# 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 and hence also known as Rohrer's index.[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