VO2max estimate
Three ways to a VO2max estimate without a lab and without a test to exhaustion. Heart rates only: your resting and maximum heart rate, the heart-rate ratio method. Bike with a power meter: a steady ride at a known power, the heart rate it settles at, and your age — the sum behind the classic Åstrand-Ryhming test, in the age-corrected form its own group published. Run at a steady pace: the same idea with your pace standing in for power. Each comes with a range: for the first two, the range the studies behind them found; for the running route, our own estimate of the error, explained under the hood.
Resting: lying down, first thing after waking, before coffee. Max: the highest figure your strap has recorded in a real all-out effort. Leave max empty and the tool falls back on an age estimate, which widens the range.
Likely somewhere between — and — ml/kg/min — the range that held 95% of the men in the study when the maximum was estimated from age.
Where it bends: the factor was measured in 46 well-trained men aged 21 to 51, with VO2max between 49 and 73 ml/kg/min — on a treadmill, so "well-trained" here means endurance-trained, not any particular sport. The authors say themselves that it has to be established separately before it is used for anyone else — women, untrained people, older athletes. If that is you, read the number as a rough indication, not a measurement. The whole thing also leans on your resting heart rate being measured in a strictly standard way: lying down, rested, repeated over a few mornings. A resting rate that is five beats too high moves the answer by about ten percent.
Under the hood
A remarkably short sum. The study behind it starts from the Fick principle — oxygen uptake equals heart rate times stroke volume times how much oxygen the muscles pull out of each litre of blood — and works out how much each of those can rise from rest to maximum. Stroke volume about 1.3 times, oxygen extraction about 3.4 times, and resting oxygen uptake of about 3.4 ml per kilogram per minute. Multiply those and the only thing left that varies between people is the ratio of maximum to resting heart rate.
If you leave the maximum empty
maximum ≈ 208 − 0.7 × age
The theory gives 15.0; when the authors measured it in ten well-trained men it came out at 15.3, and that is the figure the tool uses. Tested on 36 further men, the estimate had no systematic bias and a typical error of 2.7 ml/kg/min — about 4.5% — when the maximum heart rate was actually measured. With an age-estimated maximum that typical error grew to 4.7 ml/kg/min, about 7.8%.
The numbers that go in
| Number | What it is | Where it comes from |
|---|---|---|
| 15.3 | the conversion factor between the heart-rate ratio and VO2max | Uth, Sørensen, Overgaard & Pedersen (2004), European Journal of Applied Physiology: measured as 15.3 in 10 well-trained men — give or take 0.7 from one man to the next; the theoretical value from the Fick principle is 15.0. |
| ±5.3 · ±9.2 ml/kg/min | the range shown under the result | The same paper: the 95% limits of agreement in the 36 men used for validation — ±5.3 ml/kg/min with a measured maximum, ±9.2 with an age-estimated one (its figure 2). The error did not grow or shrink with the level, so the band is the same width for everyone. |
| 208 − 0.7 × age | the estimate used when you leave the maximum empty | Tanaka, Monahan & Seals (2001): a pooled analysis of 351 studies and 18,712 people, checked in a lab on 514 more. Individuals scatter around that line by about 10 beats per minute. |
| the range | what we chose to display | Our choice. The paper reports both a typical error (SEE) and a 95% range (limits of agreement). We show the range, because it is the honest answer to "how far off could this be for me?". |
| 30–100 · 120–230 · 10–100 | the resting, maximum and age values the tool accepts | Our limits, not the study's. Outside them the tool shows no number rather than a wrong one. The method itself was validated on results between 49 and 73 ml/kg/min and the age formula on people aged 18 to 81; outside those, the result is flagged. |
| whole numbers | the rounding of the result | Our choice. The typical error is close to 3 ml/kg/min, so a decimal would suggest a precision the method does not have. |
Bike with a power meter
This is the idea behind the Åstrand-Ryhming test from 1954: at a known power your oxygen uptake is fixed, so how high your heart rate settles tells you how much room is left before your maximum. The original is a nomogram — a chart you read with a ruler — built on people in their twenties, and it needs a separate correction for age. In 1967 the same Stockholm group fitted one equation to 84 men aged 30 to 70 that carries the age correction inside it. That is the sum used here.
