Fitness

Aerobic index

The fitness a single run reveals, from the pace you held and the heart rate it cost.

Empirical estimate

The %HRR to %VO2 reserve link is peer-reviewed (Swain), but Daniels' VDOT is a well-calibrated empirical estimator fit to pooled race data, not a lab VO2 max test.

Your Aerobic index is the VO2 max a single run demonstrates. It reads one simple relationship: at a given heart rate, a faster pace means a bigger aerobic engine. Under the hood it is a VDOT, the same number Jack Daniels uses to set training paces.

The idea in one line

Running at a steady pace costs a predictable amount of oxygen. If you are only using, say, 75% of your heart-rate reserve to run that pace, then running all-out (100%) would cost proportionally more oxygen, and that projected ceiling is your VO2 max.

VO2_max = VO2_rest + (VO2_{at pace} − VO2_rest) ÷ %HRR

Step 1: the oxygen cost of your pace

Daniels measured how much oxygen it takes to run at a given speed and fit it to a curve (v is velocity in metres per minute):

VO2_{at pace} = −4.60 + 0.182258v + 0.000104v²

The oxygen cost of running climbs with pace. The dot marks the worked example below: a 4:30/km pace costs about 41 ml/kg/min.

Step 2: project to your maximum

Heart-rate reserve closely tracks oxygen-uptake reserve (%HRR ≈ %VO2R, established by Swain, first in cycling and later confirmed for running, and built on the reserve-based Karvonen method), so we divide the oxygen cost by the fraction of reserve you were using. Reserve is measured from rest to max:

%HRR = (HR − HR_rest) ÷ (HR_max − HR_rest)

This equivalence is a very good approximation, not an exact identity, and it becomes unreliable at easy intensities where a small heart-rate change swings the estimate wildly. That is why we only read the Aerobic index from steady, genuinely aerobic efforts, never from a recovery jog.

Worked example

A steady 4:30/km (222 m/min) at 155 bpm, with a resting HR of 50 and a max of 190:

Oxygen cost of the pace: 41.0 ml/kg/min
Heart-rate reserve used: (155 − 50) ÷ (190 − 50) = 75%
Projected VO2 max: 3.5 + (41.0 − 3.5) ÷ 0.75 = 53.5

So this run demonstrated an Aerobic index of about 54 (we report it as a whole number). VO2_rest is taken as 3.5 ml/kg/min by convention, the oxygen cost of quiet rest (one MET).

Why only steady runs

The relationship above assumes one steady aerobic effort. On an interval session your average pace is dragged down by the recovery jogs while your heart rate stays high from the reps, so the average pace and average heart rate describe two different workouts and the estimate collapses. We detect this with aerobic decoupling: when heart rate drifts more than 10% from pace across the run, we read fitness from the run's fittest steady segment instead, and if there is no steady segment we show no number rather than a misleading one.

What it is not

The Aerobic index does not depend on your body weight. VO2 max is already expressed per kilogram (ml/kg/min), and the oxygen cost of running is roughly constant per kilogram per kilometre, so mass cancels out of both sides. Weight matters for calories and power, not for this.

Its single largest source of error is your maximum heart rate. An age-predicted max carries a standard deviation of about 10 bpm, which is why we always learn your max from the highest heart rate you have actually recorded rather than trusting a formula. It is an estimate of the fitness a run revealed, not a lab VO2 max test, and it reads best on runs of 10 minutes or more at a genuine aerobic effort.