VO2 Max Calculator: the Cooper 12-Minute Run, the Rockport Walk and the Heart Rate Ratio Method Side by Side, with the Gap Between Them

Q: My watch gives me a VO2 max. How does it compare with this?

A wrist or chest-strap device typically estimates VO2 max from the relationship between your running speed and your heart rate over many recorded sessions, which is a fourth method again and not one of the three here. It has one real advantage over this page: it has hundreds of data points on you rather than one, so its estimate is less at the mercy of a single bad day. It has the same fundamental limitation — it is a regression, not a measurement — plus two of its own: it depends on the device’s estimate of your maximum heart rate, and optical wrist sensors are unreliable at high intensity. Expect a device and this page to differ by several units and do not treat either as the arbiter.

Three published field estimates of maximal oxygen uptake, computed together from one set of inputs — Cooper’s 12-minute run (1968), the Rockport one-mile walk (Kline 1987) and Uth’s heart rate ratio method (2004) — each with the error its own authors published: ±5.0 mL/kg/min for Rockport, a 3.0 mL/kg/min overestimate with limits of agreement of 0.10 to 5.94 for Cooper in one Indian validation, and a constant Uth derived in well-trained men only. They are not interchangeable and this page does not average them. It prints all three, the spread between them, and where each one lands against published population means by age and sex.

Last updated 5 Oct 2026

These are estimates from published formulas, not measurements of you, and they assume you are well enough to train. Build up gradually, do not attempt a maximum effort alone or without sound technique, and stop and get advice if you have chest pain, unusual breathlessness, dizziness or palpitations.

Three field tests, one person — and how far apart they land

a 12-minute distance, a one-mile walk time and a resting heart rate → three published VO2 max estimates in mL/kg/min, with the spread between them

Which method gives the headlineEvery method you have inputs for is computed and printed in the rows below whichever you choose here, together with the spread between them. These three are not variants of one measurement. Cooper is a maximal running test on a sample of 115 US Air Force personnel in 1968. Rockport is a submaximal walk, derived on 343 people aged 30 to 69, and it works by reading how high your heart rate climbs for a given walking speed. Uth takes no exercise test at all and works off the ratio of your maximum to your resting heart rate, which is a different physiological signal again. Expect them to disagree: on this page’s own default inputs they span about 8 mL/kg/min, or 19% of the lowest.

Sex, as the Rockport equation codes itThe Rockport equation carries a flat sex term of 6.315 mL/kg/min, added for men and not for women. That term is LARGER than the equation’s own standard error of estimate of 5.0 mL/kg/min, which means which box is ticked moves the answer more than the measurement error does — worth knowing before comparing two people. It is a regression coefficient fitted on the 343 adults in the original sample, not a statement about any individual, and the sexes overlap heavily in reality. This selector also chooses which population mean the comparison row below uses. Cooper’s equation has no sex term at all, having been derived on a sample of Air Force personnel in 1968, and Uth’s has none either.

Age (years)Age enters the Rockport equation directly, at −0.3877 mL/kg/min per year, and it selects the population mean the page compares against. It is also used to predict a maximum heart rate for the Uth method when you have not measured one. The page refuses below 18 and above 90. Note which method this constrains: the Rockport equation was derived on adults aged 30 to 69, so for a reader of 20 or 75 it is extrapolating, and in independent validations it has overestimated in overweight women, underestimated in 70-to-79-year-olds, and correlated much less well in young women (r = 0.62) than in young men (r = 0.79).

Body weight (kg)Used by the Rockport equation, which was published in POUNDS: this page converts with the exact factor 1 kg = 2.20462262 lb and then applies the published coefficient of −0.0769 per pound, so 1 kg of body weight is worth −0.1695 mL/kg/min. Weight matters more than that coefficient suggests, because VO₂ max in mL/kg/min is divided by weight as well: two people with the same absolute oxygen uptake in litres per minute get different per-kilogram figures purely from mass, and a per-kg figure therefore falls when weight rises even if nothing about the heart or lungs changed. If you want the version scaled to lean mass instead, the lean body weight page in the medical set gives you the denominator.

Distance covered in 12 minutes (metres) — 0 if you did not do this testCooper’s test: cover as much ground as you can in exactly 12 minutes, running, on a flat measured course or a track. Enter 0 if you have not done it and the Cooper rows disappear rather than being guessed at. The page refuses a distance between 1 and 999 m, for a reason worth stating: the equation is a straight line that reaches zero at about 505 m and goes NEGATIVE below that, so a short distance does not produce a small answer, it produces a meaningless one. At the other end it refuses above 6,000 m, which would be a 12-minute 6 km. This test is maximal by design — it means running to the point of genuine exhaustion — and that is exactly why the submaximal walk test exists.

