Monday, 8 February 2010

The problem with BMI.

According to my Body Mass Index, I'm just obese. The word "obese" conjures-up images of people with huge fat bellies waddling along. Sure I'm overweight as I love my food, but I don't have a huge fat belly and I don't waddle! The problem with BMI is that it's a simple calculation involving body mass and height.

BMI = body mass (in kg) divided by the square of height (in metres).

I will now demonstrate how two people with identical body compositions, waist measurements and heights can have different body masses (and thus BMIs). Consider the body as a cylinder with the legs as two inverted cones each having half the diameter of the body at the top (it keeps the maths relatively simple). I will ignore the arms & head!

Volume of a cylinder = Pi x Radius squared x Length.
Volume of a cone = 1/3 x Pi x Radius squared x Length.
Mass = Volume x Density.

Length of legs + body = 160cm.
Body diameter = 30cm.
Therefore, body radius = 15cm.
Leg diameter at top = 15cm.
Therefore, leg radius at top = 7.5cm.
Leg & body density = 1g/cubic centimetre.

I have 75cm long legs + 85cm long body.
She has 100cm long legs + 60cm long body.

My legs = 4420g each. My body = 60082g. My total body mass = 68922g = 69kg. My height = 1.6m.
∴ My BMI = 26.9

Her legs = 5900g each. Her body = 42411g. Her total body mass = 54211g = 54kg. Her height = 1.6m.
∴ Her BMI = 21.1

See the difference? 1cm of legs weighs much less than 1cm of body. People with long legs and a short body (e.g. women) have a significantly lower BMI than people with short legs and a long body (e.g. me). In addition, people with narrow builds and people with very little muscle have a significantly lower BMI than people with wide builds and people with a lot of muscle.

Thanks to Wolfram Alpha for doing the calculations.

P.S. According to her BMI, this 5 year old girl is overweight.


ProudDaddy said...

I don't know if you'll get notified about this comment, but if you do, I would like to call your attention to a post I just made on Ned Koch's blog. The full text of the referenced study hardly mentions Figure 2B, but it's the one that has convinced me to drop 4" from my waist size and to never consider myself healthy based on a "normal" BMI.

ProudDaddy said...

Waist to height makes more sense to me as well, but I would consider it a refinement. What about the correlation with metabolic conditions in Figure 2B? Is the data reliable? Should I pay attention to my visceral fat? It is not often that you find a correlation where the lowest third is essential condition-free!

Nigel Kinbrum said...

A tiny man with a waist of 87.3cm would have a much fatter belly than a big bruiser like me with the same waist measurement. I therefore don't trust the data.

I prefer a waist:height ratio cut-off of 0.5. As I'm 6' tall and have a (just measured) waist of 38", my W:H = 0.53 As my last blood test results in 2008 were fine and my weight hasn't changed much since then, I'm not worrying about it.