# Body mass index miscalculation

For the first time in my life, to my horror, I noticed I had developed a spare tyre, so I put myself on a diet to get rid of it. It was a very simple diet: eat less. I lost 7 kg in three weeks and I looked trim. Bouncing triumphantly off the scales one morning, I decided to check my body mass index (BMI). To my great surprise, with a BMI of 24.1, I was at the high end of ‘normal’, defined as between 18.5 and 24.9. The charts told me I could lose another 20 kg and still be normal, but that would leave me skin and bones.

It naturally got me wondering: how scientific is the body mass index (BMI)?

It may be a 188-year-old staple of health statistics, but modern health professionals have documented many flaws. For starters, the BMI doesn’t distinguish whether body weight comes from fat or muscle, so Michelin Man and the Terminator might have the same BMI despite their very obvious differences in fat and muscle distribution. Neither does it factor in other key health criteria such as age, gender or body type. For instance, people who deposit fat around their waists are at a higher risk of disease than people who deposit it on their hips and thighs.

My concern, however, is that the BMI ignores elementary physics.

The problem traces back to Lambert Adolphe Jacques Quetelet, the Belgian statistician who invented the BMI in 1830. Quetelet failed to consider the mathematics of scaling. He defined the body mass index as weight divided by height squared. Note, however, that weight is proportional to volume, which is proportional to height cubed. The upshot of this is that, all other things being equal, BMI varies directly with height, which it clearly should not. (See formula below.)

Perhaps the fault goes back to Jonathan Swift’s wildly popular 1726 tale of Gulliver’s Travels. Swift’s giant Brobdingnagians and tiny Lilliputians could not actually exist.

For example, consider a giant twice as tall as myself but with exactly my shape and looks. If the giant was standing on a beach with no other objects in sight, a far-off observer could not tell that he was not me. Because his mass would be proportional to my height cubed, my double-height doppelganger would weigh eight times more than me. However, the cross-sectional area of his legs would be proportional to my height squared, so they would be only four times stronger. Those poor bones! They would be over-stressed by carrying eight times the weight. My giant double would collapse under his own weight. Now create a version of me half my height. He would weigh one-eighth of what I weigh, but his leg bones and muscles would be twice as strong as they needed to be.

Nature understands this, which is why elephants look like elephants and ants like ants. The BMI formula does not share this insight. It can make tall people appear overweight when they are not. Compared with a 152 cm (five foot) individual with a ‘normal’ BMI of 22, an identically proportioned 183 cm (six foot) person would have a BMI of 26.5 – overweight.

Based on BMI ranges, most Australians are too plump: 28% are classified as obese, 35% overweight, 35% normal and a mere 2% underweight. No doubt this skewing towards being overweight reflects a genuine health problem. But it might be affected by the increase in the average height of the population since 1830.

Fortunately for Quetelet, there were few Terminators back then to question his BMI. And fortunately for Jonathan Swift his satire was not questioned by an incurable engineer who would have pointed out that the Brobdingnagian giants, at 12 times the height of Gulliver, would have weighed more than 100 tonnes, with a BMI in the hundreds.

I don’t suggest changing the way the BMI is calculated, despite its flaws, because we would not want to throw out the past 188 years of BMI records (noting that in most cases the raw data – height and weight – will not have been kept). Instead, we could adjust the standard BMI numerical ranges for underweight, normal weight, overweight and obese based on height, and perhaps even gender and body shape.

Then your quite trim incurable engineer could relax instead of dieting himself to skin and bones.