New BMI (New Body Mass Index)

BMI (Body Mass Index)

Calculate your "New BMI"

In its 5 January 2013 issue the Economist published this letter from me:


Nick Trefethen
Professor of numerical analysis
University of Oxford

The appearance of this admittedly strongly worded letter has led to communications from many people around the world, and I would like to explain a formula that I think would be worth considering as an alternative.

Current formula: BMI = weight(kg)/height(m)^2 = 703*weight(lb)/height(in)^2.


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

The numbers 1.3 and 5734 are designed make the BMI reading unchanged for an adult of average height, which I take to be about 66.5 inches, i.e., 1.69 meters. (The square root of 1.69 is 1.3.) To find your "New BMI", try the New BMI Calculator written by Nick Hale.

Are these numbers "right"? No! -- for human beings are complicated, and any BMI formula will deliver just one number. No single number can be right, and indeed, the extreme reliance of today's medical and insurance establishments on a simple formula worries me a great deal. But perhaps this revised formula might reflect better than the standard one how the weights of healthy adults really depend on their heights.

Would it make a difference? Yes indeed. Roughly speaking, each person 6 feet tall would lose a point from their BMI reading, and each person 5 feet tall would gain a point. That's millions of people. If the new numbers gave a more accurate indication of actual health issues, this could be a significant change for the better.

What about the density of muscle vs. fat? We hear about this frequently in discussions of BMI (including in the Economist article I was responding to, which mentioned Olympic weight lifters), but it's a smaller effect. Muscle is about 18% denser than fat. This means that if you heroically exercised so much that you converted 10% of your body volume from fat to muscle (wow!), your BMI reading would go up just 1.8%. That's much less than the corrections just mentioned for short or tall people.

What about men vs. women? This is a fascinating question. On average women are about 8% shorter then men, and it follows that if we switched from current BMI to new BMI, a typical woman's reading would go up 2% and a typical man's reading would go down 2%. That may sound small, but it's around half a BMI point, so it would carry many people across the normal/overweight or overweight/obese boundaries (25 and 30, respectively). Sometimes it is said that women can get away with higher BMI readings than men before suffering the health effects of obesity. If true, is this partly an anomaly caused by the current definition of BMI? I don't know.

I must finish by emphasizing that I am an applied mathematician, not a doctor or an epidemiologist. The new formulas proposed above are not based on epidemiological studies and they may not be a improvement, for all kinds of reasons. To get a sense of the complexity of the BMI issue, a good place to start is the Wikipedia article on the subject, and for a key epidemiological paper supporting the use of the exponent 2.0, see S. B. Heymsfield et al., American Journal of Clinical Nutrition, 2007. Obesity will be one of the biggest health issues worldwide of the 21st century. If great reliance is going to be placed on a single formula for assessing it, the justification of that formula deserves careful discussion.


[Prof. Alain Goriely of Oxford has contributed the following fascinating remarks. It seems the inventor of the BMI formula himself mentioned the exponent 2.5!]

The BMI was first discussed by Quetelet, the first Belgian scientist (he published his research on the weight of men at different ages in 1832, 2 years after the creation of Belgium, so indeed the first one).

The BMI was known for many years as the Quetelet Index until it was renamed the BMI by the American Ancel Keys. But Quetelet himself was well aware of the [complexity of the] choice of scaling. Here is a quote from his book "A Treatise on Man and the Development of his Faculties", 1842:


[In the next paragraph, however, Quetelet does indeed suggest the exponent 2 for fully grown adults.]

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