What the ponderal index is
The ponderal index, also called Rohrer’s index, relates weight to height cubed rather than squared as BMI does. Because the body is a three-dimensional shape, dividing by height cubed makes the index less dependent on height.
Formulas
- Adults: PI = weight (kg) ÷ height (m)³, in kg/m³.
- Newborns: PI = 100 × weight (g) ÷ length (cm)³.
The newborn version is the one most used in practice, to describe body proportions at birth.
Worked example, adult
A person 5 ft 9 in (175.3 cm) tall weighing 160 lb (72.6 kg):
- Height cubed: 1.753³ ≈ 5.38 m³.
- Ponderal index: 72.6 ÷ 5.38 ≈ 13.5 kg/m³.
- BMI for comparison: 72.6 ÷ 1.753² ≈ 23.6 kg/m².
Worked example, newborn
A baby weighing 7.5 lb (3,402 g) with a length of 20 inches (50.8 cm):
- Length cubed: 50.8³ ≈ 131,097 cm³.
- Ponderal index: 100 × 3,402 ÷ 131,097 ≈ 2.59.
Reference values
| Group | Usual range |
|---|---|
| Adults | about 11 to 15 kg/m³ |
| Term newborns | about 2.2 to 3.0 |
Using it at birth
Babies who are small for their gestational age fall into two broad patterns. In symmetric growth restriction, weight and length are both low and the ponderal index is normal. In asymmetric growth restriction, often linked to placental problems late in pregnancy, weight falls behind length and the index is low. A low index flags a thin baby who may need closer feeding and glucose monitoring.
Adults: compared with BMI
BMI tends to overstate fatness in tall people and understate it in short people. The ponderal index corrects part of this effect. It still does not distinguish muscle from fat, so very muscular people score high on both. For a fuller picture, combine it with waist measurements or body fat estimates.
Measuring accurately
For newborns, length is measured lying flat with legs extended, ideally on a measuring board; a 1 cm error changes the index by about 6%. For adults, measure height without shoes and weight in light clothing.
This calculator is for general information and education. It is not medical advice and does not replace the judgment of a doctor, nurse or pharmacist who knows the full clinical picture.