The Body Mass Index (BMI) does not work well for short people nor for tall people. The alternative proposed in this article is the Better Body Mass Index (BBMI). Below is a calculator that demonstrates the BBMI.

Underweight | BMI (BBMI) <= 18.5 |

Normal weight | BMI (BBMI) = 18.5–24.9 |

Overweight | BMI (BBMI) = 25–29.9 |

Obesity | BMI (BBMI) >= 30 |

The US National Institutes of Health (NIH) advises that excessive body fat corresponds with a higher risk of various diseases including heart disease, high blood pressure, type 2 diabetes, gallstones, breathing problems, and certain cancers [1]. The NIH suggests using the Body Mass Index (BMI) in combination with the above evaluation table to assess the healthiness of body mass. The metric and imperial versions of the BMI are as follows:

Metric (kg and m): | BMI = Mass ÷ Height^{2} |

Imperial (lbs and in): | BMI = 703 x Mass ÷ Height^{2} |

The formula for the BMI was first conceived by Adolphe Quitelet (then known as the Quitelet index) and related in such works as, “A Treatise On Man”. The formula became known as the BMI after Ancel Keys’ 1972 publication, “Indices of relative weight and obesity” [2]. Its simplicity was a primary factor in its rise in popularity. Despite this simplicity though, and advancements in computing, it is still used today for such tasks as determining insurance premiums.

A common criticism of the BMI is that it disregards body composition. Muscle is denser than fat, and thus a muscular person may have a misleadingly high BMI despite having a body fat content not unconducive to good health. This short coming limits the usefulness of the index. Another issue is that the BMI is not specific to gender nor ethnicity, despite women generally having a higher body fat percentage and healthy BMI varying between ethnicities (Asians with increased BMI are at greater risk for type 2 diabetes [3]).

For both short and tall people, there is yet another problem, and that is that the relationship between mass and height suggested by the BMI formula may be in error. Though there have been studies finding the implied quadratic relationship [4], there are many that report higher order relationships, as far up as cubic [5]. So while the BMI predicts that humans scale in two dimensions, much like a sheet of paper might, the cubic relationship would imply that humans scale isometrically (proportions are maintained). Yet, taller people tend to appear skinnier than shorter people (proportions are not maintained). It is most likely that humans scale somewhere in between quadratic and cubic, as some studies have found [6].

The Better Body Mass Index (BBMI), proposed in this article, compromises between quadratic and cubic by incorporating a 2.5 exponent in the formula. A correction factor is also applied to ensure that average height people wind up with a BBMI equal to their BMI. The metric and imperial versions of the BBMI are as follows:

Metric (kg and m): | BBMI = 1.3 x Mass ÷ Height^{2.5} |

Imperial (lbs and in): | BBMI = 917 x Mass ÷ Height^{2.5} |

A 2.5 exponent is merely an estimate. The true exponent likely varies for ethnicity, gender, and many other variables. For this reason, the calculator provided at the beginning of this article provides a field for alternate exponents. Note, though, that for whatever exponent is entered for an average height person with a given weight, the reported BBMI remains the same.

By using the BBMI, short and tall people should be less likely to be marked as underweight and overweight, respectively. However, the other issues with strictly mass and height indices remain, such as not accounting for body composition. In reality, such indices are better suited for population studies rather than assessing the healthiness of an individual’s weight. A better alternative for individuals is a fat measuring caliper.

[1] National Institute of Health, Assessing Your Weight and Health Risk.

[2] Indices of relative weight and obesity, Journal of Chronic Disease

[3] Ethnicity, obesity, and risk of type 2 diabetes in women: a 20-year follow-up study

[4] Weight-height relationships and body mass index: some observations from the Diverse Populations

[5] Human allometry: adult bodies are more nearly geometrically similar than regression analysis has suggested

[6] Why is the body mass index calculated as mass/height2, not as mass/height3?