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Body and fitness numbers

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BMI, maximum and target heart rate, body surface area and calories burned — with what each number cannot tell you.

Body Mass Index (BMI)

BMI=mh2\mathrm{BMI} = \frac{m}{h^2}

Body mass index: mass divided by the square of height, the population screening ratio defined by Quetelet in 1832.

Maximum Heart Rate from Age (220 − Age)

HRmax=220−a\mathrm{HR}_{max} = 220 - a

The 220-minus-age estimate of maximum heart rate in beats per minute, the rule of thumb printed on every gym treadmill.

Target Heart Rate (Karvonen Method)

THR=HRrest+I (HRmax−HRrest)\mathrm{THR} = \mathrm{HR}_{rest} + I\,(\mathrm{HR}_{max} - \mathrm{HR}_{rest})

Training heart rate at a chosen fraction of heart rate reserve, the range between resting and maximum rate.

Body Surface Area (Mosteller Formula)

BSA=hcm⋅mkg3600\mathrm{BSA} = \sqrt{\frac{h_{cm} \cdot m_{kg}}{3600}}

Body surface area in square metres by Mosteller's 1987 square-root simplification of the older exponential fits.

Body Surface Area (Du Bois Formula)

BSA=0.007184⋅hcm0.725⋅mkg0.425\mathrm{BSA} = 0.007184 \cdot h_{cm}^{0.725} \cdot m_{kg}^{0.425}

Body surface area by the 1916 Du Bois power fit, still the reference against which newer formulas are compared.

Calories Burned from MET, Mass and Time

E=MET⋅m⋅tE = \mathrm{MET} \cdot m \cdot t

Energy expended during an activity: one MET is defined as one kilocalorie per kilogram of body mass per hour.

How they fit together

These are the formulas behind the numbers on gym equipment and in clinical charts, and every one of them is a population average wearing the costume of a personal measurement. They are useful for tracking change in one person over time, and unreliable for judging any individual against a table.

BMI was devised in the 1830s to describe populations, not to diagnose people, and it cannot distinguish muscle from fat. 220 minus age for maximum heart rate is a line eyeballed through scattered data in 1971 with a standard deviation of 10 to 12 beats per minute, so a reading well outside your predicted zone is more likely normal variation than a problem. The Karvonen method improves on it by working from heart rate reserve, which at least accounts for resting fitness.

Body surface area is the one with real clinical weight, since chemotherapy and burn treatments are dosed by it. MET-based calorie burn is the loosest of the group: the tables are measured averages and tend to run generous, which is why fitness trackers flatter their wearers.