The body mass index (BMI), or Quetelet index, is a statistical measurement which compares a person's weight and height. Though it does not actually measure the percentage of body fat, it is a useful tool to estimate a healthy body weight

Body mass index is defined as the individual's body weight divided by the square of his height. The formulas universally used in medicine produce a unit of measure of kg/m². BMI can also be determined using a BMI chart, which displays BMI as a function of weight (horizontal axis) and height (vertical axis) using contour lines for different values of BMI or colours for different BMI categories.

|- valign="center" !rowspan=2|Imperial units | $\backslash mbox\{BMI\}\; =\; \backslash frac\{\backslash mbox\{weight\}\; \backslash \; \backslash mathrm\{(lb)\}\; \backslash times\; 703\}\{\backslash mbox\{height\}^2\; (\backslash mathrm\{in^2\})\}$ |- | $\backslash mathrm\{BMI\}\; =\; \backslash frac\{\backslash mbox\{weight\}\; \backslash \; \backslash mathrm\{(lb)\}\; \backslash times\; 4.88\}\{\backslash mbox\{height\}^2\; (\backslash mathrm\{ft^2\})\}$ |}

Usage

As a measure, BMI became popular during the early 1950s and 60sFact: date=December 2007 as obesity started to become a discernible issue in prosperous Western societies. BMI provided a simple numeric measure of a person's "fatness" or "thinness", allowing health professionals to discuss over- and under-weight problems more objectively with their patients. However, BMI has become controversial because many people, including physicians, have come to rely on its apparent numerical authority for medical diagnosis, but that was never the BMI's purpose. It is meant to be used as a simple means of classifying sedentary (physically inactive) individuals with an average body composition. For these individuals, the current value settings are as follows: a BMI of 18.5 to 25 may indicate optimal weight; a BMI lower than 18.5 suggests the person is underweight while a number above 25 may indicate the person is overweight; a BMI below 17.5 may indicate the person has anorexia or a related disorder; a number above 30 suggests the person is obese (over 40, morbidly obese).

For a given height, BMI is proportional to weight. However, for a given weight, BMI is inversely proportional to the square of the height. So, if all body dimensions double, and weight scales naturally with the cube of the height (as is the case with a spherical cow), 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. This anomaly is partially offset by the fact that many taller people are not just "scaled up" short people, but tend to have narrower frames in proportion to their height. It has been suggested that instead of squaring the body height (as the BMI does) or cubing the body height (as seems natural), it would be more appropriate to use an exponent of between 2.3 to 2.7.

BMI Prime

BMI Prime, a simple modification of the BMI system, is the ratio of actual BMI to upper limit BMI (currently defined at BMI 25). As defined, BMI Prime is also the ratio of body weight to upper body weight limit, calculated at BMI 25. Since it is the ratio of two separate BMI values, BMI Prime is a dimensionless number, without associated units. Individuals with BMI Prime < 0.74 are underweight; those between 0.74 and 0.99 have optimal weight; and those at 1.00 or greater are overweight. BMI Prime is useful clinically because individuals can tell, at a glance, by what percentage they deviate from their upper weight limits. For instance, a person with BMI 34 has a BMI Prime of 34/25 = 1.36, and is 36% over his or her upper mass limit. In Asian populations (see International Variation section below) BMI Prime should be calculated using an upper limit BMI of 23 in the denominator instead of 25. Nonetheless, BMI Prime allows easy comparison between populations whose upper limit BMI values differ.