# Corpulence index

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The Corpulence Index (CI) or Ponderal Index (PI) is a measure of leanness (corpulence) of a person calculated as a relationship between mass and height. It was first proposed in 1921 as the "Corpulence measure" by Swiss physician Fritz Rohrer and hence is also known as Rohrer's Index. It is similar to the body mass index, but the mass is normalized with the third power of body height rather than the second power.

$\mathrm {CI} ={\frac {\mathrm {mass} }{\mathrm {height} ^{3}}}$ with $\mathrm {mass}$ in kilograms and $\mathrm {height}$ in metres, giving a measure with the same dimensions as density. The corpulence index yields valid results even for very short and very tall persons, which is a problem with BMI — for example, an ideal height-adjusted body weight for a person 150 cm tall will render BMI of 20.7 and CI of 13.6, while for a person 200 cm tall the BMI will be 24.84, very close to the "overweight" threshold of 25, while CI will be 12.4.

Because of this property, it is most commonly used in pediatrics. (For a baby, one can take crown-heel length for the height.) The normal values for infants are about twice as high as for adults, which is the result of their relatively short legs.[citation needed] It does not need to be adjusted for age after adolescence. It has also been shown to have a lower false positive rate in athletes.

The corpulence index is variously defined (the first definition should be preferred due to the use of SI-units kg and m) as follows:

Formula Units for mass
(body weight)
Units for height
(or length)
Values considered normal or typical
for a 12-month-old infant beyond infancy
${\text{CI}}={\frac {\mathrm {mass} }{\mathrm {height} ^{3}}}$ kilograms metres 24 12
${\text{CI}}=1000{\frac {\mathrm {mass} }{\mathrm {height} ^{3}}}$ grams centimetres (same values as above)
${\text{CI}}={\frac {\mathrm {height} }{\sqrt[{3}]{\mathrm {mass} }}}$ pounds inches 12.49 to 13.92