# 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.]

### 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

### BAI Result

Status | ||
---|---|---|

Underweight | ||

Healthy | ||

Overweight | ||

Obese |

#### Formula for BAI

## 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.

Continue reading below ⇩

## 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 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 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} = *x*√*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.

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

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Chapter menu below ⇩

Chapter Contents

- Functions and Graphs
- 1. Introduction to Functions
- 2. Functions from Verbal Statements
- 3. Rectangular Coordinates
- 4. The Graph of a Function
- 4a. Domain and Range of a Function
- 4b. Comparison calculator BMI - BAI
- 5. Graphing Using a Computer Algebra System
- 5a. Online graphing calculator (1): Plot your own graph (JSXGraph)
- 5b. Online graphing calculator (2): Plot your own graph (SVG)
- 6. Graphs of Functions Defined by Tables of Data
- 7. Continuous and Discontinuous Functions
- 8. Split Functions
- 9. Even and Odd Functions