Race time predictor
Predict your 5K, 10K, half marathon or marathon time from one recent race, by Riegel, Cameron and VDOT.
Your equivalent times
Pace shown is for the Cameron column.
| Distance | Riegel | Cameron | VDOT | Pace |
|---|
The three models
Riegel is a one-line power law. Cameron is a fitted curve, steadier over a long jump. VDOT works from oxygen cost, not race results. When they agree the prediction is solid; when they spread, that spread is your margin of error.
Riegel's power law simple, fades at a fixed rate
T₂ = T₁ × (D₂ ÷ D₁)1.06
Peter Riegel published this in 1977, fitted to world-record performances across distances. The exponent — the fatigue factor — is greater than 1 because pace fades as distance grows: doubling the distance costs a little more than doubling the time. Its virtue is that it needs nothing but arithmetic. Its weakness is the fixed exponent: a runner with a big aerobic base fades less than 1.06 predicts, and a fast-twitch 5K specialist fades more.
Cameron's model steadier over a long jump
T₂ = (T₁ ÷ D₁) × D₂ × a(D₁) ÷ a(D₂), where
a(x) = 13.49681 − 0.048865x + 2.438936 ÷ x0.7905 and distances are
in miles.
David Cameron fitted a curve instead of picking one exponent, so the effective fatigue
factor changes with distance, as it does in real runners. That makes it steadier than Riegel
over a long jump. The fit only holds inside the range it was built on. Past about 277 miles
a(x) crosses zero and the formula stops meaning anything, so this page refuses
those distances rather than printing a number.
Daniels & Gilbert's VDOT physiology, not a curve fit
Derive the VDOT your race implies, then solve for the time at the target distance that implies the same VDOT. See the VDOT calculator for the two equations.
The other two fit a curve through race results. VDOT models oxygen cost and how much of your maximum you can hold for a given duration, so it has a physiological argument behind it and not just an empirical one. It is also what the training paces in Daniels' Running Formula are built on.
What the models predict from a 20:00 5K
Watch the spread widen as the jump gets longer.
From a 20:00 5K.
| Distance | Riegel | Cameron | VDOT | Spread |
|---|---|---|---|---|
| 5K | 20:00 | 20:00 | 20:00 | 0.0% |
| 10K | 41:42 | 41:40 | 41:28 | 0.6% |
| 15K | 1:04:05 | 1:03:56 | 1:03:46 | 0.5% |
| Half | 1:32:00 | 1:31:51 | 1:31:50 | 0.2% |
| 30K | 2:13:37 | 2:14:09 | 2:13:38 | 0.4% |
| Marathon | 3:11:49 | 3:15:11 | 3:11:17 | 2.0% |
| 50K | 3:49:38 | 3:56:15 | 3:48:04 | 3.6% |
Under 10K the three sit within seconds of each other. By the marathon they're minutes apart. A predictor showing one number has hidden that.
Half marathon to marathon
The most-asked prediction, and the most trustworthy of the long ones.
Riegel equivalents, and what the “double it and add” rule works out to.
| Half | Riegel marathon | Marathon pace /km | Double + how long? |
|---|---|---|---|
| 1:15:00 | 2:36:22 | 3:42 | + 6:22 |
| 1:25:00 | 2:57:13 | 4:12 | + 7:13 |
| 1:35:00 | 3:18:04 | 4:42 | + 8:04 |
| 1:45:00 | 3:38:55 | 5:11 | + 8:55 |
| 1:55:00 | 3:59:46 | 5:41 | + 9:46 |
| 2:05:00 | 4:20:37 | 6:11 | + 10:37 |
| 2:15:00 | 4:41:28 | 6:40 | + 11:28 |
| 2:25:00 | 5:02:19 | 7:10 | + 12:19 |
| 2:35:00 | 5:23:10 | 7:40 | + 13:10 |
| 2:45:00 | 5:44:01 | 8:09 | + 14:01 |
What a predictor cannot know
- Your endurance base. Every model assumes training you may not have done. A 5K result says nothing about whether you have ever run 30 km.
- The course and the day. Hills, heat, humidity and wind all cost time no distance-to-distance model can see.
- How old the result is. A PB from two years ago predicts the runner you were.
How the app handles this it reads every result, not one
Instead of extrapolating from a single race, PaceWise blends all your personal bests, weighting each by how close it is to the target distance and how recent it is, then reports a range. That needs your full history, which is why it lives in the app rather than on this page.
Questions
How accurate is a race time predictor?
Accurate to a few percent when the distances are close, and less so as the gap widens. A 10K off a 5K is a short jump and the models agree within about 1%. A marathon off a 5K is another matter: they can differ by several minutes, and all of them assume an endurance base your 5K time says nothing about. Treat that number as a ceiling, not a target.
What is the Riegel formula?
Peter Riegel's 1977 power law: T2 = T1 × (D2 ÷ D1)^1.06. The 1.06 is a fatigue factor, above 1 because pace fades as distance grows. It caught on because it is simple and needs no lookup tables. The fixed exponent is also the weakness: for runners whose endurance lags their speed, it over-predicts long races off short ones.
Which prediction model should I use?
Over a short jump it barely matters, because they agree. Over a long one Cameron is usually steadier than Riegel, since its curve was fitted rather than pinned to a single exponent, and VDOT rests on measured oxygen cost rather than a curve fit. Read the spread rather than any one model. Three models clustered tightly means a well-constrained prediction. Three models far apart is your real margin of error.
Can I predict a marathon from a half marathon?
Yes, and it is the most reliable of the long predictions, because the two distances share most of the same endurance. Riegel comes out close to doubling your half and adding 6 to 14 minutes, more if you are slower. The popular “double it and add 10 to 20 minutes” is the more cautious version, and for a first marathon that is the one to use. What is left uncertain is not the arithmetic. It is whether your long runs support the distance.
Do these predictions account for hills, heat or wind?
No. Every model here turns one flat, still-air result into another. Hills, heat, humidity and headwind all cost time that a distance-to-distance model cannot see. Adjust down for conditions yourself, and read the number as what a good day on a fast course would give you.
Predict from all your results, not one
PaceWise reads all your personal bests together, weighted by distance and recency, and checks them against your next race. Free, offline, no account.