Corpulence index

The Corpulence Index (CI) or Ponderal Index (PI) is a measure of leanness (corpulence) of a person[1] calculated as a relationship between mass and height.[2] It was first proposed in 1921 as the "Corpulence measure" by Swiss physician Fritz Rohrer[3] and hence is also known as Rohrer's Index.[4] 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.[5]

${\displaystyle \mathrm {CI} ={\frac {\mathrm {mass} }{\mathrm {height} ^{3}}}}$

with ${\displaystyle \mathrm {mass} }$ in kilograms and ${\displaystyle \mathrm {height} }$ 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.[6] Because of this property, it is most commonly used in pediatrics.[7][8] (For a baby, one can take crown-heel length for the height.[9]) The normal values for infants are about twice as high as for adults, which is the result of their relatively short legs. It does not need to be adjusted for age after adolescence.[5] It has also been shown to have a lower false positive rate in athletes.[10]

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
${\displaystyle {\text{CI}}={\frac {\mathrm {mass} }{\mathrm {height} ^{3}}}}$[8]	kilograms	metres	24[7]	12[5]
${\displaystyle {\text{CI}}=1000{\frac {\mathrm {mass} }{\mathrm {height} ^{3}}}}$[7]	grams	centimetres	(same values as above)
${\displaystyle {\text{CI}}={\frac {\mathrm {height} }{\sqrt[{3}]{\mathrm {mass} }}}}$[1][11]	pounds	inches	12.49 to 13.92