BMI: is the body mass index formula flawed?

BMI (Body Mass Index) has been used for over 100 years in population studies, by doctors, personal trainers, and other health care professionals, when deciding whether their patients are overweight. However, BMI has one important flaw - it does not measure your overall fat or lean tissue (muscle) content.

Body Mass Index, derived from a simple math formula, was devised in the 1830s by Lambert Adolphe Jacques Quetelet (1796-1874), a Belgian astronomer, mathematician, statistician and sociologist. BMI is said to estimate how fat you are by dividing your weight in kilograms by your height in meters squared. However, as mentioned earlier, the measurement is flawed, especially if the person carries a lot of muscle.

Nick Trefethen, Professor of Numerical Analysis at Oxford University's Mathematical Institute, wrote in a letter to The Economist that the BMI formula is flawed and is only a rough guide to helping people judge whether they have a healthy weight.

Trefethen said:

"If all three dimensions of a human being scaled equally as they grew, then a formula of the form weight/height³ would be appropriate. They don't! However, weight/height² is not realistic either.

A better approximation to a complex reality, which is the reform I wish could be adopted, would be weight/height^2.5. Certainly if you plot typical weights of people against their heights, the result comes out closer to height^2.5 than height²."

The current BMI formula leads to confusion and misinformation, Trefethen believes. The height² term divides the weight by too much when people are short, and by too little when they are tall. The result is short people being told they are thinner than they really are, while tall people are made to think that they are fatter than they are.

When Quetelet devised the BMI formula, there were no computers, calculators or electronic devices, so he opted for a very simple system. Trefethen does wonder, though, why institutions today on both sides of the Atlantic continue using the same flawed formula.

Perhaps "nobody wants to rock the boat", Trefethen suggested. Various agencies and institutions have agreed on something, which is comforting.

There are probably other flawed formulae out there. There seems to be an exaggerated respect for measures which depend on mathematics. However, the BMI one probably beats them all, especially as the world population of obese people exceeds one billion.

Trefethen Offers an Alternative Formula to the Current BMI one

Trefethen said "Suppose we changed that exponent from 2.0 to 2.5 and adjusted the constant so that an average-height person did not change in BMI. Suddenly millions of people of height around 5' (five feet tall) would gain a point in their readings, and millions of people of height around 6' (six feet tall) would lose a point."

He proposes a new formula where:

BMI = 1.3*weight(kg)/height(m)^2.5 = 5734*weight(lb)/height(in)^2.5.

"In our overweight world, such changes would distress some short people and please some tall people, but the number they'd be using would be closer to the truth and good information must surely be good for health in the long run," Trefethen said.

Quetelet would probably have viewed using the 2.5 exponent favorably, said Alain Goriely, a professor of Mathematical Modelling at Oxford University's Mathematical Institute. Apparently, Quetelet wrote in a Treatise on man and the Development of his Faculties in 1842:

"If man increased equally in all dimensions, his weight at different ages would be as the cube of his height. Now, this is not what we really observe. The increase of weight is slower, except during the first year after birth; then the proportion we have just pointed out is pretty regularly observed.

But after this period, and until near the age of puberty, weight increases nearly as the square of the height. The development of weight again becomes very rapid at puberty, and almost stops after the twenty-fifth year. In general, we do not err much when we assume that during development the squares of the weight at different ages are as the fifth powers of the height; which naturally leads to this conclusion, in supporting the specific gravity constant, that the transverse growth of man is less than the vertical.

Goriely commented: "So according to Quetelet the scaling is 3 for babies (babies are spheres), 2 for kids (kids grow more like celery sticks, as we know), then 5/2=2.5 for grownups (beefing up so to speak). It seems Quetelet never cared about obesity (not a big issue in the 1840's)."

Many say that waist-to-height ratio is a better measurement than BMI. They say you should keep your waist circumference to less than half your height.

An Example of Where Body Mass Index (BMI) is Flawed

Imagine you were asked to advise two men on their bodyweight:

• The couch potato
  He is 1.83 meters tall (6 feet tall), never does any exercise, and weighs 92 kilograms (203 lbs).
  His BMI is 27
• The athlete
  He is an Olympic champion 100-meter sprinter, 1.83 meters tall (6 feet tall), does an incredible amount of exercise, and weighs 96 kilograms (211 lbs)
  His BMI is 28

If you used just the BMI formula, you would tell the athlete that he is fatter than the couch potato - which is obviously completely wrong. This is because BMI does not calculate how much fat or lean tissue (muscle) your body carries.

Clearly, the athlete is not overweight, and the couch potato is. This is because the athlete is much more muscle-bound than the couch potato - muscle weighs more than fat.

According to most criteria accepted around the world:

• A BMI of 18.5 to 24.99 means you are of normal weight
• A BMI of 25 to 29.99 means you are overweight
• A BMI of 30+ means you are obese

If you want to find out what your BMI is, use our BMI Calculator.

So, What is My Ideal Healthy Weight?

We would all love to be told clearly how much we should weigh and how to calculate this ourselves. Unfortunately, your ideal weight is not a black and white formula.

You cannot simply calculate your healthy weight from a general source - it depends on several factors, including your overall general health, height, muscle-fat-ratio, bone density, body type, sex, and age.

Working out your BMI may give people a rough idea of how much they should weigh, but as we have seen in this article, it really is a flawed formula. BMI is useful when studying large populations, but not for individuals.

BMI + Waist Measurements to Determine Body Weight Status

Researchers from the University of Toronto, and the Hospital for Sick Children in Ontario, reported in Archives of Pediatrics & Adolescent Medicine that BMI together with waist measurements are linked to lipid and blood pressure evaluations among teenagers who are overweight/obese.

"Waist measurements" means 1. Waist-to-height ratio, and 2. Waist circumference.

The researchers said what many health care professionals are saying today - that BMI alone cannot differentiate between fat and fat-free body mass. So, they have added waist measurements to the mix. However, unlike what the mathematicians from Oxford University have put forward, this is not a single mathematical formula.

Written by Christian Nordqvist