# BMI Calculator

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Lets first understand, what is BMI and how we can calculate BMI?

Body Mass Index (BMI) is a value derived from the mass (weight) and height of a person.

We can calculate BMI using below formula:

$$BMI = {{Mass_{kg}} \over {Height_m}^2}$$ $$BMI = {{Mass_{lb}} \over {Height_{in}}^2} * 703$$The BMI is a convenient rule of thumb used to broadly categorize a person as underweight, normal weight, overweight, or obese based on mass and height.

Example : Calculate BMI for mass = 56 kg and height = 170 cm

Solution:

$$BMI = {{56\hspace{0.1cm}{kg}} \over {{1.7\hspace{0.1cm}{m}}*{1.7\hspace{0.1cm}{m}}}}$$ $$ BMI = {{56\hspace{0.1cm}{kg}} \over {{2.89\hspace{0.1cm}m^2}}}$$ $$ BMI = {19.377}\hspace{0.1cm}\dfrac{kg}{m^2}$$Commonly accepted BMI ranges are:

underweight - BMI under 18.5 kg/m^{2},

normal weight - BMI between 18.5 kg/m^{2} to 25 kg/m^{2},

overweight - BMI between 25 kg/m^{2} to 30kg/m^{2} and

obese - BMI over 30 kg/m^{2}.

BMI is proportional to the mass and inversely proportional to the square of the height.
So, if all body dimensions double, and mass scales naturally with the cube of the height,
then BMI doubles instead of remaining the same.

This results in taller people having a reported BMI
that is uncharacteristically high, compared to their actual body fat levels.

BMI for Children (aged 2 to 20)

BMI is used differently for children. It is calculated in the same way as for adults, but then compared to typical values for other children of the same age. Instead of comparison against fixed thresholds for underweight and overweight, the BMI is compared against the percentiles for children of the same sex and age.

A BMI that is less than the 5^{th} percentile is considered underweight and above the 95^{th} percentile is
considered obese. Children with a BMI between the 85^{th} and 95^{th} percentile are considered to be overweight.

According to mathematician Nick Trefethen, "BMI divides the weight by too large a number for short people and too small a number for tall people. So short people are misled into thinking that they are thinner than they are, and tall people are misled into thinking they are fatter."

For calculating BMI using above BMI calculator, you have to just write the mass (in kilograms) and height (in meters) in the given input box and press the calculate button, you will get the BMI.

Proposed New BMI

A new formula for computing BMI that accounts for the distortions of the traditional BMI formula for shorter and taller individuals has been proposed by Nick Trefethen,

$$BMI_{new} = 1.3*{{Mass_{kg}} \over {Height_{m}}^{2.5}}$$BMI Prime

BMI prime, a modification of the BMI system, is the ratio of actual BMI to upper limit optimal BMI (currently defined at 25 kg/m2), i.e., the actual BMI expressed as a proportion of upper limit optimal. The ratio of actual body weight to body weight for upper limit optimal BMI (25 kg/m2) is equal to BMI Prime. BMI Prime is a dimensionless number independent of units.

Individuals with BMI Prime less than 0.74 are underweight; those with between 0.74 and 1.00 have optimal weight; and those at 1.00 or greater are overweight.