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Race Predictor Calculator

Predict race times across all distances with the Riegel formula

Marathon Prediction

3:59:47

Half Marathon

1:55:00

Source Pace

5:00/km

1.06 = trained runner, 1.07-1.08 = beginner, 1.04-1.05 = elite

Predicted Race Times

3:59:47

Marathon (5:41/km)

5K

25:00

10K

52:07

Half Marathon

1:55:00

Source Pace

5:00/km

What You'll Need

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Frequently Asked Questions

Q

What is the Riegel formula for race prediction?

The Riegel formula is T2 = T1 × (D2/D1)^1.06, published by Peter Riegel in 1977. T1 is your known race time, D1 is that distance, D2 is the target distance, and 1.06 is the fatigue exponent accounting for pace slowdown over longer distances.

  • T2 = T1 × (D2/D1)^1.06 (standard Riegel formula)
  • Exponent 1.06 works best for trained runners doing 10-60 miles/week
  • Higher exponent (1.07-1.08) for less trained runners
  • Lower exponent (1.04-1.05) for elite endurance athletes
  • Accuracy: within 3-5% for distances from 1500m to marathon
From DistanceTo DistanceDistance RatioTime Multiplier
5K → 10K10/5 = 2.02.0^1.06 = 2.0852.085x
5K → Half21.1/5 = 4.224.22^1.06 = 4.5354.535x
5K → Marathon42.2/5 = 8.448.44^1.06 = 9.4449.444x
10K → Marathon42.2/10 = 4.224.22^1.06 = 4.5354.535x
Half → Marathon42.2/21.1 = 2.02.0^1.06 = 2.0852.085x
Q

How accurate is the Riegel formula?

The Riegel formula is accurate within 3-5% for most trained runners when predicting between adjacent distances (5K to 10K, 10K to half). Accuracy decreases when predicting marathon times from short races like 5K because the marathon requires specific long-run endurance training.

  • 5K to 10K: Very accurate (±2-3%) for trained runners
  • 10K to half marathon: Good accuracy (±3-4%)
  • Half marathon to marathon: Moderate (±4-6%)
  • 5K to marathon: Least accurate (±5-10%)
  • Best predictor for marathon: recent half marathon time
PredictionAccuracy RangeBest WhenCaution
5K → 10K±2-3%Regular 5K racerRare for beginners
10K → Half±3-4%30+ miles/weekNeed long run base
Half → Marathon±4-6%40+ miles/weekNeed 18+ mile runs
5K → Marathon±5-10%50+ miles/weekOften optimistic
Q

Why does pace slow down at longer distances?

Pace slows at longer distances because the body shifts from aerobic glycolysis to fat oxidation, which produces energy slower. Glycogen stores deplete around 90-120 minutes of running. The Riegel exponent (1.06) captures this: doubling distance increases time by 2.085x, not just 2x.

  • Glycogen (fast fuel) lasts ~90-120 minutes at race effort
  • Fat oxidation is 30-40% less efficient than glycogen burning
  • Muscle fatigue accumulates with impact forces over thousands of steps
  • Core temperature rises, requiring cardiac output for cooling
  • Mental fatigue increases perceived effort at longer durations
Q

How do I adjust the Riegel exponent for my fitness?

The standard exponent is 1.06. Increase to 1.07-1.08 if you are a beginner or low-mileage runner (under 25 miles/week). Decrease to 1.04-1.05 if you are an experienced marathoner running 50+ miles/week. Compare predictions to actual race results to calibrate your personal exponent.

  • Exponent 1.04-1.05: Elite / high-mileage (50+ mi/week)
  • Exponent 1.06: Standard trained runner (30-50 mi/week)
  • Exponent 1.07: Recreational runner (20-30 mi/week)
  • Exponent 1.08: Beginner or speed-focused (under 20 mi/week)
  • To calibrate: compare prediction vs actual race, adjust exponent
Weekly MileageExponent5K to Marathon FactorProfile
50+ miles1.048.86xExperienced marathoner
30-50 miles1.069.44xTrained runner
20-30 miles1.079.75xRecreational
< 20 miles1.0810.07xBeginner
Q

What race time should I use for the most accurate prediction?