One-mile walk time (minutes) — 0 if you did not do this testThe Rockport test: walk one mile (1,609 m, or four laps of a 400 m track plus 9 m) as briskly as you can without running, and record the time in minutes and decimals of a minute — 13 minutes 30 seconds is 13.5, not 13.30. Enter 0 if you have not done it. The page refuses between 1 and 8 minutes, which would be a 12 km/h walk and is therefore a run or a mistyping, and above 24 minutes, because the equation’s coefficient of −3.2649 per minute drives the estimate towards and then below zero: at 25 to 30 minutes it returns negative oxygen uptakes for perfectly ordinary readers. The coefficient is also why this is the input to get right — 30 seconds of walk time is worth 1.6 mL/kg/min.

Heart rate at the END of the mile walk (bpm) — 0 if you did not do this testThe heart rate in the last minute of the walk, which is the other half of the Rockport measurement: the test works by asking how hard your heart had to work for that walking speed. Count for a full minute immediately on finishing, or read a chest strap; a 10-second count multiplied by six, which the original protocol allows, carries ±6 bpm of rounding on its own. Enter 0 if you did not do the test. The page refuses between 1 and 59. The coefficient is −0.1565 per beat, so 6 beats of counting error is worth about 0.9 mL/kg/min — small beside the equation’s 5.0 mL/kg/min standard error, which is the honest thing to notice about it.

Resting heart rate (bpm) — 0 if you have not measured itNeeded for the Uth method and nothing else. Taken sitting or lying quietly over a full minute, ideally on waking. Enter 0 and the Uth rows disappear. This input deserves suspicion in proportion to how easy it is to supply: Uth’s estimate is directly proportional to the maximum-to-resting RATIO, so a resting rate recorded 5 beats low at 55 rather than 60 raises the estimate by about 4 mL/kg/min — nearly as much as the whole published disagreement between methods on this page’s defaults. The lowest overnight figure a watch logged is not a waking resting rate and will push the estimate up.

Maximum heart rate (bpm) — 0 to use Tanaka’s prediction from your ageAlso for the Uth method only. A maximum you have actually measured is far better than a predicted one: enter 0 and the page falls back to Tanaka’s 208 − 0.7 × age, which carries a between-person standard deviation of about 10 beats a minute, and 10 beats of error at a resting rate of 55 is worth about 2.8 mL/kg/min in the Uth estimate. The page refuses a value between 1 and 99. If you want to see what that prediction error does to training zones rather than to this estimate, the target heart rate zones page prints five competing maximum equations and the beats between them.

42.4mL/kg/minExample

a 40-year-old man, 75 kg, 2,400 m covered in 12 minutes, a one-mile walk of 13.0 minutes ending at 115 bpm, resting heart rate 55, no measured maximum heart rate, Cooper selected

Three equations, three different signals, and the units each one was published in

Cooper (1968): VO₂max = 22.351 D − 11.288, D in km covered in 12 minutes · Rockport, per kg (Kline 1987): VO₂max = 132.853 − 0.0769 W_lb − 0.3877 A + 6.315 S − 3.2649 T − 0.1565 HR · Rockport, absolute (same paper): VO₂max = 6.9652 + 0.0091 W_lb − 0.0257 A + 0.5955 S − 0.2240 T − 0.0115 HR, in L/min · Uth (2004): VO₂max = 15.3 × HR_max/HR_rest · and the identity that makes every figure here per-kilogram: 1 MET = 3.5 mL/kg/min

D: distance in KILOMETRES covered in exactly 12 minutes. The same regression is also written as (d − 504.9)/44.73 with d in metres, which is a different rounding of the same line and differs from the form used here by about 0.013 mL/kg/min at 2,400 m. The line reaches zero at about 505 m and is negative below it, which is why this page refuses short distances
W_lb: body weight in POUNDS. The Rockport equations were published in pounds and this page converts from kilograms with the exact factor 2.20462262, so the per-kg coefficient of −0.0769 per pound becomes −0.1695 per kilogram
A: age in years, at −0.3877 mL/kg/min per year in the per-kg form. The equation was fitted on adults aged 30 to 69 and is extrapolating outside that
S: sex, coded 1 for male and 0 for female exactly as published. The 6.315 mL/kg/min it adds is larger than the equation’s own 5.0 mL/kg/min standard error of estimate
T: one-mile walk time in minutes and decimals, at −3.2649 mL/kg/min per minute — the steepest coefficient in the equation, so 30 seconds is worth 1.6 mL/kg/min
HR: heart rate in bpm at the end of the walk, at −0.1565 per beat. A 10-second count × 6, which the original protocol permits, carries ±6 bpm of rounding, worth about 0.9 mL/kg/min
15.3: Uth’s constant, fitted in well-trained men aged 21 to 51. The whole method is this one number: there is no term for age, sex, weight or anything else, and the authors said it may not be reliable in other subgroups
two Rockport forms: the same paper published a per-kilogram equation and an absolute litres-per-minute equation, and they are NOT algebraically consistent with each other: divide the absolute form by body weight and you get a figure a few tenths of a mL/kg/min away from the per-kg form. This page prints both and the difference between them, because the gap is a property of the source

