● Cardio & running

Race Time Predictor — from one result to all distances.

Enter any recent race result and predict your finish time for every standard distance — from 1500 m to marathon — using Riegel's formula and Cameron's model.

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Race Time Predictor

Riegel's formula (1981) + Cameron's model — predict finish times across all distances

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Your recent result

Pace display

Known race distance

Your finish time hh : mm : ss

: :

VDOT estimate —

Source pace per mile —

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Predicted times

Enter your race result on the left to see predictions.

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How it's calculated

Riegel's formula and the fatigue exponent

The Race Time Predictor uses Riegel's power-law formula (1981): T2 = T1 × (D2 / D1)^1.06. For example, a 22:30 5K predicts a roughly 46:56 10K and a 1:44:xx half marathon. The exponent 1.06 encodes the physiological reality that pace slows slightly as distance grows. Cameron's model refines this with distance-specific constants for better accuracy at the extremes.

Peter Riegel published the formula in American Scientist (1981) after analysing hundreds of world-record progressions. The exponent 1.06 is empirically derived — it captures the non-linear relationship between distance and performance. Cameron's model provides an alternative set of equations that use per-distance constants to reduce error for very short and very long distances.

Riegel: T2 = T1 × (D2 ÷ D1)^1.06
VDOT ≈ 0.8 × VO2max from pace at race distance
Pace (min/km) = T2 (min) ÷ D2 (km)

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Convert finish time to total seconds
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Calculate Riegel prediction for each distance
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Compute pace per km and per mile
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Estimate VDOT from source race result
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Understand the terms

Riegel exponent (1.06): The empirical constant in Riegel's formula. Values above 1.0 mean performance degrades non-linearly with distance — a slightly slower pace is needed for each doubling of distance.
Race equivalent: A predicted finish time for a distance you haven't raced, derived from a result at another distance. Useful for setting pace targets and comparing performances.
Aerobic capacity (VO2max): The maximum rate at which the body can consume oxygen during exercise. Higher values correspond to faster distance-running performances.
VDOT: A performance proxy for VO2max popularised by running coach Jack Daniels. Calculated from race time and distance, it allows comparing effort across different race distances and setting training paces.
Taper: A planned reduction in training volume in the weeks before a key race, allowing the body to recover and perform at its best on race day. Race predictions do not account for taper or detraining.

See the full glossary →

Disclaimer: estimation tool for informational and planning purposes. Predictions are based on Riegel (1981) and assume consistent aerobic fitness and similar race conditions. Actual times vary with terrain, weather, fuelling, pacing strategy and training specificity. Does not substitute coaching or professional performance assessment.

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Frequently asked questions — Race Time Predictor

What is Riegel's race prediction formula?

Riegel's formula (1981) predicts finish times using T2 = T1 × (D2/D1)^1.06, where T1 is a known result for distance D1 and T2 is the predicted time for distance D2. The exponent 1.06 accounts for physiological fatigue — performance slows non-linearly as distance increases.

How accurate is the race time predictor?

Riegel's formula is most accurate when source and target distances are within 2× of each other (e.g., 10K to half marathon). Predictions degrade for very large distance gaps. The formula also assumes similar training and race conditions. Cameron's model offers a slight refinement for outlier distances.

What is VDOT and how is it estimated?

VDOT is a performance-based proxy for VO2max popularised by Jack Daniels. It is estimated by back-calculating the oxygen cost of your race pace. A higher VDOT indicates better aerobic capacity. It is not a direct lab measurement — it is a number on the Daniels scale for comparing performances and setting training paces.

Should I use km or miles for the predictor?

The calculator works with both units. The English-language version defaults to min/mile for pace display, but predictions are identical regardless — all internal calculations use metres. Toggle the unit switch to change pace display between min/km and min/mile.

Why does the predictor show slower times than I expect for very long distances?

Riegel's exponent (1.06) means performance slows more than proportionally as distance increases. This is especially visible when projecting from a short distance to marathon. Real-world performance also depends on fuelling, heat, elevation and marathon-specific training — factors the formula cannot capture.

📚 Learn more — official sources

🔬 Study Riegel (1981) — Athletic Records and Human Endurance The original paper by Peter Riegel in American Scientist that proposed the power-law formula T2 = T1 × (D2/D1)^1.06 from world-record data analysis. See on American Scientist → 🏛️ Organization World Athletics — Official road race standards and records The governing body for track and field athletics, maintaining official world records and standards for all standard race distances from 1500 m to marathon. See official source → 🔬 Study Jack Daniels — VDOT Running Calculator Jack Daniels' VDOT system, popularised in "Daniels' Running Formula", provides training paces and race equivalents based on aerobic capacity estimated from race performances. See reference → 🔬 Study Daniels & Gilbert (1979) — Oxygen Power: Performance Tables for Distance Runners Foundational work establishing the relationship between VO2max, running economy and race performance across distances, the basis of the VDOT system. See on PubMed →

Race Time Predictor

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About the Race Time Predictor

The Race Time Predictor applies the power-law formula published by Peter Riegel in American Scientist (1981). By analysing hundreds of world-record progressions, Riegel identified that race times scale with distance raised to the power of 1.06 — not 1.0 — meaning each doubling of distance requires slightly more than double the time. This exponent encodes physiological fatigue at the metabolic level.

This tool also estimates your VDOT, the performance-based VO2max proxy popularised by Jack Daniels. The VDOT number lets you compare performances across distances and set appropriate training paces. Cameron's model adds distance-specific constants that reduce prediction error for very short (1500 m) and very long (marathon) distances where Riegel's single exponent diverges slightly from observed performance.

Use the predictions as goal times and training benchmarks — not guarantees. Real race performance depends on fitness specificity, tapering, nutrition, heat and elevation factors that no formula can fully capture.