You ran one. Three models disagree about all the others.
Off —, run on a day that went to plan. The three models put the finish between —, and the figure above is the middle one. It asks for — for the whole way — —
Every distance, all three models
The sand row is the race you actually ran, so all three agree there by definition. The boxed row is the one you asked about. Everything else is prediction.
| Predicted finish | Pace / km | |||
|---|---|---|---|---|
| Distance | Riegel | Cameron | Daniels | at the middle one |
Down a column is one model’s whole opinion of you; across a row is how much that opinion is worth at that distance. —
Where the agreement runs out
Not the pace this time. Zero is whichever model comes out in the middle — the figure this page prints — and the other two show how far the argument runs either side of it. They all meet at the race you actually ran, because there is nothing to predict there.
The exponent all three are really using
All three can be written the same way: your time, multiplied by the distance ratio raised to some power. Riegel prints that power on the box — 1.06. The other two never mention one, but every answer they give implies one, and it solves straight back out of their own numbers.
The figure on the right of each line is that model’s exponent for one pair of distances, —. Nothing in the table below is a new measurement — it is the same three predictions from the top of the page, read as powers instead of as finishing times.
| Exponent | |||
|---|---|---|---|
| Race | spread | per 0.01 | Apart |
per 0.01 is the size of the effect, not its direction: below the race you actually ran the sign flips, because a bigger exponent makes short races faster rather than slower. Apart is the same spread the table at the top of the page prints, carried down here so the two can be checked against each other.
One second of the race you ran
Every number on this page stands on one time you typed in, and that time was one day — one start line, one wind, one breakfast. This is what a different day would have done to all of it.
| Distance | 1 s becomes | Off by |
|---|
1 s becomes is how far that prediction moves for one second of the race you ran. Off by runs it the other way: how different your race would have had to be to move the prediction further than all three models are apart.
—
What to run on Tuesday
The same VDOT figure sets training paces as well as race predictions. These are ranges, not single numbers — Daniels defines each effort as a slice of your ceiling, and the slice has two ends.
Each band’s percentage is the share of your VDOT that effort sits at. Other tables print a single number per zone — one point inside these bands, usually near the fast end.
Easy is the one people get wrong. It is meant to feel easy, and the slow end of that range is where most of a week belongs.
The top two bands are hard running. General information, not a prescription — anything to do with your heart, joints or breathing belongs with a doctor, not an equation from 1979.
Every training pace is a race you could run
The five bands above are percentages of a number, and percentages are hard to feel. Each band is also a speed, and every speed on this page belongs to some race distance — so each one can be handed back as the race it would be, using nothing but the table at the top.
Why three numbers and not one
- Riegel is one exponent for everybody. Pete Riegel published t₂ = t₁ × (d₂/d₁)1.06 in 1977, and that 1.06 was fitted across running, swimming and cycling at once. It is the simplest of the three and the only one you can do on a phone calculator. It knows nothing about you, and it does not pretend to.
- Cameron bends the same idea. Instead of one exponent it runs the two distances through a fitted curve, which makes it slow down less over short distances and more over long ones. Above the half marathon it is consistently the most pessimistic of the three, which is why it tracks reality better for people who have not done the mileage.
- Daniels goes through your body instead of the clock. The Daniels–Gilbert equations turn a time and a distance into an oxygen cost, and then ask what time at another distance would cost the same. The single number that falls out is VDOT. It is the only one of the three that also tells you how fast to train, which is what the bands above are.
- They agree where the races are. From 1500 m to the half, all three land within seconds of each other, because that is the range of results they were fitted on. Inside that range, arguing about which model to use is arguing about less than one traffic light.
- The marathon is where they part, and all three are optimistic. A marathon is limited by fuel and by how many weeks you spent running, not by your aerobic ceiling, and none of these equations has an input for either. If you race 5 km well on thirty kilometres a week, the marathon figure here is not a target. It is what your engine could do if the rest of you were ready.
- Riegel said so himself. The original paper is explicit that the prediction holds for someone appropriately trained for both distances. Everyone quotes the formula and drops that sentence.
- What was checked before this page went up. A 19:57 5 km comes out at VDOT 50.0 here, and VDOT 50 predicts a 3:10:40 marathon against the 3:10:33 printed in the published VDOT tables. Every training band above was checked to contain the single figure those tables print for that zone. Feeding any model its own input distance returns the time you typed, to the second.
- No calorie figure on this page, on purpose. How much a run costs you depends on bodyweight and on the other twenty-three hours, and the daily burn page already owns that arithmetic. Two pages computing it with two sets of assumptions would just be two answers.