Worked example

a 40-year-old man, 75 kg, 2,400 m covered in 12 minutes, a one-mile walk of 13.0 minutes ending at 115 bpm, resting heart rate 55, no measured maximum heart rate, Cooper selected
Cooper first, because it is the headline. 2,400 m is 2.4 km, which is a 12 km/h average and a 5.00 min/km pace. VO₂max = 22.351 × 2.4 − 11.288 = 53.6424 − 11.288 = 42.35 mL/kg/min, printed as 42.4. Note the sensitivity before going further: one more lap of a 400 m track would have added 22.351 × 0.4 = 8.94 mL/kg/min, which is larger than the gap between the published population means for two adjacent decades of age. Run the Kolkata correction on the same distance and you get 21.01 × 2.4 − 11.04 = 39.38, nearly 3 units lower, because that validation found the standard equation overestimating in all 88 of its participants.
Now Rockport, on the same afternoon, from the same person. The equation is in pounds: 75 kg × 2.20462262 = 165.347 lb. VO₂max = 132.853 − 0.0769 × 165.347 − 0.3877 × 40 + 6.315 × 1 − 3.2649 × 13.0 − 0.1565 × 115 = 132.853 − 12.715 − 15.508 + 6.315 − 42.444 − 17.998 = 50.50 mL/kg/min. So the two field tests disagree by 8.15 mL/kg/min, which is 19.2% of the Cooper figure. Neither test was done badly. They are reading different signals.
Check Rockport against the other equation in its own paper. The absolute form gives 6.9652 + 0.0091 × 165.347 − 0.0257 × 40 + 0.5955 − 0.2240 × 13.0 − 0.0115 × 115 = 3.803 L/min. Divide by 75 kg and multiply by 1,000: 50.70 mL/kg/min, against the per-kilogram equation’s 50.50. The same paper’s two equations differ by 0.20 mL/kg/min for this reader. That is a property of the source, not of the page, and the page prints both.
Uth, which needs no test at all. No measured maximum was entered, so the page uses Tanaka: 208 − 0.7 × 40 = 180 bpm. The ratio is 180/55 = 3.273, and VO₂max = 15.3 × 3.273 = 50.07 mL/kg/min. Watch how fragile that is: a resting heart rate of 60 instead of 55 gives 15.3 × 3.000 = 45.90, which is 4.17 units lower for five beats — half the whole disagreement between the three methods, from a measurement most people take casually. And the 180 is itself a prediction with a standard deviation of about 10 beats, worth another 2.8 units either way.
The three together, which is the output this page exists for. Cooper 42.35, Rockport 50.50, Uth 50.07. Lowest 42.35, highest 50.50, spread 8.15 mL/kg/min, or 19.2% of the lowest. The published mean for a man of 40 is 47 mL/kg/min, so this band runs from 4.65 BELOW that mean to 3.50 ABOVE it. A reader who had done only the run would place himself below average; the same reader who had done only the walk would place himself above it. That is why no category label is attached to anything on this page, and why the first row under the answer is the spread.

Cooper’s 12-minute distance, both published forms of the equation, and the gap between them

VO₂ max in mL/kg/min, computed by this page’s engine. Two things to take from it. The line is steep: 400 m of distance — a single lap, or about 20 seconds of pace — is worth 8.9 mL/kg/min, which is larger than the entire disagreement between the published population means for two adjacent decades of age. A 12-minute test is therefore a pacing test as much as a fitness test. And the correction derived in 88 sedentary male university students in Kolkata runs 1.1 to 5.1 mL/kg/min BELOW the standard equation across this range, growing with distance, because the Kolkata study found the standard equation overestimating measured VO₂ max in every one of its participants. Neither line is “the” Cooper equation for a given reader; the page prints both and the gap.
Distance in 12 min (m)	Speed (km/h)	Pace (min/km)	Cooper 22.351 × km − 11.288	Kolkata correction 21.01 × km − 11.04	Difference
1000	5.00	12.00	11.1	10.0	+1.09
1400	7.00	8.57	20.0	18.4	+1.63
1800	9.00	6.67	28.9	26.8	+2.17
2200	11.00	5.45	37.9	35.2	+2.70
2400	12.00	5.00	42.4	39.4	+2.97
2800	14.00	4.29	51.3	47.8	+3.51
3200	16.00	3.75	60.2	56.2	+4.04
3600	18.00	3.33	69.2	64.6	+4.58
4000	20.00	3.00	78.1	73.0	+5.12

The same tests, six different people: where the three methods land and how far apart

All figures mL/kg/min, computed by this page’s engine; Uth uses Tanaka’s predicted maximum heart rate. Read the last two columns together. For the first row the three methods span 42.4 to 50.5 against a published mean of 47 — so Cooper places this reader 4.6 below the mean for his age and sex and Rockport places him 3.5 above it. Two tests done on the same afternoon put him on opposite sides of the average, and anything built on top of that placement inherits the contradiction. Notice too what moves the methods differently. Changing sex at a fixed set of test results moves Rockport by 6.3 (its sex term) and Cooper not at all, because Cooper’s equation has no sex term; changing age moves Rockport and Uth and leaves Cooper untouched; changing weight moves only Rockport; changing resting heart rate moves only Uth. These are not three readings of one instrument.
Person	Cooper	Rockport	Uth	Spread	as % of lowest	Published mean for that age and sex	Band vs that mean
Man 40, 75 kg (this page’s defaults)	42.4	50.5	50.1	8.1	19.2%	47	-4.6 to +3.5
Woman 40, 65 kg, same tests	42.4	45.9	50.1	7.7	18.2%	38	+4.4 to +12.1
Man 25, 75 kg, same tests	42.4	56.3	53.0	14.0	33.0%	54	-11.6 to +2.3
Man 65, 75 kg, same tests	42.4	40.8	45.2	4.4	10.8%	39	+1.8 to +6.2
Man 40, 95 kg, same tests	42.4	47.1	50.1	7.7	18.2%	47	-4.6 to +3.1
Man 40, 75 kg, resting rate 70	42.4	50.5	39.3	11.2	28.4%	47	-7.7 to +3.5

