Skip to main content
Search IntMath

New measure of obesity - body adiposity index (BAI)

By Murray Bourne, 09 Mar 2011

Scientists have proposed a new method for determining body fat, called the Body Adiposity Index.


Obesity affects 500 million people world-wide (which is crazy when one billion people are starving, but we'll leave that issue for another time.)

There are several methods for measuring body fat (including hydrodensitometry, calipers, DEXA - Dual Energy X-ray Absorptiometry, infrared, MRI, and so on. See Body Fat Analyzing for more information.)

But is there an easy, low-tech way to measure whether somebody has a healthy amount of body fat, or is overweight?

For almost 200 years, the Body Mass Index (BMI) has been used to give a measure of body fat. The calculation for BMI is as follows.

\text{BMI}=\frac{\text{weight in kg}}{\text{(height in m)}^2}

BMI is useful in that you only need to know the person's height and weight.

The problem with the BMI is that it often fails as a measure of how much unhealthy fat you are carrying. There are broad ranges in the BMI for "healthy" and "obese" to allow for athletes (who tend to be muscular, and muscles are more dense than fat) and women (who tend to have more body fat). The BMI overestimates body fat in lean people.

Also, you need a reliable set of scales to use the BMI.

In short, we need a new way to measure obesity.

The Body Adiposity Index (BAI)

Researcher Richard Bergman of the University of Southern California measured 1700 Mexican-Americans for their fat levels and has recently proposed a new index - Body Adiposity Index (BAI). The formula is as follows:

BAI=\frac{\text{hip (in cm)}}{\text{height (in m)}\times\sqrt{\text{height (in m)}}}-18

The "hip" measurement is "at the level of the maximum extension of the buttocks posteriorly in a horizontal plane" (not actually around the level of your belly button - which is usually a maximum - as reported by some news outlets).

Applying some basic index laws (fractional exponents), we can express this as:

BAI=\frac{\text{hip (in cm)}}{\text{height (in m)}^{1.5}}-18

Bergmean's team settled on this formula after cross-checking the subjects' body weight using Dual Energy X-ray Absorptiometry, mentioned earlier.

One advantage of the BAI is it doesn't depend on weight - just 2 simple length measurements.

More research needs to be done (to a wider range of ethnic groups for a start) before it will be considered a valid measure of body fat.

Calculate your own BAI

I developed a new online calculator where you can find your own BAI and compare it to your BMI.

Try it out and let me know what you think. Go to:

Comparison calculator: BMI - BAI

Final note - is it really complex?

The reporter from Reuters appears to have been a math phobe. At one point the article said:

BAI is a complex ratio of hip circumference to height that can be calculated by doctors or nurses with a computer or calculator.

Complex? Really? It's rather sad when grade 8 index laws are considered "complex". And I imagine most people would use a calculator (or an online tool, or a chart) to calculate their BMI. I don't regard the BAI as all that more difficult in this respect.

See the 73 Comments below.

Leave a comment

Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.


Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.