Guide
Race Time Prediction Explained: Using the Riegel Formula
You just ran a strong 10K. So what does that mean you're capable of over a half marathon? Race time prediction answers exactly that — it takes one recent result and estimates your time over another distance, so you can set a realistic goal.
The Riegel formula
The most widely used method is Pete Riegel's formula, published in the 1970s and still the backbone of most predictors:
- T₂ = T₁ × (D₂ ÷ D₁)1.06
Here T₁ is your known time over distance D₁, and T₂ is the predicted time over the new distance D₂. The exponent 1.06 is a "fatigue factor" — if you could hold the exact same pace forever it would be 1.0, but because we slow down as distance grows, the slightly larger number bakes in that inevitable fade.
What the 1.06 exponent actually encodes
Doubling your distance doesn't double your time — it's a bit more, because you can't sustain 5K pace for a marathon. The exponent is what makes the formula non-linear: it converts a simple ratio of distances into a slightly larger ratio of times, and that gap grows the further apart the two distances are.
Think of it as a compact stand-in for two physiological facts. First, fatigue accumulates faster than distance does — the last 5K of a marathon is run slower than the first, even for elite runners, so the "cost" per kilometre rises as the race goes on. Second, aerobic endurance has a limit that pure 5K speed doesn't reflect — a runner with a blistering 5K but little weekly mileage has less of the endurance base the exponent assumes. Riegel derived 1.06 empirically, by fitting world-record and elite performance data across distances from 400m up to marathon and beyond; it's not a physical constant, just the average decay rate that best matched the data he had. That's why it holds up well as a population-level average, and why it can miss badly for any single runner whose training doesn't match that average profile.
Worked example: from a 24:00 5K
Say you've just run 24:00 for 5K (4:48/km) and want to know what that implies for longer distances. Feeding that time into the race time predictor — which runs the exact Riegel formula above — gives:
- 10K: 50:02 (5:00/km)
- Half marathon: 1:50:24 (5:14/km)
- Marathon: 3:50:11 (5:27/km)
Notice the predicted pace gets progressively slower as the distance grows — that's the exponent at work. Going from 5K to marathon is an 8.4× increase in distance, but a 9.6× increase in predicted time, not a flat 8.4×. If Riegel used an exponent of 1.0 (flat pace) instead of 1.06, the marathon prediction would come out to 3:22:32 — nearly 28 minutes faster than the actual formula gives, and unrealistically fast for almost anyone attempting to hold 5K-derived pace for 42.195 km.
Table: predictions from common 5K times
The same formula, run across a spread of typical 5K results, so you can see roughly where you'd land without typing your own numbers into the predictor first:
| 5K time | Predicted 10K | Predicted half marathon | Predicted marathon |
|---|---|---|---|
| 18:00 | 37:32 | 1:22:48 | 2:52:38 |
| 20:00 | 41:42 | 1:32:00 | 3:11:49 |
| 22:00 | 45:52 | 1:41:12 | 3:31:00 |
| 24:00 | 50:02 | 1:50:24 | 3:50:11 |
| 26:00 | 54:12 | 1:59:36 | 4:09:22 |
| 28:00 | 58:23 | 2:08:48 | 4:28:33 |
| 30:00 | 1:02:33 | 2:18:00 | 4:47:44 |
These are all computed with the same T₂ = T₁ × (D₂ ÷ D₁)1.06 formula — plug your own 5K, 10K or any other time into the race time predictor for an exact figure rather than interpolating from the table.
How accurate is it?
Prediction is most reliable when:
- The two distances aren't wildly different (predicting a half from a 10K beats predicting a marathon from a 5K).
- You've actually trained for the target distance — the formula assumes appropriate endurance.
- Your input result was a genuine effort on a fair course.
Treat the output as a smart starting point, not a guarantee.
When Riegel over-promises
The formula has no idea what your training actually looks like — it only sees one time and one distance. That means it will happily hand you an optimistic number in situations where your real result would be worse:
- Marathon predictions without an endurance base. Riegel's exponent assumes a runner whose long-run training matches their speed. If your weekly mileage is thin and your longest run tops out at 15K, the formula's marathon time is a ceiling you're unlikely to hit — the last 10K will cost you far more than 1.06 predicts. Adjust by: discount the predicted marathon time by a few percent for every long run you're missing relative to a standard build (16-20 week block topping out at 32-35K), or better, use a shorter input distance (a recent 10K or half result) rather than a 5K, since it already reflects more of your endurance.
- Heat and humidity. The formula assumes comparable conditions between your input race and your target race. Running the target race in significant heat can cost several percent off your predicted pace, more the longer the distance. Adjust by: add time proportional to distance — a rule of thumb many coaches use is roughly 1-3% per race for mild heat (18-22°C) and more for hot, humid days, with marathons hit hardest since there's more time for heat stress to compound.
- Hilly or technical courses. Riegel's baseline data comes from broadly flat, record-eligible courses. A hilly target course — or a flat input race that flatters you relative to a hilly target — breaks the comparison. Adjust by: compare elevation profiles before trusting the raw number; on a genuinely hilly course, treat the prediction as a best case and expect several extra minutes over a half or marathon distance.
- Very different race distances. The formula extrapolates worse the further apart D₁ and D₂ are. A 5K-to-marathon prediction (8.4× the distance) carries much more uncertainty than a 10K-to-half prediction (2.1× the distance), because there's more room for the exponent's "average" assumption to miss your individual profile.
Alternatives to Riegel
Riegel isn't the only race predictor in use, and it's worth knowing the landscape even though StrideForever's tool uses the Riegel model. The Cameron model (David Cameron, 2003) is a more elaborate formula that adds extra correction terms on top of a Riegel-style base, aiming to fit real-world race results — including the marathon's characteristic extra slowdown — more closely than a single fixed exponent can. Jack Daniels' VDOT system, from his book Daniels' Running Formula, takes a different approach entirely: instead of one time-to-time conversion, it estimates a single "VDOT" fitness number from a race result using running economy and VO2max research, then reads training paces and equivalent race times for every distance off that same number. VDOT tables tend to be prized for translating a result into day-to-day training paces (easy, tempo, interval) as much as for predicting other race times. Both are reasonable alternatives; Riegel remains the most widely implemented because it needs only two numbers — a distance and a time — and no lookup tables.
Common mistakes
- Treating the prediction as a guarantee. It's a formula-driven estimate from one data point, not a promise. Race-day execution, pacing, and conditions still decide the outcome.
- Predicting a marathon from a 5K or 10K alone. The wider the gap between input and target distance, the more the prediction leans on the "average trained runner" assumption rather than your specific endurance. Use the longest recent race you have.
- Ignoring the input race's conditions. A 5K time run in perfect weather on a flat course predicts differently than the same time run into a headwind on a rolling course — but Riegel can't tell the difference; only you can adjust for it.
- Re-running the formula on a stale result. A time from eight months ago, before or after a big training block, doesn't reflect your current fitness. Use your most recent genuine effort.
- Skipping the pace check. A predicted finish time is only useful once you know what pace it requires per kilometre or mile — always convert it before race day.
Put it to work
Enter a recent distance and time into the race time predictor and it applies the Riegel formula for you. Then take the predicted time over to the pace calculator to see the exact pace you'll need to hold on race day.