Published population means for directly measured VO2 max, by age and sex

Mean maximal oxygen uptake from the HUNT3 Fitness Study: 3,816 healthy Norwegian men and women aged 20 to 90, measured directly by treadmill running with gas analysis, published open-access under a Creative Commons Attribution licence by Loe and colleagues in 2013, and tabulated to the nearest whole number by the authors’ own research group. The overall means in that study were 44 mL/kg/min for men and 35 for women, and the decline is about 3.5 mL/kg/min per decade. Four cautions, all of which matter more than the numbers. These are MEANS, not categories and not targets: about half of a healthy population sits below each one by arithmetic necessity, and no row here carries a grade, because a grade would be a judgement about a person rather than a fact about a measurement. The spread is wide — the published standard deviations for the 20-to-29 group are 8.4 mL/kg/min for men and 7.7 for women, which is more than two decades’ worth of the mean column, so a healthy individual can sit two age brackets either side of their own mean. The sample is Norwegian and self-selected into a fitness study, which is not a world population. And these were MEASURED values, while everything above on this page is ESTIMATED with its own error of 3 to 6 mL/kg/min, so the comparison is coarse by construction. WHAT COULD NOT BE ESTABLISHED for this page: the per-decade standard deviations beyond the 20-to-29 group could not be transcribed reliably from the source available here, so they are not printed.
Age group	Men (mL/kg/min)	Women (mL/kg/min)
20–29	54	43
30–39	49	40
40–49	47	38
50–59	42	34
60–69	39	31
70 and over	34	27

Where each figure on this page comes from, and what was deliberately left out

The row worth dwelling on is the first. Cooper’s 1968 paper tested 115 US Air Force officers and airmen and reported a correlation of 0.897 between 12-minute distance and treadmill-measured VO₂ max; the linear equation now attributed to it everywhere, including on this page, could NOT be traced to that paper in the material available here, and the Cooper Institute’s own retrospective of the test does not print it either. The coefficients are stable across every secondary source consulted and are used here for that reason, but the attribution is weaker than its ubiquity suggests and the page says so rather than implying a provenance it could not check.
Figure	Source	Status on this page
22.351 × km − 11.288	Universally attributed to Cooper 1968 (JAMA 203:201–4)	Computed; see the provenance note — the 1968 paper reported r = 0.897, not this regression
21.01 × km − 11.04	Bandyopadhyay 2015, Biol Sport 32(1):59–63	Computed and shown beside the standard form
Rockport per-kg and absolute equations	Kline et al. 1987, Med Sci Sports Exerc 19:253–9	Both computed; the inconsistency between them is printed
Rockport SEE 5.0 mL/kg/min, R = 0.88	Kline et al. 1987, via a US Army technical report	Printed as a ± envelope; a conflicting figure is recorded in the references
15.3 × HRmax/HRrest	Uth et al. 2004, Eur J Appl Physiol 91(1):111–15	Computed; its derivation sample is stated
208 − 0.7 × age	Tanaka et al. 2001	Used only as a fallback maximum heart rate for the Uth method
Population means by age and sex	Loe et al. 2013, PLoS One 8(5):e64319 (CC BY)	Reproduced; it is the only reference table on this page, and it is freely licensed
1 MET = 3.5 mL/kg/min	Definition	An identity, used freely
Fitness categories such as “excellent” or “poor”	Not used	Deliberately absent — a category label on a measurement of a person is a judgement, and this batch does not make them
Percentile tables from commercial or subscription registries	Not used	Not reproduced; see the licensing note
Oxygen extraction ratio	A different quantity entirely	Not linked and not computed — it is the fraction of delivered oxygen a tissue takes up, not an exercise capacity

Why three field tests of the same quantity disagree by a decade of age, and why no category label is attached to the answer

VO₂ max is a measurement, and nothing on this page is one. The measurement is made in a laboratory with a mask, a gas analyser and a treadmill or cycle ramped to exhaustion, and it is the highest rate at which your body can take up and use oxygen. Everything here is a regression that predicts that measurement from something easier to obtain: a distance, a walk time, two heart rates. Each regression was fitted on a particular sample doing a particular thing, each carries a published error, and — the point of this page — they do not agree with each other. On this page’s own default inputs the three span 42.4 to 50.5 mL/kg/min, a gap of 8.1 units or 19% of the lowest. Since the published population means fall by about 3 to 5 mL/kg/min per decade of age, that is a gap of roughly two decades. Which test you happened to do therefore moves the answer more than ten years of ageing would.

