# How to Calculate the Ponderal Index

## Ponderal (Rohrer) Index Calculator

Ponderal Index Calculator
Mass in kg kg
Height in cm cm

Like body mass index, the ponderal index gives a number based on person's weight-height ratio. While the BMI is proportional to mass over height squared, the ponderal index (occasionally written "pondural") is a function of mass over height cubed.

The ponderal index was developed by F. Rohrer as a leanness or corpulence measure, similar to the way BMI is currently used. The basic equation for a person's P.I. is

P.I.
= (Mass in kg)/(Height in m)³
= 1000000*(Mass in kg)/(Height in cm)³

A second equation is also used in some medical sources:

P.I. = 1000*∛(Mass in kg)/(Height in cm)

This second equation is proportional to the cube root of the first equation. Both formulations are encoded in the calculator on the left.

### Normal Ranges of Ponderal Indices

One can use the healthy ranges of BMI indices to find the equivalent healthy ranges for ponderal indices. The table below shows the range of a "normal" ponderal index for adult heights of 140 to 210 cm. (To convert US customary units to metric units, use the length converter.)

 Adult Height Normal Ponderal Index Range 140 cm Equation 1:   13.2 - 17.8Equation 2:   23.6 - 26.1 150 cm Equation 1:   12.3 - 16.6Equation 2:   23.1 - 25.5 160 cm Equation 1:   11.6 - 15.6Equation 2:   22.6 - 25.0 170 cm Equation 1:   10.9 - 14.6Equation 2:   22.2 - 24.5 180 cm Equation 1:   10.3 - 13.8Equation 2:   21.7 - 24.0 190 cm Equation 1:   9.7 - 13.1Equation 2:   21.4 - 23.6 200 cm Equation 1:   9.3 - 12.5Equation 2:   21.0 - 23.2 210 cm Equation 1:   8.8 - 11.9Equation 2:   20.7 - 22.8