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VO₂ Max (Cooper)

Aerobic fitness from a 12-minute run distance (metres).

Formula

VO2=d−504.944.73VO_2 = \frac{d - 504.9}{44.73}

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Variables

dDistance in 12 min (m)

Example

2400 m ⇒ 42.4

How it works

This equation estimates VO₂ max, an athlete’s maximal aerobic capacity, from how far they can run in 12 minutes. It comes from Cooper’s field test, which was calibrated by comparing 12-minute run distances with laboratory measurements of oxygen uptake; the constants in the formula convert distance into an estimated mL/kg/min value. Because it is based on a submaximal-to-maximal endurance performance, it gives a practical estimate rather than a direct physiological measurement.

When to use it

Use this when you want a quick estimate of aerobic fitness from a 12-minute run test, especially in sports science, PE classes, or personal training settings. It is useful for comparing fitness over time or between athletes when lab equipment for direct VO₂ measurement is not available.

Worked example, step by step

Suppose an athlete runs 2600 m in 12 minutes. Step 1: Substitute into the formula: VO_2 = (d - 504.9) / 44.73 Step 2: VO_2 = (2600 - 504.9) / 44.73 Step 3: VO_2 = 2095.1 / 44.73 Step 4: VO_2 ≈ 46.8 Final answer: estimated VO₂ max ≈ 46.8 mL/kg/min

Common mistakes to avoid

  • Using kilometres instead of metres for d
  • Forgetting that this is an estimate from a 12-minute test, not a direct lab measurement
  • Rounding too early and losing accuracy in the final VO₂ value

Did You Know?

Elite endurance athletes have VO₂ max values roughly double those of untrained adults.

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Reviewed & maintained by the FormulaWon editorial teamLast reviewed September 2026