Use your most recent all-out race effort within the last 8-12 weeks. A recent 10K or half marathon gives the best marathon predictions. Avoid using training runs or time trials as they are typically 3-5% slower than race-day performances due to adrenaline and competition effects.

  • Use a race from the last 8-12 weeks (fitness-specific)
  • Half marathon is the best predictor for marathon time
  • 10K is the best predictor for half marathon time
  • Race-day adrenaline adds 3-5% performance boost vs training
  • Use a flat course result (hills distort predictions)

Example Calculations

125-Minute 5K to Marathon Prediction

Inputs

Known Distance5K
Known Time25:00
Exponent1.06

Result

Marathon Prediction3:56:06
10K Prediction52:08
Half Marathon1:53:23
Marathon Pace9:01/mile

T1 = 1500 sec. Marathon ratio = (42.195/5)^1.06 = 8.44^1.06 = 9.444. T2 = 1500 * 9.444 = 14166 sec = 3:56:06. 10K: (10/5)^1.06 = 2.085, T2 = 1500*2.085 = 3127 sec = 52:07. Half: (21.0975/5)^1.06 = 4.535, T2 = 1500*4.535 = 6803 sec = 1:53:23.

250-Minute 10K to Half Marathon

Inputs

Known Distance10K
Known Time50:00
Exponent1.06

Result

Half Marathon Prediction1:50:20
5K Equivalent23:59
Marathon Prediction3:48:09
Half Pace8:22/mile

T1 = 3000 sec. Half ratio = (21.0975/10)^1.06 = 2.10975^1.06 = 2.176. T2 = 3000*2.176 = 6527 sec = 1:48:47. 5K: (5/10)^1.06 = 0.4796, T2 = 3000*0.4796 = 1439 sec = 23:59. Marathon: (42.195/10)^1.06 = 4.535, T2 = 3000*4.535 = 13606 sec = 3:46:46.

31:45 Half Marathon to Marathon

Inputs

Known DistanceHalf Marathon (21.0975 km)
Known Time1:45:00
Exponent1.06

Result

Marathon Prediction3:39:29
5K Equivalent23:08
10K Equivalent48:13
Marathon Pace8:23/mile

T1 = 6300 sec. Marathon ratio = (42.195/21.0975)^1.06 = 2.0^1.06 = 2.085. T2 = 6300*2.085 = 13136 sec = 3:38:56. 5K: (5/21.0975)^1.06 = 0.2205, T2 = 6300*0.2205 = 1389 sec = 23:09. 10K: (10/21.0975)^1.06 = 0.4596, T2 = 6300*0.4596 = 2895 sec = 48:15.

Formulas Used

Riegel Formula

T2 = T1 × (D2 / D1)^exponent

Predicts race time at distance D2 based on a known time T1 at distance D1. The exponent (default 1.06) models fatigue accumulation over distance.

Where:

T2= Predicted time at the target distance (seconds)
T1= Known race time at the source distance (seconds)
D2= Target race distance (km or miles)
D1= Source race distance (km or miles)
exponent= Fatigue exponent, typically 1.06 for trained runners

Equivalent Pace

Pace = T2 / D2

Calculates the average pace per unit distance for the predicted race time.

Where:

Pace= Predicted average pace (seconds per km or mile)
T2= Predicted total race time in seconds
D2= Target distance in km or miles

How Race Time Prediction Works

1

The Riegel Exponent and Training Level

The standard Riegel exponent of 1.06 assumes a trained runner logging 30–50 miles per week. At this exponent, doubling the race distance multiplies finish time by 2.085× rather than 2.0×. A 22:00 5K predicts a 45:53 10K (22:00 × 2.085), not 44:00. That extra 1:53 represents the cumulative cost of fatigue over the additional distance.

