# Calculation of the Body Indices

In order to determine whether a body model deviates from the norm or also involves a health risk, various indices have been developed. These indices can indicate whether there is an overweight or underweight or a health risk. The indices use different input variables to close the body scheme. The simplest uses only weight and body size, e.g. The Ponderal Index. The body shape index is a major extension as it incorporates the waist circumference as an essential parameter. The waist circumference is a good indicator of fat distribution in the body. The weight itself does not tell whether the weight is in the form of muscles or in the form of abdominal fat or hypodermic fat.

On this page, the calculation formulas for the following body measure indexes are summarized: Body Mass Index (BMI), Broca Index, Ponderal Index, A Body Shape Index (BSI, ABSI), Waist-to-Size Ratio (WHtR)), Waist Hip Ratio (WHR).

## Body Mass Index (BMI)

The body mass index (BMI) is a measure that sets the weight in the ratio to the square of the body weights. The BMI is a rough guide because it does not take into account either stature or weight distribution. Since the beginning of the 1980s, the BMI has also been used by the World Health Organization. The present BMI classification of the WHO has essentially existed since 1995.

$\mathrm{BMI}=\frac{m}{{L}^{2}}$

with m : Body Weight in kg, L : Body Height in m

## Broca Index (BI)

$\mathrm{BI}=\frac{m}{{L}^{3}}$

with m : Body Weight in kg, L : Body Height in m

## Ponderal Index (PI)

$\mathrm{PI}=L-100$

with L : Body Height in cm

## Body Shape Index (BSI oder ABSI)

The Body Shape Index (ABSI) says something about the body sheer division. The higher the ABSI, the higher the proportion of abdominal fat compared to other body parts such as musculature or under-skin fat on arms, legs or upper body.

$\mathrm{ABSI}=\frac{U}{{\mathrm{BMI}}^{\frac{2}{3}}\cdot \sqrt{L}}$

with U : Waist Size in m, L : Body Height in m and the BMI : Body Mass Index

The risk index ADSIz is calculated using the empirically determined table values for the ABSI for men and women.

$\mathrm{ABSIz}=\frac{\mathrm{ABSI}-{\mathrm{ABSI}}_{\mathrm{mean}}\left(\mathrm{Alter}\right)}{{\mathrm{ABSI}}_{\mathrm{std}}\left(\mathrm{Alter}\right)}$

with the indices mean : Average and std : Standard Deviation

## Area Mass Index (AMI)

The area mass index (AMI) is a characteristic of anthropometry and represents the ratio of the body mass of a person measured in kilograms (kg) to its actual body surface measured in m², And the sex of a person. The body surface of a person is at the same time the area of ​​his heat exchange with the environment. The heat generation of man, which is necessary for the maintenance of the body temperature, depends on the mass, or rather, on the mass of the muscle. The ratio of body mass to body surface is not constant but is determined by the body shape. Impacted bodies always have a much smaller body surface area per kg body mass than lean body shapes. To this extent, lean body shapes give considerably more energy in the form of heat to the environment than compact ones, provided that the conditions of the heat exchange (ambient temperature, insulation by clothing, etc.) are identical.

AMI for Woman:

$\mathrm{AMI}=0.865\frac{m}{{L}^{2}}-18.65$

AMI for Man:

$\mathrm{AMI}=1.048\frac{m}{{L}^{2}}-16.08$

with m : Body Weight in kg, L : Body Height in m

## Waist-to-Height Ratio (WHtR)

WHtR (waist-to-height ratio) is the ratio between waist circumference and body size. It is to make a statement about the distribution of the body fat and thus allow a greater meaningful weight regarding the health relevance of overweight. For under-40s, a value above 0.5 is critical. Between 40 and 50, the liwith is between 0.5 and 0.6, and over 50 is 0.6.

$\mathrm{WHtR}=\frac{U}{L}$

with U : Waist Size , L : Body Height

## Waist-to-Hip Ratio (WHR)

The Waist-Hip Ratio (Waist-to-Hip Ratio) (WHR) ratio is the ratio between waist and hip circumference. In sports medicine, the quotient of the circumference of the abdomen and hip circumference is also referred to as HBU. The circumference of the belly is measured in the middle between the pelvic crest and the ribs parallel to the floor. The hip circumference is the greatest measure above the buttocks. The DGSP provides the following values for the HBU in the guideline Precautionary Survey in Sport: Women: Normal weight < 0.8; Overweight 0.8-0.84; Obesity > 0.85. Men: Normal weight < 0.9; Overweight 0.9-0.99; Obesity > 1.0

$\mathrm{WHR}=\frac{U}{H}$

with U : Waist Size , H : Waist Circumference

## Basic consumption, Performance consumption und Sports consumption

The entire energy conversion consists of several components. The basic conversion describes the energy expenditure to maintain body temperature and basic body functions. In addition, there is the performance turnover reflecting the expenditure on activities and the sports turnover.

Reduced mass for a BMI from 30 kg/m2

${m}_{r}=\frac{3\left(L-100\right)+m}{4}$

with mr : Reduced Body Weight in kg, m : Body Weight in kg, L : Body Height in cm

Basic consumption GU

$\mathrm{GU}=10m+6.35L-5a+s$

with GU : Basic consumption in kcal, m : Body Weight in kg, L : Body Height in cm, a : Age in years, s specific gender value s= 5 Man and s= -161 Woman

Performance consumption LU

$\mathrm{LU}=\left(\frac{\sum {\mathrm{PAL}}_{i}\cdot {h}_{i}}{\sum {h}_{i}}-1\right)\mathrm{GU}$

with LU : Performance consumption in kcal, GU : Basic consumption in kcal, PAL : PAL-Factor for the activity, h : Duration of the activity in hours

Sportumsatz SU

$\mathrm{SU}=\sum {\mathrm{MET}}_{i}\cdot {h}_{i}\cdot m$

with SU : Sports consumption in kcal, MET : MET-Factor for the activity, h : Duration of the activity in hours, m : Body Weight in kg

Total consumption GG

$\mathrm{GG}=\frac{\sum {\mathrm{PAL}}_{i}\cdot {h}_{i}}{\sum {h}_{i}}\cdot \mathrm{GU}+\mathrm{SU}$

Calculation of the Body Indices Calculator for the Body Indices BSI Calculator BMI Calculator AMI Calculator Broca Calculator Ponderal Calculator