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# 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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