Free tool
Predict your 5K, 10K, half, and marathon times.
Predict your race finish time at any distance from one recent race result. The Riegel formula projects 5K to 10K, 10K to half marathon, half to full marathon, and any custom distance you enter - assuming you train for it. Free, no signup, runs in your browser and the math is the same one elite coaches have used since 1981.
Free · no signup · your file stays on your device
Your known race
hours
minutes
seconds
Predicted race times
| Distance | Time | Pace /km | Pace /mi |
|---|---|---|---|
| 5K | 22:00 | 4:24 | 7:05 |
| 10K | 45:52 | 4:35 | 7:23 |
| Half Marathon | 1:41:12 | 4:48 | 7:43 |
| Marathon | 3:31:00 | 5:00 | 8:03 |
Custom distance
Time
1:10:30
Pace /km
4:42
Pace /mi
7:34
How it works
- 1
Pick a recent race
Use a 5K, 10K, or half-marathon time from the last 4-6 weeks in flat, neutral conditions.
- 2
Enter the result
Distance in km or miles, finish time in hours/minutes/seconds.
- 3
Read the projections
Riegel-derived predictions for 5K, 10K, half marathon, marathon, and a custom distance.
- 4
Translate to training
The predicted race pace is your target. Plan tempo and threshold workouts around it.
The math
The Riegel formula scales time with distance using a fixed exponent:
T₁ and D₁ are your known race time and distance. T₂ is the predicted time at distance D₂. The 1.06 exponent encodes the slowdown - if it were exactly 1.0, doubling distance would exactly double time (impossible to sustain).
Worked example: 5K in 22:00 → half marathon
D₁ = 5000 m. T₁ = 1320 sec. D₂ = 21097.5 m. T₂ = 1320 × (21097.5 ÷ 5000)^1.06 = 1320 × 4.219^1.06 ≈ 1320 × 4.598 ≈ 6,069 sec ≈ 1:41:09. So a 22:00 5K runner has the leg speed to break 1:42 in a half if they've trained the distance.
Worked example: 10K in 40:00 → marathon
D₁ = 10000 m. T₁ = 2400 sec. D₂ = 42195 m. T₂ = 2400 × (42195 ÷ 10000)^1.06 = 2400 × 4.62 ≈ 11,090 sec ≈ 3:04:50. A 40-minute 10K projects to a sub-3:05 marathon - for runners who can hold the discipline and the long-run base.
Cameron's formula for ultras
Cameron (1998) uses a variable exponent that smooths the slowdown beyond marathon distance. It is a better fit for 50K and longer. We use Riegel here because 5K-to-marathon is the most common case; for ultra projections, manually plug into Cameron or check the splits a trusted ultrarunner has hit at your equivalent shorter-distance fitness.
Why the formula limits matter
Riegel works best when both races require the same primary energy system. Predicting an 800m time from a marathon is nonsense - they're different physiological events. The sweet spot is 5K-to-half-marathon for trained runners.
How to use this in training
- Set a race goal in concrete terms. A goal of "sub-1:40 half" needs a 4:44/km target. The predictor turns abstract fitness into a specific pace.
- Calibrate weekly tempo and threshold workouts. Tempo pace is roughly 15-20 sec/km slower than half-marathon pace. Threshold (LT) is roughly 10K race pace. With a predicted half pace, both targets fall out.
- Spot training gaps. If your predicted marathon is 3:30 but your longest run was 22 km, you don't have the base to deliver the prediction. Train the distance specifically.
- Use it for time-trial selection. If predictions show your half-marathon time is competitive but your marathon time isn't, race halves until you build endurance.
- Re-run after every key time trial. A small 5K PR is information. Re-predict marathon time and re-target your training paces.
Common mistakes & misconceptions
Using a "fitness benchmark" rather than an all-out test
A 5K run at 90% effort is not a 5K race time. The predictor assumes the input is a maximal effort. Garbage in, garbage out.
Trusting the marathon prediction without long-run base
A great 10K predicts a great marathon only if your weekly mileage and long-run distance support it. Without a 30km+ long run in training, the marathon prediction will fail by 5-15 minutes.
Using old PRs
A two-year-old race time reflects a two-year-old runner. Use a result from the last six weeks for a current projection.
Ignoring course profile
Riegel assumes flat. A hilly target course will be slower; a net-downhill course faster. Adjust manually - typically 2-3% per 100m of elevation gain.
Treating the prediction as a guarantee
Race day weather, GI distress, pacing errors, and unfueled training rides all sit between the predictor and the result. The number is achievable, not assured.
Predicting from sprints
A blazing 1-mile time does not predict a half-marathon time reliably. The exponent assumes both events are aerobic. Stick to 5K and longer as your input.
Related tools
FAQ
What is the Riegel formula?
Pete Riegel published the formula in 1977 as a statistical fit to race-time data. It says that doubling the distance produces a time slightly more than double, captured by a fixed exponent of 1.06. It is the standard race predictor used by coaches and platforms.
Why is the exponent 1.06?
Empirically, 1.06 produced the lowest residual error across thousands of race results in Riegel's original analysis. The exponent represents the rate at which pace slows as distance grows - closer to 1.0 means flatter pace decay, closer to 1.10 means steeper.
How accurate is Riegel for marathon prediction from 5K time?
Surprisingly good for trained runners - usually within 5-10% - but it consistently over-predicts marathon performance for runners who haven't built specific endurance. A fast 5K does not automatically produce a fast marathon if the long-run base isn't there.
Does Riegel work for ultra distances?
It drifts beyond marathon. Cameron's formula, published in 1998, uses a variable exponent that better fits longer events. Beyond 50K, plug your number into Cameron or use comparable race-pace data from runners of your fitness who've done the distance.
Should I use my best 5K or a recent race?
A recent race in good conditions. Your best 5K from three years ago when you were peak-fit is not your fitness today. Use a time from the last six weeks; otherwise the prediction reflects who you were, not who you are.
Why is my actual marathon time slower than the predictor?
Riegel assumes equal training specificity at every distance, but most runners specialize. A 20-minute 5K runner who hasn't run more than 15 km in training won't hit the 3:08 marathon the formula predicts. The number is potential, not destiny.
How does altitude affect predictions?
Sea-level race times don't transfer cleanly to altitude. Subtract roughly 1-2% per 1000m of elevation above 1500m for an honest comparison. The formula doesn't know about your venue.
Does Riegel work for cycling time trials?
It works directionally but with much wider error bars. Cycling aerodynamics and pacing physics differ. For TT predictions, use FTP-based models rather than pace-based extrapolation.
Can I use it for downhill or net-elevation-loss races?
No. Riegel assumes flat, neutral conditions. A net-downhill course like the Boston Marathon or Tunnel Vision will deliver faster times than the formula predicts; net-uphill courses will be slower.
How is Riegel related to VDOT?
VDOT, developed by Jack Daniels, maps race times to a single fitness number that predicts performance across distances. The underlying assumption - that one race time implies a fitness level usable elsewhere - is the same. Riegel is simpler; VDOT is calibrated against physiology more directly.
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