Race Predictor Formulas Compared

From a 22:00 5K, Riegel predicts a 3:31 marathon, Cameron says 3:35 and the Daniels VDOT tables say 3:30. Same runner, same input, four minutes apart. The calculator above runs Riegel's formula with the standard 1.06 exponent, the same one the race time predictor uses; this page puts it next to the alternatives so you know what the number means and when to trust a different one.

The formulas from one 5K

Every row starts from the same 22:00 5K and predicts three longer races.

At 10K the five predictions sit inside a minute of each other. At the marathon they spread across nine. That spread is the whole lesson: the formulas agree on the next distance up and disagree on the big jump, and the disagreement is about how much a runner fades over two hours plus, which is the thing no formula can measure from a 5K.

Start from a half marathon and the spread shrinks. From a 1:40 half the marathon predictions are 3:28:30 for Riegel 1.06, 3:29:57 at 1.07, 3:31:25 at 1.08, 3:32:30 for Cameron and 3:27:47 for VDOT, which is a five-minute range instead of nine. The closer the input race is to the target, the less the choice of formula matters.

Riegel

Peter Riegel published the formula in 1981 after fitting a power law to record performances across running, swimming, cycling and other endurance sports. The running version says time at the new distance equals time at the old distance multiplied by the distance ratio raised to 1.06. Double the distance and the time goes up by a factor of 2.08, which is a fade of about 4 percent in pace.

It is one line, it needs one input, and it is close to right for any jump of two to one. Those are the reasons it became the default in nearly every race predictor on the web, ours included. The weakness is the fixed exponent. It was fitted to record holders, athletes trained to the limit at every distance, and analyses of large recreational marathon fields generally find that ordinary runners fade more than 1.06 allows for over 42 km. That is why many coaches quietly use 1.07 or 1.08 for the marathon jump, and the table shows what that does: each hundredth adds four to five minutes to the marathon prediction from a 5K.

Cameron

David Cameron built his model in the late 1990s by fitting a curve to record times from 400 m to 50 miles, then converting between distances along that curve. It is more complicated than Riegel and it behaves differently in one useful way: it fades faster than Riegel 1.06 between the half and the marathon, so from a 5K it lands near the Riegel 1.07 number, and from a half it lands a little slower than either. A lot of runners who tried both found Cameron closer to their real marathon, which is the same finding as the recreational-field studies expressed in a different way.

Its limit is the same as Riegel's. It was fitted to records, so it describes a runner trained for the target distance.

Daniels VDOT

Jack Daniels and Jimmy Gilbert approached it from physiology instead of curve fitting. Their equations give the oxygen cost of running at a pace and the fraction of VO2max a runner can hold for a given duration; a race time fixes the VDOT score, and the score fixes the equivalent time at every other distance. Run the VDOT calculator on the 22:00 5K and you get 44.5, and the reverse VDOT calculator turns that into the times in the table.

VDOT gives the fastest marathon prediction of the set, because its sustainable-fraction curve was fitted to well-trained runners who hold a high percentage of their maximum for a long time. Daniels says as much in his own tables: the marathon equivalent assumes marathon training. Its strength is what comes with it, five training paces from the same number, which none of the pure predictors offer.

Which formula to trust

None of them is a promise. Every model in the table is an equivalence: it says what an equally trained runner who ran your 5K would run at the longer distance, not what you will run off your current training. The formulas cannot see your long run, your fuelling, your heat tolerance or the fact that you have never raced past 10K.

So the choice depends on the jump. For 5K to 10K, or 10K to half, take any of them; they agree within a minute. For the marathon from a short race, treat Riegel 1.06 and VDOT as the ceiling, the time you could run with marathon training behind you, and Cameron or Riegel 1.08 as the more likely result for a first or second marathon. For the marathon from a recent half, the formulas agree closely enough that the half itself is the better predictor than any of them, provided it was run on a similar course in similar weather.

The best predictor of all is a race at the target distance, raced hard, in the last eight weeks. Everything on this page is a substitute for not having one.

Why our calculator runs Riegel

Three reasons. It is transparent, one line that anyone can check on a phone. It is close to right for adjacent distances, which is what most people use a predictor for. And an honest note next to the result does more than a fourth decimal in the exponent: the race time predictor says on every result that the model assumes solid endurance training for the longer distance, and that undertrained for the jump, the real time will be slower.

The calculator takes a recent race at the mile, 5K, 10K, half or marathon and predicts the 5K, 10K, half or marathon from it, with the pace per kilometre the prediction needs. It does not run Cameron or VDOT; the table above is computed for this page so you can see the comparison, and the VDOT column is one click away in the reverse VDOT calculator.

How Movement Rebels fits

A formula predicts from one number. The coach in Movement Rebels reads the training instead. Connect Garmin Connect or Apple Health and every run lands with pace, cadence and per-kilometre splits, so when your 30 km long run holds goal pace to 24 km and drifts after that, the coach can see it and say so in the debrief, which is the fade information a 5K can never carry.

It plans the block in your calendar, long runs with race-pace inserts included, and when auto push is on the planned sessions land on your Garmin watch as structured workouts. It cannot tell you your marathon time in advance either. It can tell you, week by week, whether the runner in the data is closing on the row you picked. The build that turns a 5K into a half is in Half Marathon Training Plan.

Related calculators

The race time predictor runs Riegel from any recent race. The VDOT calculator and reverse VDOT calculator give the Daniels equivalents in both directions. The reverse age grade calculator says what a target time is worth for your age, the weight vs pace calculator estimates what a change in body mass does to it, and the pace band calculator and marathon pace chart turn any prediction into the pace and splits it needs on the day.

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