What is VDOT and why does it matter?

VDOT is Jack Daniels' aerobic-index number — a surrogate for VO2max derived from race performance rather than a lab test. A 3:30 marathon corresponds to roughly VDOT 46. Once the calculator knows your VDOT it can pinpoint the exact velocity for each training zone, because each zone is defined as a percentage of the effort at which you run out of oxygen.

How is the marathon pace calculated from a shorter race?

When you enter a recent race result the tool first derives your VDOT from the Daniels formula: VDOT = VO2(v) / %VO2max(t), where v is your race velocity in m/min and t is your race duration in minutes. It then solves the inverse — finding the marathon time at which that VDOT corresponds — using numerical bisection. This is more physiologically grounded than a straight Riegel extrapolation because it accounts for the diminishing oxygen utilisation at longer efforts.

What are the five training zones shown?

The five zones come from Jack Daniels' Running Formula (3rd ed., 2014). Easy (E) is 59–74% VDOT effort — conversational aerobic base work that makes up most of weekly mileage. Marathon pace (M) is 75–84% — the sustained effort you can maintain for a full marathon. Threshold (T) at 83–88% is "comfortably hard," used in cruise intervals to raise lactate threshold. Interval (I) at 95–100% targets VO2max, run as 3–5 minute hard reps. Repetition (R) at 105–120% builds speed and economy with full-recovery short reps.

What is a negative split and how much should I aim for?

A negative split means running the second half of a marathon faster than the first. Most elite world records are set with a 1–3% negative split — for a 3:30 marathon that means running the first half in about 1:46 and the second in about 1:44. Running the first half too conservatively wastes energy; running it too fast blows up your glycogen before 35 km. The slider lets you model any degree of split from even pace (0%) up to 6% so you can see the actual per-km targets before race day.

How accurate is the Riegel formula for the race equivalents table?

Pete Riegel's formula T2 = T1 × (D2 / D1)^1.06 is accurate within about 2–4% for distances within a factor of 4 of each other — so a 10K to half prediction is very reliable, while a 5K to marathon jump (8x the distance) assumes you have done the marathon-specific long-run training to back it up. Without an adequate aerobic base your real marathon will be slower than the formula suggests.

Can I use this for a half marathon instead of a full marathon?

The training zones and the race-equivalents table work for any race distance because they derive from VDOT, not from the marathon specifically. However, the 5-km split card and the negative-split slider are marathon-specific (42.195 km). Use the Running Pace Calculator Pro or the Marathon Time Predictor tools for non-marathon target distances.

Marathon Pace Predictor

Whether you are targeting a 3-hour breakthrough, a first sub-4 or a comfortable finish, racing 42.195 km successfully comes down to one decision made weeks before the start line: knowing your correct training paces and your race-day split strategy. This tool derives both from a single number — either your goal finish time or a recent all-out race result.

How it works

The calculator uses two interlocking models developed by running-science researchers.

Jack Daniels VDOT (aerobic index)

Jack Daniels’ Running Formula (2014) defines VDOT as a performance-derived surrogate for VO2max. Given a race time T (minutes) over distance D (km), your running velocity is v = D × 1000 / T metres per minute. The oxygen cost at that velocity is:

VO2(v) = −4.60 + 0.182258v + 0.000104v²

The fraction of VO2max a runner can sustain for duration T is:

%VO2max(T) = 0.8 + 0.1894 × e^(−0.012778T) + 0.2989 × e^(−0.19327T)

Dividing gives VDOT = VO2(v) / %VO2max(T). Once VDOT is known, the tool inverts the same equation to find the velocity — and therefore the pace — at any target percentage of that number. Easy running sits at 59–74%, marathon effort at 75–84%, threshold at 83–88%, intervals at 95–100%, and speed repetitions at 105–120%.

Riegel equivalent-race prediction

For the cross-distance equivalents table the tool uses Pete Riegel’s (1981) formula:

T₂ = T₁ × (D₂ / D₁)^1.06

The exponent 1.06 encodes how pace fades over longer efforts — an exponent of 1 would assume constant pace at every distance, which no human achieves.

Negative split modelling

Studies of major marathon results show that even-paced or mildly negative splits (second half 1–3% faster than first) produce the fastest times. The slider adjusts the first-half target by the chosen percentage while keeping the total time fixed, then recomputes each 5-km marker accordingly.

Worked example

Suppose you ran a half marathon in 1:45:00:

Velocity = 21,097.5 m ÷ 105 min = 200.9 m/min
VO2(200.9) = −4.60 + 36.60 + 4.19 = 36.19
%VO2max(105) ≈ 0.8 + 0.0093 + 0.0001 ≈ 0.810
VDOT ≈ 44.7

From VDOT 44.7 the tool predicts a marathon of approximately 3:41:30 (pace 5:15 /km). Your Easy training runs should target 5:55–7:25 /km, and your Threshold sessions roughly 5:05–5:20 /km.

Zone	Pace range (km)	Session type
Easy	5:55 – 7:25 /km	Daily runs, long slow distance
Marathon	5:05 – 5:40 /km	Long run last third, marathon-pace tempo
Threshold	4:58 – 5:15 /km	Cruise intervals, 20-min continuous tempos
Interval	4:35 – 4:50 /km	1-km reps, track sessions
Repetition	3:55 – 4:25 /km	200 m / 400 m speed work

Setting a 2% negative split turns those 5-km markers into 5:20/km for the first half and 5:10/km for the second, reaching halfway in about 1:52 and finishing in approximately 3:41. Every figure updates live as you adjust the slider.