What Are the Kaup Index and Rohrer Index? Formulas and Reference Ranges for Children's Body Size

Why adult BMI cut-offs don't work for children

The balance between height and weight changes a lot as children grow. Babies are chubby and have a fairly high BMI; it drops as they shoot up during early childhood, then rises again towards puberty. If you judge children by a single adult standard such as "18.5 to under 25 is normal", perfectly healthy children can come out as "underweight" or "obese".

That is why separate measures have been used depending on age: the Kaup index for infants and young children (from about 3 months to 5 years) and the Rohrer index for elementary and junior high school children. The adult BMI formula and cut-offs are explained in The BMI formula and obesity classes.

Kaup index formula and reference ranges (infants and toddlers)

The Kaup index is calculated as weight (kg) ÷ height (cm) ÷ height (cm) × 10,000. Dividing by the height in centimetres twice and then multiplying by 10,000 gives exactly the same value as adult BMI (weight in kg ÷ height in m²). What differs is how the value is judged.

For example, a child 75 cm tall weighing 10 kg has 10 ÷ 75 ÷ 75 × 10,000 = 17.8, which is "normal". At 86 cm and 12 kg it is 16.2, and at 100 cm and 16 kg it is 16.0, both within "normal".

Rohrer index formula and reference ranges (school-age children)

The Rohrer index is calculated as weight (kg) ÷ height (cm)³ × 10,000,000. Where BMI and the Kaup index divide by height twice, the Rohrer index divides by it three times.

A child 130 cm tall weighing 27 kg has 27 ÷ 130³ × 10,000,000 = 123, which is "normal". At the same height and 35 kg it is 159, "slightly heavy". Working out the "normal" weight for each height gives the following.

The Rohrer index comes out lower for taller children

Because the Rohrer index divides by the cube of height, it tends to read high for short children and low for tall ones. For example, a child who is 120 cm and 23 kg has a Rohrer index of 133. At 150 cm, the weight giving the same 133 is 44.9 kg, but in BMI terms that build is 20.0, much sturdier than 120 cm and 23 kg (BMI 16.0).

In other words, a tall child can be on the heavy side and still fall within "normal". For junior high school students who have shot up, don't rely on the Rohrer index alone; it's a good idea to look at the obesity degree described next as well.

The obesity degree used in Japanese school health checks

Japanese school health checks today rely more on the obesity degree (degree of overweight) than on the Rohrer index. It compares a child's weight with a standard weight set for their sex, age and height, and shows how many percent heavier or lighter they are.

• Obesity degree (%) = (measured weight − standard weight for height) ÷ standard weight for height × 100
• +20% to under 30% is mild obesity, 30% to under 50% is moderate obesity, and 50% or more is severe obesity
• −20% or below is underweight, and −30% or below is severely underweight

The standard weight for height is calculated using sex- and age-specific coefficients published by Japan's Ministry of Education (MEXT). Growth curves and the obesity degree are often included in the health check results the school hands out, so check those too if the Rohrer index gives a result that worries you.

Calculate your child's body size

1. 1

   Open the "Children (Kaup / Rohrer)" tab

   In the "Children (Kaup / Rohrer)" tab of the BMI & Healthy Weight Calculator, choose infants (Kaup index) or school age (Rohrer index).

2. 2

   Enter height and weight

   Enter your child's height (cm) and weight (kg). These are entered separately from the adult fields.

3. 3

   See the index, the category and the "normal" weight range

   You'll see the Kaup index (or Rohrer index), its reference category, and the weight range that counts as "normal" for that height.

The result is a guide to growth and not a diagnosis of health. If you are concerned about how your child is growing, talk to a paediatrician or the school nurse, using the results from infant or school health checks. From age 18, you can compare against the adult standard weight by height.

FAQ

What is the formula for the Kaup index?

Kaup index = weight (kg) ÷ height (cm) ÷ height (cm) × 10,000. For 75 cm and 10 kg, that is 10 ÷ 75 ÷ 75 × 10,000 = 17.8, which falls in the "normal" range (15 to under 19). The value is the same as adult BMI.

What is the formula for the Rohrer index?

Rohrer index = weight (kg) ÷ height (cm)³ × 10,000,000. For 130 cm and 27 kg, it is about 123, which is "normal" (115 to under 145); at the same height and 35 kg it is about 159, "slightly heavy" (145 to under 160).

At what ages are the Kaup and Rohrer indexes used?

The Kaup index is generally used for infants and toddlers from about 3 months to 5 years, and the Rohrer index for elementary and junior high school children. From 18, adult BMI cut-offs apply. For high school students, Japanese school health checks usually use the obesity degree (comparison with the standard weight for height).

How is a child's obesity degree calculated?

Obesity degree (%) = (measured weight − standard weight for height) ÷ standard weight for height × 100. The standard weight for height comes from sex- and age-specific coefficients. +20% or more counts as obese (20% to under 30% mild, 30% to under 50% moderate, 50% or more severe), and −20% or below as underweight.