How to Calculate the Ponderal Index

Ponderal (Rohrer) Index Calculator

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

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