Last updated: 31 July 2026
A single race time yields two things. Realistic times over other distances — and the paces you should train at. The model behind it is called VDOT and comes from Jack Daniels’ Running Formula. The calculator below uses the same equations as Runnerd — including the correction that keeps long distances honest.
Your VDOT —
Predictions — each with the range Runnerd applies to that distance
Training paces per kilometre
The maths runs in your browser. Your values never leave the page.
VDOT is not a measured maximum oxygen uptake. It is a performance measure with three parts. How much oxygen you can process at most. How economically you run while doing it. And what share of your maximum you hold over a given duration.
The calculation has two parts. The first estimates how much oxygen your pace costs — a regression over velocity. The second estimates what share of your maximum you sustained across the duration you ran. That share falls with time. Together they give VDOT.
The advantage over a lab value: VDOT describes what you actually delivered on the course. Two runners with the same oxygen uptake can have different VDOT values, because one runs more economically.
This is where Runnerd departs from most VDOT calculators, and it is the most important section on this page.
In the Daniels/Gilbert model the sustainable-share curve tends towards 80 %. The model therefore believes 80 % is sustainable indefinitely. Up to marathon duration that holds up well. Beyond it, the overestimation is severe: a 6-hour effort is predicted about 30 % too well, and a 24-hour result lands at world-record level.
So Runnerd computes a hybrid. Pure Daniels/Gilbert up to the 3-hour mark. Beyond it, a Riegel-style endurance decay anchored exactly at that point.
The exponent is 1.15, not Riegel's original 1.06. The reason: 1.06 is only validated to around marathon distance and flatters ultras. Analyses of real recreational marathon times also show 1.06 predicting slow marathons around 10 minutes too optimistically. At 1.15 both ends hold, and a 24-hour prediction stays just below the world record.
What that means in practice: run 10 km in 45:00 and pure Daniels/Gilbert gives you a marathon of 3:27:15. Runnerd says 3:30:21. Three minutes less flattering — and closer to the truth.
Beyond 24 hours Runnerd offers no prediction at all. In multi-day races, sleep strategy decides more than running fitness, and there is no equation for that.
Runnerd shows a range, not a single time. Its width depends on two things.
First on the distance. The longer the race, the more fuelling, pacing and weather have a say:
Second on where the value comes from. A real race result is the narrowest basis. A personal best detected in training gets 1.5 times the width. A prediction from Apple's oxygen-uptake estimate gets double. And training consistently earns a slightly narrower range — regular training makes performance more predictable.
Without a race time, Runnerd can fall back on the VO2max value from Apple Health. It is not taken at face value though, but multiplied by 0.93.
The reason: Apple estimates fitness from the relationship between heart rate and speed during walks and runs. That does not measure running economy. Studies report a systematic overestimation of 5 to 10 per cent against lab measurements. Without the correction, every prediction would be too optimistic.
As soon as a real race result exists, that counts — and the correction drops away.
Runnerd derives five bands from VDOT. Runnerd computes through oxygen consumption. It applies each share to your VDOT, then inverts the oxygen equation to recover velocity. That is exactly the reverse of the calculation that turned your race time into a VDOT.
At VDOT 50 that gives easy 5:26 to 6:02, marathon 4:30, threshold 4:15, interval 3:50 and repetition 3:36 per kilometre.
It assumes even training. VDOT presumes you are similarly well prepared across all distances. Race only 5 km events and you get a marathon prediction the long-run base does not support. The number is then arithmetically right and practically wrong.
It knows nothing about race day. Heat, wind, elevation and a botched pacing plan appear in no equation.
It needs a real race time. A fast training run on your own is almost always slower than the same race with a number pinned on.
And the gap matters. The further the target distance sits above your input, the less certain it gets. A marathon prediction from 5 km is an extrapolation by a factor of 8.
Download Runnerd and let it read your Apple Health data once. If Runnerd finds a personal best in your history, the prediction grows out of it. Enter a real race result and the range narrows. And the training paces land directly in your plan instead of staying in a table.
Runnerd is free. Pro unlocks the full analytical depth, a one-time 8.99 € for Mac and iPhone together. No subscription.
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Runnerd is not a medical product and does not replace medical advice. The equations used here are implemented from published literature; table values from Daniels' book are not reproduced. Apple, Apple Health, Apple Watch, HealthKit and App Store are registered trademarks of Apple Inc.