Additional Math Pages & Resources

Tuesday, January 11, 2011

How Fat Am I? Part II

Yesterday I gave you a brief introduction to the Body Mass Index. A magic, mathematical number. Or is it? Even a person who only uses elementary school math can see its shortcomings.

From a math point of view, the formula (weight over height squared) does not accurately reflect how weight changes with height.  For an extended discussion of this, go here. It also does not reflect the makeup of athletes, because increasing your muscle mass causes you to appear even more overweight (muscle weighs more than fat).

There are lots of other issues with BMI, so concerned scientists, doctors, etc. have come up with lots of other ways to answer the question How Fat Am I? which is where we started yesterday (the question behind many New Year's Resolutions).

The US Navy, who measures and employs lots of fit young men and women, has came up with an enhanced version of the BMI test. This was published about 25 years ago, from research work done right here in San Diego. It adds several measurements of circumference (the distance around the perimeter of an object).

You should aim for accuracy of 1/4" while using a non-stretching, flexible measuring tape around the body. Note that if you cannot easily (or honestly) measure yourself this accurately, you might want a helper.

Follow this process:
  1. Measure weight in the morning after going to the toilet but before dressing or eating
  2. Measure height with shoes off
  3. Measure circumference of the neck below the Adam's Apple
  4. Men measure waist at the belly button
  5. Women measure waist at point of smallest circumference
  6. Women measure hips at point of largest circumference
Then you want to find a website that calculates the body mass for you, OR a scientific calculator (because this is a bit above the elementary-level math taught in Excel Math).

men: body fat % = 86.010 x log10(abdomen - neck) - 70.041 x log10(height) + 36.76
women: body fat % = 163.205 x log10(waist + hip - neck) - 97.684 x log10(height) - 78.387
Using this process, I get BMI of 26.9 kg/m2 with a Waist-to-Height ratio of .51
The web calculator I used suggest that I have 16.9% body fat, and lean body mass of 151 lbs.
That's a bit better than yesterday's BMI of 27.3 (only because it makes me feel less fat).

By the way, this procedure is based on testing lots of young active people from European countries, not older, sedentary people (like me), or people with different ethnic backgrounds such as Pacific Islanders, Asians, blacks, etc. But it's more reflective of reality than the simple BMI that does not measure girth.

There are many other, more elaborate ways to measure, calculate, estimate and understand your body composition and the fat you carry around. We'll look at a few more tomorrow.

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