Undertrained runners should increase the exponent to 1.07–1.08. A runner logging under 20 miles per week who races a 22:00 5K but attempts a marathon without adequate long-run preparation will find the standard 1.06 prediction overly optimistic. At exponent 1.08, the same 22:00 5K predicts a 3:49 marathon instead of 3:27 – a 22-minute difference that could mean hitting the wall versus finishing strong.

Elite or high-mileage runners (50+ miles per week) often use exponents of 1.04–1.05. Their superior aerobic development and fat oxidation capacity mean they slow less proportionally over longer distances. A 1.04 exponent predicts a 3:14 marathon from a 22:00 5K – realistic for a runner with the specific endurance base to support it.

Marathon predictions from a 22:00 5K at different exponents
ExponentWeekly Miles5K → 10K Factor5K → Marathon Factor22:00 5K → Marathon
1.0450+2.055×8.86×3:15:00
1.0630–502.085×9.44×3:27:00
1.0720–302.100×9.75×3:35:00
1.08< 202.115×10.07×3:41:00
2

Prediction Accuracy by Distance Gap

The Riegel formula is most accurate when predicting between adjacent distances. A 5K-to-10K prediction is accurate within 2–3% for trained runners because both distances rely primarily on the same aerobic energy system. A 5K-to-marathon prediction stretches accuracy to 5–10% because the marathon introduces glycogen depletion, thermal stress, and muscular fatigue that shorter races do not test.

The best marathon predictor is a recent half marathon result. The half-to-marathon jump is only a 2× distance increase, keeping the Riegel multiplier at 2.085×. A 1:42:00 half marathon predicts a 3:32:42 marathon – and this prediction holds within 3–5% for runners who have completed at least one 20-mile training run in the past 3 weeks.

Predictions from very short distances (1500m, mile) to the marathon are unreliable regardless of exponent. A 4:50 miler does not necessarily run a 2:58 marathon because the two events demand completely different physiological profiles. Use the interval training calculator to derive training paces from short-distance results, but rely on half marathon or 10K races for marathon prediction.

Always use a flat-course race time for prediction. A 23:00 5K on a hilly trail course may predict a 3:38 marathon, but the same runner might clock 21:30 on a flat road – predicting 3:23 instead. That 15-minute difference is entirely course artifact.

3

Calibrating Your Personal Exponent

If you have results at two different distances from the same training cycle, you can calculate your personal Riegel exponent. The formula is: exponent = ln(T2/T1) / ln(D2/D1). A runner with a 21:00 5K and a 1:37:00 half marathon: exponent = ln(5820/1260) / ln(21.0975/5) = ln(4.619) / ln(4.219) = 1.531 / 1.440 = 1.063.

Personal exponents vary by 0.02–0.04 between runners of the same weekly mileage. A runner with a personal exponent of 1.04 is an endurance-optimized athlete who slows less over distance (strong fat oxidation, efficient running economy). A personal exponent of 1.08 indicates a speed-optimized athlete who shines at shorter distances but fades at marathon length.

Recalibrate your exponent every 6–12 months as fitness evolves. A runner who adds weekly long runs and increases mileage from 25 to 45 miles per week will typically see their personal exponent drop from 1.07–1.08 to 1.05–1.06 over a single training cycle. Use the marathon pace calculator to apply your calibrated exponent to race-day split planning.

  1. 1

    Run two races within 4–6 weeks

    Use results from the same training block. Ideally one short (5K or 10K) and one long (half marathon).

  2. 2

    Convert times to seconds

    Example: 21:00 5K = 1,260 sec; 1:37:00 half = 5,820 sec.

  3. 3

    Calculate the exponent

    exponent = ln(T2/T1) / ln(D2/D1). Use a calculator for the natural log (ln) function.

  4. 4

    Apply to target distance

    Enter your exponent and shorter race result into this calculator for marathon prediction.

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Last Updated: Jun 20, 2026

This calculator is provided for informational and educational purposes only. Results are estimates and should not be considered professional financial, medical, legal, or other advice. Always consult a qualified professional before making important decisions. UseCalcPro is not responsible for any actions taken based on calculator results.

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