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.
"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/height2.5. Certainly if you plot typical weights of people against their heights, the result comes out closer to height2.5 than height2."
As the fight against obesity becomes an ever more urgent issue, health professionals disagree about the best way to measure it.
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."
"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.
Even Adolphe Quételet, who invented the BMI formula, warned of its limitations
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)."
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
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
Usain Bolt, the fastest sprinter ever. His BMI would class him as overweight, which he is clearly not.
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
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.
"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
Copyright: Medical News Today
Not to be reproduced without permission of Medical News Today
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Visitor Opinions (latest shown first)
I am Not overweight
posted by Ariel on 18 May 2013 at 1:08 pm
I am 5'4 and I weigh 130 pounds, I checked my BMI, and it was 23, the healthy range. My doctor said I was a little over weight, and that I should exercise more, I WORK OUT DAILY AND RUN, I am in track and I'm a varsity distance runner, so I run about 5-8 miles a day. And I do daily work outs, I didn't lose any weigh! But I am noticing that my waist I'd getting smaller and my stomach is becoming more firmer. So I just think I am getting muscles and my doctor thinks I'm over weight! Ha! Probably because when I was younger, I did dance and was small, like in pounds, and after I stopped dance, I was gaining weight rapidly and now I'm trying to lose weight again but I'm gaining muscles. My goal is to be 110!!! Hopefully /:
posted by nicholas paschalis on 13 Mar 2013 at 10:17 am
Back in the early 80's @ McGill University we discussed the value of the BMI and concluded that the BMI method of assessment was flawed. I will not use the BMI in my course of study for phys ed student, rather, I will conduct skinfold test at multiple sites to determine one's percentage body fat and compare them to norm-refenced groups.
I agree BMI is flawed, anything that relies on 1 number would be flawed. The correct "equation" would be something that takes in body composition, BMI, waist line, age & gender, but you would not likely be able to plug this into a calculator. In reality, BMI sort of works if you really are overweight/obese, average height and do not exercise. If you already try to be healthy (i.e. exercise and are not obese) then you will need to look into better methods if you want trackable numbers.
That said, I find 2 things wrong with the alternate BMI formula by Trefethen, the first issue is that it must be copied wrong (I would hope...) since it is invalid as written and does not balance.
BMI = 1.3*weight(kg)/height(cm)^2.5 = 5734*weight(lb)/height(in)^2.5 This is wrong because for the metric side to be equal the coefficient would have to be 130000 not 1.3 or it would have to be in kg/m^2.5 not kg/cm^2.5
in > m = 0.0254 in > cm = 2.54 m > in = (1 / 0.0254) cm >> in = (1 / 2.54)
lbs >> kg ~ 0.45359237 kg >> lbs ~ 2.20462262
So: lbs/in^2.5 >> kg/m^2.5 ~ (0.45359237 / 0.0254^2.5) ~ 4411.45
1.3 * 4411.45 = 5734.885... So altogether it should be: BMI = 1.3*weight(kg)/height(m)^2.5 = 5734.9*weight(lb)/height(in)^2.5
The second issue is the basis of Quetelet's Treatise being the basis for a 2.5 exponent. kg^2/m^5 is absolutely not the same as kg/m^2.5, it would not even scale similarly.
Additionally, the except from Quetelet's Treatise is describing the relationship/correlation between a change in height to a change in weight "during development" stages ONLY. This means ONLY during growth, i.e. while still growing, and only how the change in height (on average) effects a change in weight. As an example: growing 2in (in the last growth stage) would increase weight by about 5.66 lbs. (in^5=lbs^2)
The excerpt could be abstracted to give an average weight at a given height (for ages 1 - 25) but it really is not about obesity (just the you comment Goriely on saying) or body mass, just how growing effects weight statistically.
As a concept for population statistics BMI is not a flawed calculation, whichever equation variant it is calculated on. What is flawed is the method in which it is applied and the total lack of understanding about the underlying statistics.
Ultimately, like every model, it is a simplified representation of reality based on a population group, not an individual and this is where it all goes wrong. The practitioner that applies it to an individual as a stand alone measurement without identifying the parameters of the population that the individual is a member is already failing. But we (the human race) do suffer an issue in that we fail to understand uncertainty and always approach from a deterministic standpoint, hence hard lines and defined trends, thus we have difficulty applying 'blurring' to the boundaries and will commonly always pick one that applies to us individually and stick to it.
Or to apply this another way, 15 years ago I was a serious mountaineer and outdoors man, lots of upper body muscle mass for hanging from cliff faces, BMI over 32, yet the exercise regime I was on and proved to the medical profession showed that actually this wasn't as bad as it sounds. Role on 15 years and less exercise and muscle becomes body fat, yet the BMI remained the same....I had an issue. Which shows without understanding the individual in the population then BMI as per the usual guidelines may not apply, I was fortunate that most medical professionals I encountered understood this....
Not saying it's perfect, but what do you recommend instead?
With DEXA you have radiation concerns, even if it's .1 percent of that in a normal X-Ray, you still have people complaining. Water displacement tests? Well very few offices have pools, but that might work if you can convince your patients to bring swim gear and pay for the costs. There is BIA which more or less fluctuates with hydration levels than body fat, sending incorrect measurements. After that things get expensive and up the costs of healthcare.
The point is to have a cost-effective formula that can easily be computed in a office and still allow for a general idea of health and weight of a patient.
Argued this for years!!! Doc always told me that its a guideline but I asked for whom...
I am 5'4", 149 lbs and less than 20% bodyfat, I was told I was too fat. I needed to lose about 25lbs. I asked him based upon a formula that is way too old to be realistic...please! Then came the life insurance folks and they too started questioning this when they saw how fit I was...this is a definite flawed formula but if the numbers pan out with the adjustments, I might reconsider this!
The BMI gives us a number. If the number correlates with disease mortality and morbidity then it has value. I do wish that the boundaries between the categories were more blurred rather than being so rigid.
This is important because insurance and other BMI number based decisions need some flexibility if people are to get the best out of the measurement.
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