Statistical
VO2 Max & Aerobic METs formulas: Cooper 12-Minute Run & Uth-Sorensen HR Ratio
Practice arithmetic for two indirect VO2max estimates using fictional data, and convert an estimate into conventional MET units.
Estimates are not laboratory measurements
These are spreadsheet exercises with fictional measurements, not a clinical fitness assessment or a recommendation to perform maximal exertion. Field estimates have individual error and population-specific limitations; they do not replace measured oxygen uptake.
The Cooper distance relationship uses meters covered in 12 minutes. The HR-ratio equation uses measured maximal and resting heart rates; the original 15.3 coefficient was studied in well-trained men and is not universal. Medication, illness, training status and measurement conditions can affect applicability.
Dividing by 3.5 expresses the estimate in conventional MET units. It does not measure a person's actual resting metabolism or prove safe exercise capacity. The numeric guards below reject impossible arithmetic inputs but do not validate a test protocol or clinical suitability.
| Cardio Fitness Metric | Formula / Inputs | Athlete Field Data | Calculated VO2max / METs |
|---|---|---|---|
| Cooper 12-Min Run (2,800 m) | (B2 - 504.9) / 44.73 | 7 laps on 400m track | 51.31 mL/(kg*min) |
| Peak Aerobic Capacity (METs) | Cooper_VO2max / 3.5 | 51.3101 / 3.5 | 14.66 METs |
| Uth-Sorensen HR Ratio | 15.3 * (B3 / B4) | HRmax = 188, HRrest = 60 bpm | 47.94 mL/(kg*min) |
| Hypothetical distance (3,400 m) | B2 set to 3,400 m | 8.5 track laps in 12 min | 64.72 mL/(kg*min) |
Cooper 12-Minute Run VO2max in mL/(kg*min)
B2 is a fictional 12-minute distance in meters. Values at or below 504.9 produce a nonpositive prediction and are reported as Outside estimate domain; that cutoff is algebraic, not a clinical validation threshold.
=IF(COUNT(B2)<>1,"Invalid inputs",IF(B2<=504.9,"Outside estimate domain",ROUND((B2 - 504.9) / 44.73, 2)))Uth-Sorensen Heart-Rate Ratio VO2max and Peak METs
Multiplies 15.3 by max-to-resting heart rate ratio B3 / B4.
=IF(COUNT(B3:B4)<>2,"Invalid inputs",IF(OR(B4<=0,B3<B4),"Invalid inputs",ROUND(15.3 * (B3 / B4), 2)))Express the Cooper estimate in conventional METs
Use the unrounded estimate before dividing by 3.5. This remains an indirect estimate.
=IF(COUNT(B2)<>1,"Invalid inputs",IF(B2<=504.9,"Outside estimate domain",ROUND(((B2 - 504.9) / 44.73) / 3.5, 2)))Try the example
Use the original values or change them to test your understanding.