They disagree because they are not three readings of one instrument. Cooper’s test reads how far you can run in 12 minutes, which depends on aerobic capacity but also on running economy, pacing judgement, leg strength, footwear, surface, heat and willingness to suffer. The Rockport test reads how high your heart rate climbs for a given walking speed, so it is an index of cardiovascular strain, and everything that moves heart rate independently of fitness — caffeine, heat, anxiety, dehydration, a beta-blocker — moves its answer. Uth’s method reads nothing but the ratio of your maximum to your resting heart rate, so it measures a property of your autonomic nervous system and infers fitness from it. The sensitivity table on this page makes the difference concrete: at fixed test results, changing the sex box moves Rockport by 6.3 mL/kg/min and Cooper by nothing at all; changing weight moves only Rockport; changing resting heart rate moves only Uth. A single number from any one of them conceals the fact that the other two would have said something else.

Each method’s own authors published an error, and the errors are large relative to the differences people care about. Kline and colleagues derived the Rockport equation on 174 adults aged 30 to 69 and cross-validated it on a further 169, reporting a multiple R of 0.93 and a standard error of estimate of 0.325 L/min, which becomes 5.0 mL/kg/min once divided by body weight. Five units is about a sixth of a typical middle-aged value. Cooper reported a correlation of 0.897 on 115 US Air Force officers and airmen — and a correlation of 0.9 still leaves a fifth of the variance unexplained, which is why a strong correlation and a wide individual error sit together comfortably. Uth and colleagues gave the constant 15.3 and said plainly that it was derived on well-trained men aged 21 to 51 and may not be reliable in other subgroups. One validation deserves particular attention given who reads this site: in 88 sedentary male university students in Kolkata, the standard Cooper equation overestimated directly measured VO₂ max by a mean of 3.0 mL/kg/min with limits of agreement from 0.10 to 5.94 — it overestimated in every participant — and the authors proposed 21.01 × km − 11.04 for that population. This page computes both lines and prints the difference, in the same spirit in which the paediatric weight estimation page prints what happens when a formula derived in one population is applied in another.

The Rockport paper contradicts itself slightly, and the page shows that rather than smoothing it. The same 1987 article published two equations: one giving VO₂ max per kilogram directly, and one giving absolute uptake in litres per minute. Divide the absolute form by body weight and you do not get the per-kilogram form — for this page’s default inputs the two land about 0.2 mL/kg/min apart, and the gap grows at the extremes of weight. Both are printed, with the difference between them, because the inconsistency belongs to the source and a calculator that picked one silently would be hiding it. The same goes for the standard error: one technical report gives Kline’s figures as a 0.325 L/min standard error of estimate with R = 0.93 absolute and R = 0.88, SEE 5.0 mL/kg/min relative; a university teaching handout for the same equation says the prediction falls within 0.335 L/min, or ±4.4 mL/kg/min. Those are different numbers for the same thing. This page uses the 5.0 figure as the more conservative and records the disagreement.

There are no fitness categories on this page, and that is deliberate rather than a gap. The published reference data it uses is the HUNT3 Fitness Study: 3,816 healthy Norwegian adults aged 20 to 90, measured directly with gas analysis, published open-access under a Creative Commons Attribution licence. What that gives is a MEAN for each age group and sex, which is a fact. Turning a mean into a grade — excellent, good, poor — requires someone to choose where the lines go, and the choosing is a value judgement dressed as data. It also produces an output that reads as a verdict on a person, which this site does not do on measurements of bodies. The page therefore prints the mean for your age and sex, your distance from it in both directions, and the distance from it of the lowest and highest of your estimates, so you can see that the band frequently straddles the mean. The standard deviations in that study for the youngest group were 8.4 mL/kg/min for men and 7.7 for women — more than two decades’ worth of the mean column — so a perfectly healthy individual can sit two age brackets either side of their own average, and a label would be reporting noise as character.

What the number is actually good for. Three honest uses. Tracked over months, with the same test and the same conditions, the direction of change is far more reliable than the absolute value, because the systematic error of a given equation mostly cancels when you subtract one of its outputs from another. As a rough input to an exercise prescription, where it is used to set an intensity — and intensity set by heart rate carries its own separate problem, which the target heart rate zones page works through. And as a prompt: a field estimate well below what you expected is a reason to get a proper test if that matters to you, not a reason to conclude anything. Aerobic capacity is one of the better-studied predictors of long-term health outcomes, and it is also trainable at every age and from every starting point, which is the more useful fact about it. The strength-side counterpart on this site is the one-rep-max page, which has the same structure: several published equations, a large disagreement between them, and a maximal test nobody needs to perform. For the energy side, the energy requirement page compares five predictive equations for resting energy expenditure.

