## 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.
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.