load (kpm/min) = power (W) × 6.12 · ml/kg/min = litres/min × 1000 ÷ weight
| Number | What it is | Where it comes from |
|---|---|---|
| 1.29 · 60 · 0.00884 | the three constants of the equation | von Döbeln, Åstrand & Bergström (1967), Journal of Applied Physiology, equation 3: fitted on 84 male construction workers aged 30–70 tested at 600 and 900 kpm/min; typical error 8.4%. The 60 is the heart rate the whole family of these sums subtracts, carried over from earlier studies. |
| ×6.12 | watts into kilopond-metres per minute | A unit definition, not a finding: one kilopond-metre is 9.80665 joules, and a watt is 60 joules a minute. |
| ±16.5% | the range shown under the result | Our choice of presentation: 1.96 times the typical error of 8.4%, the usual way of turning a typical error into a 95% band (Sartor and colleagues, 2013, spell that rule out). |
| 50–400 W · 100–180 · 35–150 kg | the inputs the tool accepts | Our limits. The study's own range was narrower — ages 30 to 70, loads of about 100 to 150 W, heart rates of 125 to 170 — and the result is flagged outside any of those. |
| a road bike counts as an ergometer | the assumption that lets you use your own power meter | Our extrapolation. The study rode a laboratory ergometer; a well-calibrated power meter measures the same quantity, but nobody has checked this sum against one. |
Run at a steady pace
The same logic as the bike, with one extra step: a power meter tells you your work rate, a watch only tells you your pace, so the pace has to be turned into oxygen uptake first. The tool does that with a published average of ten treadmill studies, with the cost of pushing through still air added. Then your heart rate says what fraction of your maximum that uptake was — the relation the 1954 nomogram was drawn from, which differs between men and women — and the age factor from the 1967 equation scales it to your age.
fraction of your max = 50% + 0.77 × (heart rate − 128) for men, − 138 for women
VO2max = oxygen cost ÷ fraction × e−0.00884 × (age − 25)
| Number | What it is | Where it comes from |
|---|---|---|
| 2.209 · 3.163 · 0.000525542 | oxygen cost of running at a speed, on a track | Léger & Mercier (1984), Sports Medicine, equation 4: a weighted average over 130 adults in ten treadmill studies, plus Pugh's wind resistance. Valid between 8 and 20 km/h. The authors' own warning: between people the cost at one speed spans about 10 ml/kg/min. |
| 128 · 138 · 0.77 per beat | heart rate into a fraction of your maximum | Åstrand & Ryhming (1954), figure 1: at half of their capacity, 17 men averaged 128 beats/min and 16 women 138; at seventy percent, 154 and 164. The line through those two points, extended, is the logic of their nomogram. Aged 20 to 30. |
| e−0.00884 × (age − 25) | the age correction | von Döbeln, Åstrand & Bergström (1967), table 3: the age factor of their equation, normalised to 1.00 at 25 — the age the 1954 relation belongs to. |
| ±21% and ±5 ml/kg/min, combined | the range shown under the result | Our combination, not a measured figure. Sartor and colleagues (2013) put a heart-rate estimate at about ±15% when oxygen uptake is measured and say it "could increase to 21%" when it is worked out from the load, as here. Léger and Mercier report a 10 ml/kg/min spread in running economy at any pace, so ±5 ml/kg/min on the cost of your pace. We add the two as independent errors (the square root of the sum of squares), which is why the band is wider at slow paces: about ±25% at 5:30 per km, ±28% at 7:30. |
| 3:00–7:30 · 125–180 · 10–100 | the inputs the tool accepts | Our limits: the pace range is 8 to 20 km/h, where the cost equation holds; below a heart rate of 125 the tool refuses (the studies chose their loads to land between 125 and 170; the 1954 chart itself starts near 120), above 170, outside ages 20–70 and above a result of 73 ml/kg/min the result is flagged. |
| a straight line through two points | how the heart-rate step is read from the 1954 figure | Our reading. The paper gives two averages (50% and 70% of capacity) with a standard deviation of 8 to 9 beats; we draw the line through them and use it beyond those points, which is what the nomogram does. |
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What the number means once you have it, and the three ways of getting one — read the VO2max explainer.