Before you do either field test. The 12-minute run is a maximal effort by design and the mile walk is not; that difference is the main reason to pick one over the other. If you have not been exercising, or you have heart or lung disease, uncontrolled high blood pressure, diabetes, a joint problem, or you are over about 40 and starting from a low base, the walk is the sensible choice and a conversation with a doctor before a maximal effort is the sensible first step. Stop either test for chest pain or pressure, disproportionate breathlessness, dizziness, feeling faint, or a pounding or irregular heartbeat, and get advice rather than a number.

Frequently asked questions

Which of the three methods should I trust?

None of them individually, which is why the page prints all three and the gap. If you have to pick one: the Rockport walk has the best-documented derivation and validation of the three and a stated standard error of 5.0 mL/kg/min, but only inside its 30-to-69 age range. Cooper’s test has a strong correlation (r = 0.897) on a young, fit, male military sample and is a reasonable choice if you can run hard for 12 minutes and pace it sensibly. Uth’s ratio is the weakest — one constant fitted in well-trained men aged 21 to 51 — and is best used as a free cross-check. If two of them agree, that is worth more than any one of them alone. If they disagree by 15% or more, the honest answer is that your VO₂ max is somewhere in that band and a field test cannot narrow it further.

Why not just average the three?

Because the average of three disagreeing estimates is not more accurate than the best of them, it only looks more confident. Averaging is only justified when the errors are independent and unbiased, and these are neither: Cooper’s equation has a documented systematic overestimate of about 3 mL/kg/min in at least one population, Rockport has documented systematic errors in opposite directions in different subgroups, and Uth’s constant is biased by construction outside well-trained men. Averaging a known overestimate with a known underestimate produces a number whose error you can no longer reason about. The page prints the midpoint of the band as one row among many, clearly labelled as a midpoint rather than an answer.

My watch gives me a VO2 max. How does it compare with this?

A wrist or chest-strap device typically estimates VO₂ max from the relationship between your running speed and your heart rate over many recorded sessions, which is a fourth method again and not one of the three here. It has one real advantage over this page: it has hundreds of data points on you rather than one, so its estimate is less at the mercy of a single bad day. It has the same fundamental limitation — it is a regression, not a measurement — plus two of its own: it depends on the device’s estimate of your maximum heart rate, and optical wrist sensors are unreliable at high intensity. Expect a device and this page to differ by several units and do not treat either as the arbiter.

Why does the page refuse a 12-minute distance under 1,000 metres?

Because Cooper’s equation is a straight line that crosses zero at about 505 m and goes negative below it, and a calculator that printed a negative oxygen uptake, or a plausible-looking small positive one just above the crossing, would be presenting arithmetic as a measurement. A distance of a few hundred metres in 12 minutes is also far outside anything the equation was fitted on — its sample was Air Force personnel — so there is nothing behind a number computed there. The walk test is the appropriate choice for anyone in that range, and the page says so instead of answering.

Why does the page refuse a mile walk time over 24 minutes?

Same reason, at the other equation. The Rockport walk-time coefficient is −3.2649 mL/kg/min per minute, which is steep enough to drive the estimate below zero: a 30-minute mile at an ordinary weight, age and heart rate returns a negative oxygen uptake. Rather than clamp that at zero, which would print a confident-looking floor, or at some invented minimum, the page refuses and says why. Twenty-four minutes for a mile is about 4 km/h, which is a slow walk; below that the test’s own premise — walk as briskly as you can — is no longer being met.

Is it normal for Cooper and Rockport to put me on opposite sides of the population mean?

It is common, and the worked table on this page shows it happening on the page’s own default inputs: Cooper puts a 40-year-old man 4.6 mL/kg/min below the published mean for his age and sex, Rockport puts the same man 3.5 above it. Both are using real test results from the same person. The explanation is simply that the two equations are reading different signals with different errors, and the published mean happens to lie between them. The useful conclusion is not which one is right but that a single field estimate is not precise enough to place anyone relative to a population mean, and that the placement should not be treated as information about health.

Does a low estimate here mean something is wrong with my heart or lungs?

No, and this page is not screening for anything. A field estimate is moved by how hard you were willing to push, how well you paced, the temperature, your sleep, your caffeine, how practised you are at the movement, your body weight (which is the denominator), and the error in the equation itself — before anything about the heart or lungs enters. If you have symptoms on exertion — chest pain or pressure, breathlessness out of proportion to the effort, dizziness, feeling faint, palpitations — those are the reason to see a doctor, and they are the reason whatever number this page produced. A cardiopulmonary exercise test is the investigation that actually answers the question, and it measures VO₂ max as a by-product.

Why is there no “excellent / good / poor” rating?

Because that rating would be a judgement about a person derived from an estimate with an error of 3 to 6 mL/kg/min, placed against a population whose own standard deviation is around 8. The page gives the published mean for your age and sex, the distance from it, and the distance from it of both ends of your estimate band — all facts — and leaves the adjective out. In practice the band frequently straddles the mean, which is the clearest demonstration that a one-word grade was never available from these inputs.

Should I link this to the oxygen extraction ratio page in the medical set?

