Body mass index

Body mass index (abbreviated BMI) is a rough measure of proportionality between a person's height and weight, and is used to estimate whether a person is at a healthy weight for their height. BMI is calculated as weight in kilograms divided by height in meters squared. For english units, a conversion factor is applied.

${\textrm {BMI}}={\frac {\textrm {W(kg)}}{{\textrm {H(m)}}^{2}}}=4.88{\frac {\textrm {W(lbs)}}{{\textrm {H(ft.)}}^{2}}}=703{\frac {\textrm {W(lbs.)}}{{\textrm {H(in.)}}^{2}}}$.

Healthy BMI is between 18.5 and 24.9. Less than 18.5 is considered underweight; between 25 and 29.9 is considered overweight, over 30 is considered obese, and over 45 is considered morbidly obese.

BMI is a rough diagnostic tool for estimating body fat, and has limitations. Chief among these are that it may overestimate body fat in athletes and others who have a muscular build, and that it may underestimate body fat in older persons and others who have lost muscle mass.

Another limitation is in the choice of exponent. If humans scaled proportionally in all three dimensions as they become taller, the appropriate exponent would be 3, instead of the 2 used for BMI calculation. However, 2 is too low. Data from the United States indicates that an exponent of 2.6 is most appropriate. Relatedly, the government of Singapore has set different cutoff levels of BMI, based on the shorter average stature and somewhat different body shape of Southeast Asians as compared to Europeans.