Race Time Predictor

The finish line clock said 22:04 when you crossed, and by the time you have caught your breath and stopped congratulating strangers, the question has already formed: what does that make my 10K? Because the 5K was not the goal — it was a measurement. One hard effort, honestly given, and somewhere in that number is information about every distance you might ever race: the 10K you signed up for in October, the half your friends keep mentioning, the marathon that has started appearing in your idle thoughts on long runs.

Runners have been extracting the future from single races for fifty years, and the tool that does it best is charmingly simple: Riegel's formula, one line of math published in 1981, still the backbone of nearly every race predictor on the internet. It is not magic and it is not perfectly honest — it flatters marathoners, as we will discuss at length — but it converts one race into a whole table of equal-effort times with an accuracy that has kept it alive through four decades of running-science fashion.

This race time predictor takes your known race — distance and time — and returns predicted times from 5K to marathon using Riegel, alongside the Cameron alternative and a per-distance pace table you can take to the start line. It runs free in your browser, and its favorite user is the runner six weeks out from a goal race who needs a number to pace by, not a fantasy to be broken by at mile 18.

Peter Riegel was an aircraft-engineering researcher and a runner, and in the late 1970s he asked a tidy question: how do running records slow as distance increases? Gathering world and national records across distances, he found that the relationship held to a power law — and in 1981, in American Scientist, he published the equation that still carries his name.

T2 = T1 × (D2 / D1)^1.06

T1: your known race time      D1: that race's distance
T2: predicted time            D2: target distance

Example: 5K in 22:00 → 10K?
T2 = 1320 s × (10 / 5)^1.06 = 1320 × 2.0849 ≈ 2752 s ≈ 45:52

The exponent is the whole personality of the formula. At 1.06, doubling your distance multiplies your time by about 2.08 — you slow about six percent per doubling, the compounding toll of glycogen, fatigue, and the fact that nobody sprints 42 kilometers. If the exponent were 1.0, pace would never fade; every runner would run marathon pace equal to mile pace, and the sport would be unrecognizable and briefly lethal. The 0.06 above unity is where all of your suffering is stored.

It is worth saying what the formula is not. It is not a model of you — no physiology, no training history, no lactate curve. It is a scaling law fitted to the best performances in the world, applied to everyone with cheerful egalitarianism. That is both its genius and its bias, and the bias has a name we will keep coming back to: elites fade less than the rest of us, and Riegel was fitted to elites.

1. 1

   Enter your reference race

   Distance and finish time — a recent, honestly-run effort. The closer it is to your target distance, the more trustworthy the prediction.

2. 2

   Read the full prediction table

   Times for 5K, 10K, 15K, half, and marathon appear together with per-kilometer and per-mile pace, so one input yields the whole map of your current fitness.

3. 3

   Compare the Cameron column

   Where the two methods disagree — mostly at the marathon — you have found the honest uncertainty band, and the truth usually lives nearer the slower number for recreational runners.

4. 4

   Sanity-check the input race

   Hills, heat, a tactical sprint start, or a training run masquerading as a race? Garbage in, fantasy out. Use your best recent flat-terrain effort.

5. 5

   Export the pace bands

   Take the per-mile or per-kilometer table to your watch or your crew. Pacing by band beats pacing by vibe, and by mile 20 beats it by a lot.

Let us run the full table for the runner from the opening — a 22:00 5K (4:24 per kilometer) — and watch what Riegel does at every distance. The arithmetic for each row is the same one-liner: 1320 seconds times the distance ratio raised to 1.06.

Two details in that table deserve a slow nod. First, the pace column is the real story: equal effort does not mean equal pace, and the formula prices the fade explicitly — eleven percent from 5K to 10K, another eleven to the half, another eleven to the marathon. Second, the marathon line lands on exactly 5:00 per kilometer, one of arithmetic's little jokes: a 22:00 5K is precisely the 3:31 marathon in Riegel's world, which makes the prediction memorable and the pacing table trivial to hold in your head.

Now the honest correction, printed in bold because it matters more than the table: almost no recreational runner runs their first marathon at Riegel's number. A 22:00 5K typically matures into a 3:35–3:45 marathon with proper marathon training — the range where the Cameron method and most coaches' experience put it — because Riegel's exponent was trained on world-record fades, and world-record runners are anomalies of durability. Use 3:31 as the ceiling. Pace the first attempt like it is 3:40. Thank us at mile 22.

The systematic error has a shape: the bigger the jump between your reference race and your target, the rosier the prediction. A 5K predicting a 10K is a small extrapolation over a distance nearly everyone's physiology covers — the error is minutes at most. A 5K predicting a marathon is a 8.4-fold distance ratio across a boundary the formula's training data barely represents: records set by runners whose glycogen storage, running economy, and mental durability are the top fraction of a percent of the species.

The practical distortions are well known to anyone who has coached first-timers. Undertrained marathoners blow past Riegel by twenty minutes and worse. Runners with speed but little endurance — the classic 5K specialist — see their marathon predictions land fastest of all, because the formula cannot see that their reference time was built on capacities that do not scale. Heat multiplies the error further: warm marathons run minutes slower than the same fitness predicts, and the penalty grows with finish time, so the slowest runners pay the most for a sunny day. Every one of these factors pushes real outcomes in the same direction — slower — which is why experienced users read Riegel's marathon number the way sailors read a lighthouse: a fixed point to steer by, not a harbor to dock at.

