Body mass index

We recently commented on obesity trends in the US. As we noted there, the CDC provides an online calculator that allows input of weight (in pounds or kilograms) and height (in inches or centimeters) and returns body mass index (BMI) in kilograms per meter squared. No calculator of any kind should be trusted blindly, of course, so today let us look at some examples of calculating BMI "from scratch".

The measurements of height and weight used in the derivation of BMI are based on the (metric) International System of Units (SI). This is customary in scientific work, even in the US, where SI units are generally used less commonly than in other countries. For the calculation of BMI, weight is measured in kilograms (or, if measured in other units, converted to kilograms) and height is measured in or converted to meters. These SI units for height and weight are not always familiar to persons in the US, where it is much more common to report height in feet and inches, and weight in pounds. Thus in the US, people can probably determine based on experience that a woman who is 5' 6" tall and weighs 140 pounds is not terribly overweight, whereas a woman the same height but who weighs 250 lbs would seem quite heavy. On the other hand, if a person is 1.67 meters tall and weighs 63.6 kilograms, many in the US would not have a good feel for whether she is underweight, just right, or obese. (In fact, this height and weight are the same as 5' 6" and 140 pounds, respectively).

According to the CDC, adults who have BMIs below 18.5 are considered underweight; those with BMIs from 18.5 to 24.9 are considered to be at a healthy weight; those with BMIs from 25.0 to 29.9 are considered overweight (but not obese); and those with BMIs 30 and above are considered obese:

So how does one calculate the BMI of a woman who is 5' 6" tall and weighs 140 pounds, from scratch? There are many ways to go about it, of course. Here's one:

Step 1: convert the height to inches. Each foot is 12 inches, so 5 feet is 60 inches (5 × 12 = 60), and thus 5' 6" = 60 + 6 = 66 inches.

Step 2: convert inches to centimeters. Each inch is 2.54 centimeters, so 66 inches = 66 × 2.54 = 167.64 cm.

Step 3: convert centimeters to meters. Each meter is equal to 100 cm, so 167.64 cm = 167.64 ÷ 100 = 1.6764 meters.

Step 4: square the height: (1.6764 meters)^{2} = 2.81031696 m^{2}.^{}

Step 5: convert 140 pounds to kilograms. One kilogram is equal to 2.2 pounds (approximately). Thus 140 pounds = 140 ÷ 2.2 = 63.6 kilograms.

Step 6: divide (weight in kilograms) by (the square of the height, in meters squared):

BMI = 63.6 kg ÷ 2.81031696 m^{2} = 22.64 kg/m^{2}

According to the CDC, a woman who is 5' 6" tall and weighs 140 pounds would fall into the "healthy weight" category.

Repeating the steps above for a woman who is 5' 6" tall and weighs 250 pounds, we obtain a BMI of 40.44 kg/m^{2}. According to the CDC's guidelines, this height and weight combination falls into the "obese" category.

The calculations are simple enough and even simpler if one has measurements of height and weight in kilograms and meters from the outset (just square the height and divide). However, even with simple calculations, it is easy to err at various steps. Some common sense (does the weight-for-height I am considering seem extreme one way or the other?) will usually prevent egregious errors from "going to press". And using the CDC's calculator as a check is probably a good way to prevent many errors. If your own calculations and the CDC's do not agree, don't assume the CDC is correct. Re-calculate both. Though the CDC calculator is unlikely to have an internal error of calculation, user input errors are frustratingly common.

We leave you with a few statistics on average heights, weights, and calculated BMIs (from the average heights and weights given) for some well-known professions.

a. NBA = National Basketball Association. Data from John Grasso's NBA database, available here.

b. The information on Playboy Centerfolds was compiled by Reynolds RJ from publically available records.

c. MLB = Major League Baseball. Data taken from Sean Lahman's database, available here.

d. Information on sumo wrestlers taken from here.

e. NFL = National Football League. The *NFL combine* is a week-long event occurring in February where college football players perform physical and mental tests in front of NFL coaches, managers, and scouts. Data are taken from here.

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