# Race time predictor

> Markdown copy of https://pacewise.doughworks.dev/race-time-predictor, generated from the page. The page is canonical. The page has an interactive calculator; this copy carries its method, formulas and reference tables. Every page on this site has one; the index is https://pacewise.doughworks.dev/llms.txt.

Predict your 5K, 10K, half marathon or marathon time from one recent race, by Riegel, Cameron and VDOT.

## 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 ÷ x^0.7905` 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](https://pacewise.doughworks.dev/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.

## Other calculators

- [**VDOT calculator** The Daniels number behind the third column.](https://pacewise.doughworks.dev/vdot-calculator)
- [**Pace calculator** Pace, time, distance and splits.](https://pacewise.doughworks.dev/pace-calculator)
- [**Age grade calculator** Your time against the world standard for your age.](https://pacewise.doughworks.dev/age-grade-calculator)