Cooper test to VO₂max: formula and table

The formula

For a 12-minute run, Cooper’s equation is:

VO₂max = (distance in metres − 504.9) ÷ 44.73

The result is in ml of oxygen per kilogram of body weight per minute. Distance is the total covered in exactly 12 minutes, including the last partial lap.

Worked example: you cover 2,650 m. 2,650 − 504.9 = 2,145.1. Divided by 44.73, that is 47.96, so a VO₂max of about 48.0.

The table

Distance in 12 min	Average speed	VO₂max
1,600 m	8 km/h	24.5
1,800 m	9 km/h	29.0
2,000 m	10 km/h	33.4
2,200 m	11 km/h	37.9
2,400 m	12 km/h	42.4
2,600 m	13 km/h	46.8
2,800 m	14 km/h	51.3
3,000 m	15 km/h	55.8
3,200 m	16 km/h	60.3
3,400 m	17 km/h	64.7

The speed column is the distance divided by 200. The VO₂max column comes from Cooper’s equation, rounded to one decimal.

From a target VO₂max to a distance

Reverse the equation: distance = 44.73 × VO₂max + 504.9.

Target VO₂max	Distance needed in 12 min
30	1,847 m
40	2,294 m
50	2,741 m
60	3,189 m

Each point of VO₂max is worth about 45 m.

What the number is, and is not

The equation comes from a study published in 1968. Cooper compared the distance run in 12 minutes with VO₂max measured on a treadmill, and found the two strongly correlated in US Air Force men. The formula is a fit to that group.

Three consequences follow.

• It is an estimate. Two people with the same distance can have different measured VO₂max values.
• It assumes a maximal, even effort. A runner who walked for two minutes, or who started too fast, will get a number that says nothing about their capacity.
• It was fitted on men. Nothing on this page claims it fits women, children or older adults equally well.

A second model

Cadlo also computes VO₂max from a timed run with the Daniels and Gilbert model, which starts from speed and duration. For 2,400 m it gives 36.3, against 42.4 from Cooper’s equation. The gap is large, which is a reason to use one method consistently and not to compare a number from one calculator with a number from another.

Comparing with a beep test

A VO₂max from a Cooper run and one from a beep test come from two equations built on two groups, and they will not match exactly. For the beep test method, see Beep test score to VO₂max. To place a result on the same scale, use the VO₂max calculator and treat gaps of a few points as noise.

For your own tracking, the better comparison is your own earlier Cooper. Run it again after four to six weeks, on the same course, at the same time of day. The Cooper calculator turns any distance into speed, MAS and VO₂max, and the test is described on the Cooper test page.