When coaches say Riegel flatters your marathon, the correction they are making is arithmetic in disguise: raising the exponent. The 1.06 was fitted to world records; population race data keeps suggesting that recreational runners fade more like 1.07 to 1.08 over the marathon, and first-timers nearer 1.10. Watch a single input move through those exponents — a 50:00 10K, predicting the marathon.

The sensitivity is easy to see once you know where the exponent acts: it multiplies the natural log of the distance ratio. For the 10K-to-marathon jump that ratio is 4.22, its log is about 1.44, so each 0.01 of exponent adds 0.0144 in log space — a 1.45 percent shift in predicted time, which at a 3:50 marathon scale is almost exactly three and a half minutes. That is the entire mechanism behind the over-prediction: a small error in one constant becomes minutes at the finish line, in direct proportion to how far your target sits from your reference.

The same math explains why the half marathon is the golden input. At a ratio of 2.0, each hundredth of exponent moves the prediction by about 0.7 percent — roughly a minute on a marathon — half the leverage of the 10K jump, because the log of 2.0 (0.69) is less than half the log of 4.22 (1.44), so the exponent barely gets room to work. Which is the practical rule hiding in the arithmetic: the closer your reference race to your target, the less the constant you do not know can hurt you. Predict from a half, and even a wrong exponent stays inside your pacing margin.

Riegel is the default but not the only citizen. Serious running calculators typically offer a small parliament of predictors, and their disagreements are informative rather than embarrassing — the spread between methods approximates your honest uncertainty. Here is the field as this tool presents it.

A note on the VDOT column: Jack Daniels' system is less a formula than a lookup table built from lab physiology and decades of athlete data, and it doubles as a training-pace calculator — which is why it pairs naturally with our Running Pace Calculator for the everyday work of converting goals into split times. If you want the aerobic-capacity angle, the VO2 Max Estimator estimates the number the VDOT tables lean on.

A prediction is only as good as the pacing plan attached to it, and the evidence here is refreshingly old-fashioned: even splits, or a slight negative split, win. Bank time early — running the first half faster than the prediction's pace — and the marathon's famous wall moves to meet you halfway through what should have been your strong half. The classic error pattern is three race segments: a hero first 10K, a survival shuffle through 30K, and a last 12K that takes longer than the first 15.

The tool's pace bands encode the discipline for you: take the predicted marathon pace, run the first third two to four seconds per kilometer slower, hold the middle third at pace, and let the final third negotiate with the day. Write the target kilometer splits on your arm, your shoe, or your crew's signboard — analog, sweatproof, and immune to watch-battery failure — and let the plan carry you past the point where judgment gets optimistic.

One more time-honored detail: fueling is pacing. Carbohydrate intake during the race — the standard guidance runs to tens of grams per hour for marathon efforts — is not optional garnish on top of a Riegel prediction; it is part of what makes the prediction achievable at all. The formula assumes a runner who has solved the logistics. Be that runner.

The formula cannot see your training. A 22:00 5K run on 25 kilometers a week and the same 22:00 run on 70 kilometers a week produce identical predictions and wildly different marathons, because endurance training changes how much you fade — the exact quantity the exponent pretends is constant. It cannot see your course profile either: a 400-meter-elevation marathon is a different race than a flat one, and no power law has ever climbed a hill for you. Weather, altitude, shoes, sleep, and the thousand small states of a body on race day all sit outside the parentheses.

So the right reading of any output is a band with a story attached: Riegel's number is your best-case ceiling with everything going right, Cameron's is the mortal estimate, and your first-ever attempt at a new distance should be paced nearer the slow end of the gap. Runners who internalize this — prediction as a range, pace as a discipline — get faster. Runners who treat the fast number as a contract spend mile 20 renegotiating with a creditor.

• Marathon trainees converting a half or 10K tune-up race into a goal-time and pacing plan
• Runners stepping up a distance for the first time, wanting a number to aim at that is not pure invention
• Club athletes tracking fitness across a season — the same input race, re-predicted as the training block deepens
• Coaches setting goal paces for athletes' tempo runs and interval sessions off one benchmark performance
• Triathletes pacing the run leg off a standalone open run — with all the brick-variability caveats that implies
• The curious, three days after a first 5K, wondering what they are

The seasonal pattern is real, too: every April, May, September, and October — the spring and fall race blocks — the same sequence plays out. Tune-up race, predictor, pacing plan, goal race. This page is the middle two steps of that ritual, kept honest on purpose.

The prediction is one exponentiation per distance — arithmetic your phone could do in its sleep — so there is no server, no account, and no training log required. Your reference race and your ambitions live in the page's memory for exactly as long as the tab is open. The tool works on a plane to the race city, which is both the privacy statement and the traditional time when the pacing question becomes urgent.

The predictor is one station in the training loop. The Running Pace Calculator converts any goal time into the splits your watch needs, the VO2 Max Estimator sizes the aerobic engine underneath the predictions, and the One-Rep Max Calculator handles the strength work that keeps the whole machine injury-free. Prediction, pace, capacity, strength — the full dashboard, all free, all in your browser, all between you and your next finish line.