# BAI calculator with BMI comparison

This is an interesting real-life application of graphs of functions. For background on this, see New measure of obesity – body adiposity index (BAI).

Enter your age, gender, height, weight, and hip circumference ("at the level of the maximum extension of the buttocks posteriorly in a horizontal plane") below. (Some typical values are given.)

[If you still think in feet, pounds and inches, you can convert your measurements to metric here.]

Age:

Gender:

### BMI Result

Weight Status BMI
Underweight Below 18.5
Normal 18.5 – 24.9
Overweight 25.0 – 29.9
Obese 30.0 and Above

#### Formula for BMI

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

### BAI Result

Status
Underweight
Healthy
Overweight
Obese

#### Formula for BAI

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

## Points to Note and Disclaimer

The above cut-off values for the BAI (% body fat) are based on this table.

Determining your body fat from height, weight and hip measurements (and your health status) is certainly not an exact science! Go to your doctor and get proper body fat measurements done before acting on anything above.

Any comments? Go to: New measure of obesity – body adiposity index (BAI) and leave your thoughts.

## Graphs of BMI and BAI

The following graph shows the BMI for various weights (40 kg in green, 60 kg in blue, 80 kg in red and 100 kg in magenta).

text(BMI)=(text(weight in kg))/((text(height in m))^(\ 2))

Here now is the BAI, for typical hip measurements ranging from 70 cm (in green) through to 130 cm (in magenta).

text(BAI)=(text(hip in cm))/((text(height in m))^(\ 1.5))-18

## Graphs of the Functions

For completeness, let's zoom out and see the graphs of the BMI and BAI functions for some typical values of weight and height.

BMI (weight 80 kg): The graph of

y=80/x^2

has 2 arms, shown in red below. The domain is all x except x = 0 and the range is y > 0.

BAI (hip 100 cm): The graph of

y=100/x^1.5 - 18

shown in blue has only one arm, since the square root of a negative number is not defined for the real numbers. This is an issue since x^1.5 = xsqrt(x), in the denominator (bottom) of the fraction. In this case, the domain is x > 0 and the range is y > 0.

See more on domain and range.

Of course, for the BMI and BAI graphs, we only take positive values for the height, since negative values have no practical meaning.

Any comments? Go to: New measure of obesity - body adiposity index (BAI) and leave your thoughts.

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