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

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

Male
Female

20 to 40
41 to 60
61 to 79

### BMI Result

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

#### 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.

## 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).

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

## 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 $y=\frac{80}{x^2}$ 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 $y=\frac{100}{x^{1.5}}-18$ 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 x1.5 = xx, 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.

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