# Ponderal index

The Ponderal Index (PI) is a measure of leanness of a person[1] calculated as a relationship between mass and height.[2] It was first proposed in 1921 as the "Corpulence Index" by Rohrer.[3] 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.

$\mathrm{PI} = \frac{mass}{height^3}$

with $mass$ in kg (kilograms) and $height$ in m (meters), giving a measure with the same dimensions as density. The ponderal index yields valid results even for very short and very tall persons.[4] Because of this property, it is most commonly used in pediatrics.[5][6] The normal values for infants are about twice as high as for adults, which is the result of their relatively short legs.

The ponderal 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 corresponding to "normal"
BMI in a 180 cm tall person
$\text{PI}=\frac{mass}{height^3}$[6] kilograms metres 10.3 to 13.9, 24 for 12 month old infant[5]
$\text{PI}=100\frac{mass}{height^3}$[5] grams centimetres 2.4 for 12 month old infant
$\text{PI}=1000\times\frac{\sqrt[3]{mass}}{height}$[2] kilograms centimetres 21.75 to 24.0[7]
$\text{PI}=100\times\frac{\sqrt[3]{mass}}{height}$[8] kilograms centimetres 2.175 to 2.4
$\text{PI}=\frac{height}{\sqrt[3]{mass}}$[1] pounds inches 12.49 to 13.92

## References

1. ^ a b Foods and Nutrition Encyclopedia, Audrey H. Ensminger, Marion Eugene Ensminger. p. 1645
2. ^ a b EXSS 323: LAB 1 - BIOMECHANICS TOOLS: Computers, Algebra and Trig Oregon State University
3. ^ Rohrer, Fritz (1921). "Der Index der Körperfülle als Maß des Ernährungszustandes" [The index of corpulence as measure of nutritional state]. Münchener medizinische Wochenschrift (in German) 68: 580–2.
4. ^ Lawrence F. Ditmier: New Developments in Obesity Research. Nova Science Publishers, Hauppauge, New York 2006, ISBN 1-60021-296-4 [Amazon-US | Amazon-UK]
5. ^ a b c Davies, D. P. (2007). "Size at birth and growth in the first year of life of babies who are overweight and underweight at birth". Proceedings of the Nutrition Society 39 (1): 25–33. doi:10.1079/PNS19800005. PMID 6988835.
6. ^ a b ACC/SCN NUTRITION POLICY PAPER No. 19 - Glossary by Lindsay H. Allen and Stuart R. Gillespie
7. ^ The source quoted (Oregon State University) states that typical healthy PI values range between 20 and 25.
8. ^ Medical Dictionary University of Newcastle upon Tyne

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