No, and the page deliberately does not. The oxygen extraction ratio is the fraction of oxygen DELIVERED to the tissues that is actually taken up, computed from arterial and venous oxygen content in a clinical setting. It is a different quantity, with different inputs, answering a different question about a patient rather than about a person’s exercise capacity. The names overlap and the physiology does not, and a link between them would mislead rather than help.

Related calculators

References

Cooper KH. A means of assessing maximal oxygen intake. Correlation between field and treadmill testing. JAMA 1968;203(3):201–4. 115 US Air Force officers and airmen asked to cover as much distance as possible in 12 minutes, compared against treadmill-measured maximal oxygen uptake; the reported correlation between the two was 0.897. WHAT COULD NOT BE ESTABLISHED, and it matters because this page computes it: the linear equation universally attributed to this paper — VO₂max = 22.351 × km − 11.288, equivalently 35.971 × miles − 11.288 — could not be traced to the 1968 article in anything reachable from here, and the Cooper Institute’s own fiftieth-anniversary retrospective of the test reports the correlation and the protocol but does not print this regression either. A second form of the same line, (d − 504.9)/44.73 with d in metres, is also widely quoted and is a different rounding: it differs from the form used here by about 0.013 mL/kg/min at 2,400 m. The coefficients are consistent across every source consulted and are used for that reason, with the provenance recorded rather than asserted.
Bandyopadhyay A. Validity of Cooper’s 12-minute run test for estimation of maximum oxygen uptake in male university students. Biol Sport 2015;32(1):59–63. 88 sedentary male university students at the University of Calcutta, Kolkata, by simple random sampling — 58 in the study group and 30 in a confirmatory group. Directly measured VO₂ max 39.8 ± 4.0 mL/kg/min (range 33.5 to 47.7); Cooper-predicted 42.8 ± 4.0 (range 33.7 to 50.9); r = 0.93, p below 0.001. The standard equation OVERestimated by a mean of 3.0 mL/kg/min with limits of agreement from 0.10 to 5.94 — the lower limit being above zero means it overestimated in every participant. The author proposed Y = 21.01X − 11.04, with X in km, for this population, and this page computes that line alongside the standard one. This is the single most locally relevant validation available for the Cooper test on this site and is why the correction is printed rather than mentioned.
Kline GM, Porcari JP, Hintermeister R, Freedson PS, Ward A, McCarron RF, Ross J, Rippe JM. Estimation of VO2max from a one-mile track walk, gender, age, and body weight. Med Sci Sports Exerc 1987;19(3):253–9. The Rockport test. 174 subjects aged 30 to 69 in the validation sample and a further 169 of the same age range in cross-validation, 343 in total; the cross-validation results were reported as strikingly similar to the validation. Multiple R = 0.93 with a standard error of estimate of 0.325 L/min for the absolute equation, and R = 0.88 with a standard error of estimate of 5.0 mL/kg/min once adjusted for body weight. Both published equations are computed on this page. CONFLICT recorded rather than resolved: a university teaching handout for the same equation states that the predicted value falls within 0.335 L/min, or ±4.4 mL/kg/min, of the actual — different figures for both the absolute and the relative error. This page uses the 5.0 mL/kg/min figure as the more conservative of the two and prints the disagreement here. Independent validations summarised in the same source found inconsistent performance: overestimation in overweight women, underestimation in 70-to-79-year-olds, and correlations of 0.79 in young adult males against 0.62 in young adult females. The derivation figures above were read from a US Army Research Institute of Environmental Medicine technical report rather than from the 1987 article itself, which was not reachable from here.
Uth N, Sørensen H, Overgaard K, Pedersen PK. Estimation of VO2max from the ratio between HRmax and HRrest — the Heart Rate Ratio Method. Eur J Appl Physiol 2004;91(1):111–15. Source of VO₂max = 15.3 × HR_max/HR_rest. The authors cautioned that the conversion rule was based on measurements in well-trained men aged 21 to 51 only and may not be reliable when applied to other subgroups, and the constant 15.3 is given for well-trained men. WHAT COULD NOT BE ESTABLISHED: neither the sample size nor any correlation coefficient or standard error of estimate for this method could be obtained from any source reachable from here — the publisher’s page, the preprint repositories and the abstracting services were all either unavailable or rate-limited. This page therefore states the method’s derivation population and its proportionality to the heart rate ratio, and makes NO claim about its numerical accuracy. That absence is itself the reason the page calls it the weakest of the three.
Loe H, Rognmo Ø, Saltin B, Wisløff U. Aerobic capacity reference data in 3816 healthy men and women 20–90 years. PLoS One 2013;8(5):e64319. Open access under the Creative Commons Attribution licence, which is why this is the one reference table reproduced on this page. 3,816 healthy Norwegian participants, VO₂ max measured directly during treadmill running with gas analysis, tests terminated at exhaustion or at a plateau defined as VO₂ not increasing by more than 2 mL/kg/min despite increased workload. Verified figures: men aged 20 to 29 averaged 54.4 ± 8.4 mL/kg/min and women of the same age 43.0 ± 7.7, with aerobic capacity declining about 3.5 mL/kg/min per decade; the overall study means were 44 mL/kg/min for men and 35 for women. The per-decade figures in this page’s table are the whole-number means tabulated from this study by the authors’ own research group at NTNU. PROVENANCE NOTE: the full Table 2 of the article could not be transcribed reliably from the material reachable here — two readings of the article returned inconsistent per-group figures and the second reading reported the table itself as not visible — so the page prints the research group’s rounded whole-number means, which agree with the two cell values verified from the abstract, and does NOT print the per-decade standard deviations, which could not be verified at all.
