# 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][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] It took almost a century after Rohrer proposed it, before Sultan Babar showed that CI does not need to be adjusted for height after adolescence.[4]

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

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 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.[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 for mass
(body weight)
Units for height
(or length)
Values considered normal or typical
for a 12-month-old infant beyond infancy
${\displaystyle {\text{CI}}={\frac {\mathrm {mass} }{\mathrm {height} ^{3}}}}$[10] kilograms metres 24[9] 12[6]
${\displaystyle {\text{CI}}=1000{\frac {\mathrm {mass} }{\mathrm {height} ^{3}}}}$[9] grams centimetres (same values as above)
${\displaystyle {\text{CI}}={\frac {\mathrm {height} }{\sqrt[{3}]{\mathrm {mass} }}}}$[1][13] pounds inches 12.49 to 13.92

## References

1. ^ a b Foods and Nutrition Encyclopedia, Audrey H. Ensminger, Marion Eugene Ensminger. p. 1645
2. ^ EXSS 323: LAB 1 - BIOMECHANICS TOOLS: Computers, Algebra and Trig Oregon State University
3. ^ F. Rohrer (1921). "Der Index der Körperfülle als Maß des Ernährungszustandes". Münchner Med. WSCHR. 68: 580–582.