulation. The expected middle value uses k=1.06.

Why does the predictor show unusual times for shorter distances?

For distances shorter than your input race, the formula predicts faster times. If results look unusual, ensure your input time is in HH:MM:SS format and the distance is correct.

Is this the same formula as VDOT?

No. VDOT (Jack Daniels) uses oxygen cost curves and is more accurate at level-specific predictions. Riegel's formula is simpler and requires only one data point, making it ideal for a quick cross-distance estimate.

How recent should my race time be?

For best accuracy, use a race or time-trial from the past 4–8 weeks that reflects your current fitness. Older results or untapered efforts will produce conservative predictions.

Race Time Predictor — Free Running Calculator

Input Guide

A field-by-field walkthrough of every input — what it does and how it affects your predictions.

Race Distance

select

Choose a standard distance from the dropdown or select "Custom" to enter any distance in kilometres. The predictor works best when your known and target distances are within 3× of each other — e.g., a 5K predicting a half marathon is more accurate than a 5K predicting a marathon.

Options

1500mMile5K10K15KHalf MarathonMarathonCustom

For marathon predictions, a half marathon input gives the tightest confidence bands.

Finish Time

number

Enter your race finish time in hours, minutes, and seconds. Use a recent, maximal-effort race from the past 4–8 weeks. A tempo run or easy run will underestimate your fitness and produce slower predictions.

Chip time is more accurate than gun time — use the time printed on your official results.

Fatigue Profile

radio

Controls the Riegel exponent (k), which determines how much performance degrades as distance increases. A lower k means less degradation (you hold pace well over distance). A higher k means more degradation (you lose pace at longer distances).

Options

Speed Biased (k=1.03) — best at shorter distancesBalanced (k=1.06) — scientific defaultEndurance Biased (k=1.10) — best at longer distances

If your 5K and half marathon predictions have consistently been off, try adjusting the fatigue profile before assuming the model is wrong.

Predict Your Race Times in Seconds

The Race Time Predictor uses Riegel's power-law formula — the most widely cited model in sports science — to translate a single known race result into accurate finish-time predictions across seven standard distances. Whether you're targeting a 5K PR or planning your first marathon, enter one result and instantly see what you're capable of.

What Is the Riegel Race Predictor?

Peter Riegel introduced the formula T₂ = T₁ × (D₂ / D₁)^k in a 1977 paper in American Scientist. The exponent k (default 1.06) encodes how fatigue accumulates as distance increases. This calculator extends Riegel's model with three fatigue profiles — Speed Biased (k=1.03), Balanced (k=1.06), and Endurance Biased (k=1.10) — plus a confidence band derived from minimum and maximum published k-values, giving you a realistic range rather than a single number.

Why Use a Race Time Predictor?

Set realistic goal times before entering a race
Evaluate whether a current fitness level supports a target finish
Compare how different fatigue profiles affect long-distance estimates
Understand pace-distance trade-offs with visual confidence bands
Plan training races with predictive insight into peak-distance potential
Free, instant, and based on peer-reviewed sports science

Who Uses the Race Time Predictor?

First-time marathoners

Use a recent 10K or half marathon time to set a realistic target for your debut — avoiding a painful positive split.

Track athletes

Translate 1500m form into projected road race times, or estimate what a strong 5K means for 10K potential.

Coaches & training plans

Provide athletes with predicted race windows based on time-trial or tune-up race results throughout a training cycle.

Age-group runners

Understand what a strong 5K age-group finish implies about full marathon potential before committing to 16+ weeks of training.

Ultrarunners

Compare endurance-biased k-value predictions against balanced estimates to quantify how much pacing strategy matters at extreme distances.

Running researchers

Visualise how the Riegel exponent affects performance predictions across a full distance spectrum with the confidence-band chart.

Under the Hood

The mathematical model and design decisions behind each prediction.

Riegel Power-Law Formula

T₂ = T₁ × (D₂ / D₁)^k — Peter Riegel's 1977 formula from American Scientist. The exponent k encodes how fatigue accumulates with distance. The default k=1.06 is the most widely cited value in sports science literature.

Fatigue Exponent Range

Published studies report k values from 1.01 to 1.15 depending on athlete population and distance range. This calculator uses three profiles: Speed Biased (k=1.03), Balanced (k=1.06), and Endurance Biased (k=1.10). The confidence bands always span k=1.03 to k=1.09 regardless of selected profile.

Confidence Bands

The best-case bound uses k=1.03 (less fatigue accumulation) and the conservative bound uses k=1.09 (more fatigue). These bounds are fixed — they represent the range of population-level variability, not measurement error. The gap between bounds widens as the target distance moves further from the input distance.

Seven Standard Distances

Predictions are generated for 1500m (1,500m), 1 Mile (1,609.34m), 5K (5,000m), 10K (10,000m), 15K (15,000m), Half Marathon (21,097.5m), and Marathon (42,195m). Custom input distances are converted to meters internally.

Privacy

All predictions run entirely in your browser. Your race times are never sent to any server or logged in any analytics system.

Example Scenarios

Real inputs and the exact output from the engine — so you know what to expect before you start.

Sub-20 5K to Marathon

A 20:00 5K using the Balanced profile (k=1.06) predicts a half marathon of 1:32:00 and a marathon of 3:11:49. The confidence band ranges from 3:01 (best case, k=1.03) to 3:22 (conservative, k=1.09).

5K 20:00 → HM 1:32:00 · Marathon 3:11:49

Half Marathon to Marathon

A 1:45:00 half marathon predicts a marathon of 3:38:55 using Balanced. Since the input and target are only 2× apart, the confidence band is narrow — a good indicator of prediction reliability.

HM 1:45:00 → Marathon 3:38:55

Recreational 10K Runner

A 50:00 10K predicts a half marathon of 1:50:19 and a marathon of 3:50:01 using Balanced. This is typical for a solid recreational runner — note how the margin between HM and marathon doubles compared to faster runners.

10K 50:00 → HM 1:50:19 · Marathon 3:50:01

Research & References

The models and parameters used in this calculator are grounded in peer-reviewed sports-science research.

Riegel, P. S. (1981). Athletic Records and Human Endurance. American Scientist, 69(3), 285–290.
Daniels, J., & Gilbert, J. (1979). Oxygen Power: Performance Tables for Distance Runners. Tempe, AZ.
Jones, A. M., & Vanhatalo, A. (2017). The "Critical Power" Concept: Applications to Sports Performance. European Journal of Sport Science, 17(10), 1275–1284.

Race Time Predictor

Input Parameters