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"body mass index" is a correct and usable phrase in written English
It is commonly used in scientific and medical writing, as well as in discussions about health and fitness. Example: "According to his body mass index, Jason is considered to be obese and at risk for numerous health problems."
Dictionary
Body mass index
noun
A statistical measure of the weight of a person scaled according to height, used to estimate if a person is underweight or overweight. BMI units are defined as \mathrmkg/\mathrmm^2 ≈ \mathrm703*lb/\mathrmin^2.
synonyms
Exact(60)
Body mass index.
Body mass index (kg/m2).
Body mass index was below 25.
Body mass index: body mass index; IAP: intra-abdominal pressure.
Body mass index was 21.
Body mass index was calculated.
Body mass index was documented.
Body mass index was divided into two categories, ie, normal (body mass index < 25) or overweight (body mass index ≥ 25).
Body mass index (BMI) was also calculated.
Body mass index (BMI) was a covariate.
Body mass index, in kg/m.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com