# 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

### BAI Result

Status
Underweight
Healthy
Overweight
Obese

#### Formula for BMI

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

#### 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).

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

100 kg
80 kg
60 kg
40 kg
height (m)
BMI (kg/m2)

Graph of BMI for various weights.

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

130 cm
110 cm
90 cm
70 cm
height (m)
BAI (% body fat)

Graph of BAI for various hip girths.

## Graphs of the Functions

For completeness, let's zoom out and see the graphs of the BMI and BAI functions.

BMI: The graphs of

y=n/x^2

for various n each have 2 arms. The domain is all x except x = 0 and the range is y > 0.

Graphs of y=n/x^2 for n=40,60,80,100.

BAI: The graphs of

y=n/x^1.5 - 18

for various n have 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 > -18.

Graphs of y=n/x^1.5-18 for n=70,90,110,130.

See more on domain and range.

Of course, for the BMI and BAI graphs, we only consider positive values for the height, BMI and BAI, 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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