The Corpulence Index (CI) (also Ponderal Index (PI) or Rohrer's Index) is a measure of corpulence, or of leanness in other variants, 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][4] and hence is also known as Rohrer's Index.^[5] 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.^[6] In 2015, Sultan Babar showed that CI does not need to be adjusted for height after adolescence.^[4][6]

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

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,^[7] which is a problem with BMI — for example, an ideal body weight for a person 152.4 cm tall (48 kg) will render BMI of 20.7 and CI of 13.6, while for a person 200 cm tall (99 kg), the BMI will be 24.8, very close to the "overweight" threshold of 25, while CI will be 12.4.^[8]

Because of this property, it is most commonly used in pediatrics.^[9][10] (For a baby, one can take crown-heel length for the height.^[11]) 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.^[6] It has also been shown to have a lower false positive rate in athletes.^[12]

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	Values considered normal or typical
		for a 12-month-old infant	beyond infancy
${\displaystyle {\text{CI))={\frac {\mathrm {mass} }{\mathrm {height} ^{3))))$[9][10]	kg/m3	24[9]	12[6]
${\displaystyle {\text{CI))={\frac {\mathrm {height} }{\sqrt[{3}]{\mathrm {mass} ))))$[1][13]	inch * pound -1/3	12.49 to 13.92

Significance

• It plays a role in assessing whether the intrauterine growth restriction of a child is symmetrical or asymmetrical.^[14]
• CI has been shown to have higher sensitivity, specificity, and positive and negative predictive values than body mass index for determining adiposity.^[6]
• It is used to calculate ectomorphy in the Heath–Carter formula.^[15][16]

Categories

For infants, units of grams and centimeters are used instead, then the value is multiplied by 100.^[17]

${\displaystyle {\text{PI))_{\text{child))=0.1\times {\text{PI))_{\text{adult))=100\times {\dfrac ((\text{mass))_{\text{g))}((\text{height))_{\text{cm))^{3))))$