Training paces (VDOT)
From one recent race the tool works out your VDOT with the Daniels and Gilbert formulas and turns it into the five training paces, each with its range and its session cap.
A hard time trial works too, as long as it is from the last 4 to 6 weeks and on flat ground. A race run at half effort is no use, because the calculation reads it as your limit.
Weekly volume is used only to work out how long each session may last, following Daniels rules on volume caps. Leave it at zero and you still get every pace.
What VDOT actually is
VDOT is not a lab measured VO2max, it is a performance index: one number summing up how fast you are today, aerobic engine and running economy together. It comes from the two Daniels and Gilbert formulas, the oxygen cost of running at speed v, VO2 = -4.60 + 0.182258 v + 0.000104 v² with v in metres per minute, and the fraction of VO2max you can hold for t minutes, f(t) = 0.8 + 0.1894393 e^(-0.012778 t) + 0.2989558 e^(-0.1932605 t). VDOT is the ratio between the two. Two runners with the same VDOT train at the same paces even with different physiologies, and that is exactly what makes the index useful.
Where the five paces come from
Each pace is a percentage of VDOT, printed under the range on every card, and the pace itself comes from inverting the oxygen cost parabola (a quadratic solved exactly, not by trial and error). Marathon pace is the exception, since it is not a fixed percentage: it is the 42.195 km time this same model predicts for you, found by bisection, and it lands by itself around 80 to 83% of VDOT. The other three check themselves: threshold at 88% matches, within two or three seconds per kilometre, the pace you could hold for an hour; interval at 100% always stays faster than predicted 5,000 metre pace and lands within a few seconds of 3,000 metre pace; repetition around 107% lands on 1,500 metre pace. Those matches loosen at very low VDOT values, because there a 3,000 takes far longer than the eleven or so minutes anyone can hold at VO2max speed.
Why the volume caps matter
A correct pace inside an overlong session becomes a wrong pace. So when you enter your weekly volume the tool applies Daniels caps for each type of work: the long run no more than two and a half hours or a quarter of your volume, marathon pace no more than 110 minutes or 29 km, threshold within a tenth of weekly volume, interval within 8% and never above 10 km, repetition within 5% and never above 8 km. Recovery jogs do not count towards those totals.
When the number does not hold
The maths holds if the race was recent, all out and on flat ground. Hills, wind, heat, altitude and treadmills all distort it in the same direction: they make the performance look worse, so VDOT comes out lower than the real one. Below 1,500 metres the model overrates you because it does not describe the anaerobic side of the effort; past four hours in a marathon it underrates you, because there fuelling and muscular durability decide the day. GPS matters too: one kilometre measured long moves VDOT by a full point.
An index, not a training plan
This page tells you how fast to run, not which sessions to do or in what order, and it knows nothing about your injury history, your sleep or your job. It is informative material, not medical advice and not a personal plan, so it does not replace a professional. If you have heart or breathing problems, or you are coming back from an injury, talk to a sports physician first, and leave the programming to a coach. Every calculation runs inside your browser and no data is sent anywhere.