A new way of calculating Body Mass Index (BMI) has been proposed - but does it really solve any of the BMI's well-known problems?

How often have we heard that Brad Pitt at the time of Fight Club, and England rugby player Jonny Wilkinson in his prime, were "overweight" - according to their BMI?

Any system that tells people whether they are "normal", "underweight", "overweight" or "obese" is bound to be controversial, but one obvious weakness of the BMI is that it doesn't distinguish between fat and muscle.

First devised by Adolphe Quetelet more than 150 years ago, BMI is calculated by taking your weight (in kilograms) and dividing it by your height squared (in metres).

In simple terms, it is a way to compare the weights of groups of people of different heights.

Letter to the Economist 05/01/13 Sir, The body-mass index that you (and the National Health Service) count on to assess obesity is a bizarre measure... As a consequence of this ill-founded definition, millions of short people think they are thinner than they are, and millions of tall people think they are fatter. Prof Trefethen's letter in full (third in list) His explanation of his formula

But mathematician Nick Trefethen, Professor of Numerical Analysis at Oxford University, thinks that the old formula is wrong, as he explained in a letter to the Economist newspaper published earlier this month.

He thinks that people have put too much trust in it in part because it looks so precise - like, say, Einstein's famous equation E=MC².

"That's an equation of physics and it's really right. The BMI formula looks similar. It seems to have the same character but it doesn't reflect a precise truth about our world, it's an approximation to a very complicated reality," he told the BBC.

With that in mind he has proposed a new formula: 1.3 x weight, divided by height to the power 2.5.

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The change means that some tall people previously deemed "overweight" are "normal" under the new proposal, and some short people who were "normal" are now "overweight".

BMI can't do better than make a guess as to how much fat there is Tim Cole, University College London

But why did Prof Trefethen choose those numbers - 1.3 and 2.5?

"That can't be explained simply. People do scaling arguments to explain as an animal gets longer how, if its bones aren't to break, how much thicker the need to be and out of this kind of mathematical analysis come some rather complicated and unexpected results," he says.

"My fundamental interest is in the physics and mechanics of how bodies behave and there is a body of literature that suggest [the power] should be 2.5, or even two and two-thirds."

But Prof Trefethen stresses he doesn't have a medical background and that his work isn't based on real life observations of people's weight and height.

One man who does have a medical background is Tim Cole, Professor of Medical Statistics at University College London. He says Prof Trefethen's new equation is just one of a long line of papers that have questioned the equation, and he's not convinced it will change anything.

Evolution of an index Belgian mathematician Adolphe Quetelet noted in 1832 that "the weight increases as the square of the height" (though he sketched a formula similar to Prof Trefethen's in a later publication)

Quetelet had no interest in obesity - his goal was to define the "average man"

Actuaries began to study links between obesity and life insurance claims before World War I - the Quetelet Index came to be seen as a useful tool

It was re-christened the Body Mass Index in 1972, by Ancel Keys, an American scientist who studied the influence of diet on health

Categories such as "obese" or "overweight" were proposed by JS Garrow and JD Webster in 1980s BBC Health: Your weight Where are you on the global fat scale?

"I think he's aware of the deficiencies of BMI but I don't think his index goes anywhere to addressing those shortcomings. BMI is an imperfect index and you can tinker about with the power of height as much as you like but [the equation] shouldn't be expected to do what it can't do which is to measure fatness, because it doesn't include fatness," he says.

"BMI can't do better than make a guess as to how much fat there is. If your weight is excessive then the implication is that the excess is fat and, of course, people's body composition varies enormously and BMI doesn't know anything about that so it's a very imprecise index when applied to individuals."

So why do we continue to use it?

"It is useful when applied to populations. The population does mean you get a more precise estimate of BMI simply by averaging over large numbers."

It's been a controversial measure in part because of the way it is divided up into different weight categories. "Underweight" is a BMI under 18.5. "Normal" is between 18.5 and 25. Between 25 and 30 is "overweight" and above 30 is "obese". Some countries have moved the boundaries to better reflect their populations. In India for example anyone over 23 is "overweight" and over 25 is "obese".

The boundaries, were proposed in the mid-1980s by two scientists, Garrow and Webster, and just kind of stuck. But are they in the right place?

"They are to some extent based on health premises as understood by Garrow and Webster in 1985 when the world looked rather different, but also they are a statistical construct," says Prof Cole.

I don't think weight is synonymous with health Dr Katherine Flegal, US National Center for Health Statistics

Trying to draw a line somewhere on that spectrum and say below this cut-off is healthy, and above this cut-off is unhealthy, is obviously a rather arbitrary exercise.

The boundaries are the source of endless debate and a recent meta-study in the United States looking at 100 studies including three million people suggested that the people who were overweight had a slightly lower risk of early death than those in the normal category.

"I think the moral of this study is that these BMI categories are weight categories and they're not exact health categories," says Dr Katherine Flegal from the US National Center for Health Statistics who did the study.

"I don't think weight is synonymous with health and I think our study shows that at least it's not synonymous with mortality."

But are we likely to see a change to the way BMI is calculated or a move away from using it altogether?

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Prof Cole doesn't think so.

"It's a cheap and cheerful way of getting a handle on whether or not you might be overweight. The alternatives are rather more complicated and expensive.

"You can go for an MRI scan or a dexa scan and those will measure your whole body fat, but that really is using a sledgehammer to crack a nut… BMI does separate those people who are normal from those who are obese and there is some area of uncertainty in the middle."

If people hear from their doctor that their BMI has gone up or down, they can usually be fairly sure that the change in their weight is connected with a change in fat rather than muscle. It's therefore a "good and simple indicator" of whether someone is gaining or losing fat, he says.

So it looks like BMI is here to stay but it's worth remembering that, strictly speaking, it is a measure of your weight relative to your height, not fatness or how healthy you are.

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