# Do You Trust The Body Mass Index? Here’s Why You Shouldn’t

What’s Wrong With The BMI And Why Your Doctors Shouldn’t Be Using It

Most of us have heard of the BMI. Many of us have been told at some point that we’re overweight or underweight, maybe even “OBESE” according to the BMI scale. And many of us have questioned this as the results can often seem unfair. Well, the theory behind the BMI is fairly logical and based on mathematical principles of proportion. The only problem with it is the fact that when they came up with the equation (BMI = Weight/Height²) they made a mathematical error.

So let me outline what the BMI is and the principles behind it. For those of you who haven’t heard of it, it stands for BODY MASS INDEX and is a system used to provide weight guidelines for humans. It’s based on the simple principle that if someone is taller than you, they should weigh* more than you. More specifically, if someone of a similar shape to you is taller than you, they must be wider than you. I’ve put a couple of diagrams below to show you what I mean by this.

Here are Dave and Pete, two men of exact size and proportion. Assuming they are both made of the same material, they both have the same BMI (because their proportions are identical) and both weigh exactly the same (because they are the same height and width).

Now let’s assume Pete has doubled in size. He still has the same proportions as Dave as he has doubled in width as well. Proportionally they are still the same shape and due to this their BMIs will remain the same.

In this diagram Pete is the same height but half the width of Dave. He is now a skinny version of Dave and his BMI will have lowered accordingly. This principle can be explained using simple mathematics. If we simplify our diagram and use squares instead of stick men we can manipulate the equation and see the results.

Square 1 and square 2 are the same shape. They are both of the same proportions which means they should have the same BMI. To check this we can give them some metrics. If each square is 1 metre tall and weighs 1kg we get the following:

BMI = 1kg/1m²

BMI = 1/1 x 1

BMI = 1

Here, square 1 is half the height of square 2 and half the width. So assuming that the BMIs are the same because they are proportionally the same size we should be able to use the BMI to find the weight of cube 1.

Remember BMI = Weight/Height² and we know the squares have a BMI of 1

So….

1 = Weight/0.5²

If we manipulate the equation we get the following:

Weight = BMI x Height²

Or…

Weight = 1 x 0.5²

Or…

Weight = 0.25kg

So although square 1 is now half the height of square 2 it weighs just a quarter of the amount. This makes sense because square 2 is essentially 4 times the size of square 1. See diagram:

So based on the principles of the BMI, if I have the perfect BMI and my friend who is 10% taller than me also has the perfect BMI he will be 10% wider than me as well, but not necessarily 10% heavier.

Here lies the problem

This is all very well but humans are not two dimensional. In reality if one were to double in height, they should also double in width AND breadth (or depth). The equation BMI = Weight/Height² works for two dimensional objects, but not for 3 dimensional objects. To incorporate 3 dimensions we must use cubes instead of squares and the equation must use a “cubed” sign instead of a “squared” sign. If we replace the ² with a ³ we get a completely different result. Height² literally means Height X Height. Height³ means Height X Height X Height, which is a very different number. I can explain this using the cubes below.

These cubes should all have the same BMI as they are all proportionally the same as each other. They are just bigger versions of each other. None of them are skinny, none of them are fat, they are simply bigger or smaller than their counterparts. But their weights are different. If we assume the smallest cube weighs 1kg then it looks like the second should weigh 8kg (because it is made up of 8 smaller cubes), not 2kg (because it is twice the height) or 4kg which is what the BMI  would suggest. Using the same logic the third will be 27kg and the fourth 64kg. They should have the same BMI but they don’t because the BMI equation is wrong. Try working it out yourself. But if we use this equation instead: BMI = Weight/Height³ you will find that they do all have the same BMI.

Let’s try it. Assume each little cube is 1metre high and weighs 1kg

Cube 1

BMI = 1kg/1m³

BMI = 1

Cube 2

BMI = 8kg/2m³

BMI = 1

Cube 3

BMI = 27kg/3³

BMI = 1

Cube 4

BMI = 64kg/4³

BMI = 1

So why has nobody noticed this before? Well they have, and they’ve called it the “Ponderal Index”, ponderal meaning “estimated or ascertained by weight”. The question is, why hasn’t the medical profession changed its system to use the Ponderal Index? It’s a fairly simple principle. I worked it out on my own in a single evening! (before I googled it to discover that many others had already done the work before me)

What are the consequences of the flaw in the BMI?

The use of the wrong formula means inaccuracies in readings the further we deviate from the average, the average being those heights used when the studies were first carried out. By memory I think it is 5’8″ (1.77m) for guys and 5’4″ (1.63m) for girls. People taller than the average will find that their BMI readings are very unforgiving and very tall people will almost always be overweight according to the BMI. For short people the opposite occurs and you’re able to be fairly overweight whilst being perfectly fine according to the BMI.

Is The Ponderal Index The Perfect Solution?

No, but it’s a far better solution than the BMI. There is still the fact that both of these scales don’t differentiate between fat and muscle, and there could be a pretty heavy muscular guy with virtually no body fat, who has the same PI or BMI as an unfit slightly chubby guy of a similar height.

What Is A Good Ponderal Index?

Using the BMI as a reference, below are the equivalent ranges** on the Ponderal Index:

Now if we use me as an example, at 1.85m tall I have a “healthy” PI range from around 70-95kg. My weight usually fluctuates between 83-90kg so as someone who considers himself “healthy” I would say that the estimates on the PI are fairly accurate. However, if I were to use the BMI it would suggest my “healthy” range is from 64-85kg. As a “not overly muscular” guy with a six pack at 89kg I’d say this is a good case to suggest that the BMI is fairly rubbish. On the BMI scale I’m 26 which would put me in the “overweight” category. Really? Don’t make me post any more photos of me with my shirt off.

Have a go yourself. If you’ve used BMI before and you’re short, you’ll get a nasty shock. If you’re tall you may be pleasantly surprised.

*I’ve used the terms “weigh” and “weight” instead of the scientifically correct term “mass” for the benefit of the reader as these are the terms which the general public tend to use on a day to day basis.

**I couldn’t find these records online so I used the BMI Study’s average height of 1.7m to retrospectively convert the BMI scale into PI by factoring the two equations to come up with the following equation:

BMI = PI x Height