Tanaka H, Monahan KD, Seals DR. Age-predicted maximal heart rate revisited. J Am Coll Cardiol 2001;37(1):153–6. Used on this page for one purpose only: to supply a maximum heart rate for the Uth method when the reader has not measured one. 208 − 0.7 × age, from a meta-analysis of 351 studies covering 18,712 subjects and a laboratory study of 514 subjects aged 18 to 81 in which the standard deviation around the regression line was about 10 beats a minute. That ±10 beats is why a predicted maximum is flagged on this page as adding roughly 2.8 mL/kg/min of error to the Uth estimate at a resting rate of 55. The target heart rate zones page works through that equation and four competitors in full.
Shookster D, Lindsey B, Cortes N, Martin J. Accuracy of 5 common age-predicted maximal heart rate equations. Int J Exerc Sci 2020;13(7):1242–50. Cited here only as the source of the statement that an age-predicted maximum heart rate agrees poorly with a measured one: across 99 graded treadmill tests the Bland–Altman limits of agreement for 220 − age ran from −23.11 to +22.80 beats a minute, and the standard deviation usually quoted for that equation is 10 to 12 beats. Relevant to this page because the Uth estimate is proportional to the maximum heart rate it is given.
The Cooper Institute. 50 years of the Cooper 12-minute run. Cited for the composition of Cooper’s 1968 sample — 115 US Air Force officers and airmen — and for the correlation of 0.897, both of which it states, and for the fact that it does NOT print the regression equation attributed to that study, which is part of the provenance note above.
LICENSING POSITION taken for this page, recorded because it determined what the page contains. The three prediction equations are regressions published in journal articles: arithmetic statements, used freely, with their coefficients and units reproduced exactly as published because changing them would be worse than quoting them. The reference table of population means is reproduced because Loe et al. 2013 is published under a Creative Commons Attribution licence, which permits reproduction with credit, and credit is given in full. No percentile table from a commercial, subscription or registry source is reproduced anywhere here — in particular no fitness classification table from a textbook or a professional body — and no fitness category or grade is assigned at all, which disposes of the licensing question and the editorial one in the same move. No guidance from the UK national institute is used, because its open content licence is United Kingdom-only and forbids display beside advertising, and this site carries advertising. No World Health Organization material is used or reached through a republisher, because WHO publications are licensed non-commercially and copyright is not laundered by passing through a third party. The Bandyopadhyay and Shookster figures are measurements reproduced with attribution from open-access articles.
Derivations and checks performed for this page rather than taken from a source, recorded so they can be checked. (1) On this page’s default inputs — a 40-year-old man, 75 kg, 2,400 m in 12 minutes, a 13.0 minute mile walk ending at 115 bpm, resting rate 55, no measured maximum — Cooper gives 42.35, Rockport 50.50 and Uth 50.07 mL/kg/min: a spread of 8.15 units, or 19.2% of the lowest. The published mean for that age and sex is 47, so Cooper places him 4.6 below it and Rockport 3.5 above it. (2) Cooper’s line reaches zero at 505.0 m and is negative below that, which is the reason for the 1,000 m floor. (3) The Rockport per-kg equation reaches zero at a mile walk time of about 29 to 30 minutes for ordinary inputs, which is the reason for the 24 minute ceiling; at the default weight, age, sex and walk heart rate it gives 14.6 mL/kg/min at 24 minutes and −1.1 at 30. (4) The paper’s two published forms disagree: dividing the absolute equation by body weight gives 50.70 against the per-kg equation’s 50.50 at the defaults, a gap of 0.20 mL/kg/min that widens at the extremes of weight. (5) Cooper’s line is steep in practical terms: 400 m of 12-minute distance is worth 8.94 mL/kg/min, more than the gap between two adjacent decades of the published means. (6) Sensitivity at the defaults, computed by the same engine: the Rockport sex term moves its answer by 6.315 mL/kg/min, 1 kg of body weight by 0.170, 30 seconds of walk time by 1.63, and 6 bpm of walk heart rate by 0.94; a 5 bpm error in resting heart rate moves the Uth answer by about 4 mL/kg/min at a resting rate near 55, and a 10 bpm error in a predicted maximum by about 2.8. (7) Every figure in this page’s worked example and in its three computed tables was produced by the same engine that answers the calculator.

CalcEngines health calculators are for education and for checking arithmetic that has already been decided elsewhere. They are not medical advice, they do not decide what to give, and they do not replace the judgement of a doctor, nurse, midwife or dietitian who knows the person in front of them. Every figure depends on the values you enter and on the assumptions stated on the page — check it against the prescription, the product label and your local policy before acting on it.