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Broca Formula – Calculate Your Ideal Body Weight

The Broca Formula is a simple method for estimating ideal body weight based on height. It is widely used as a quick reference in nutrition and general health counseling.

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Things worth knowing about "Broca Formula"

The Broca Formula is a simple method for estimating ideal body weight based on height. It is widely used as a quick reference in nutrition and general health counseling.

What Is the Broca Formula?

The Broca Formula is a classic method for estimating a person´s ideal body weight. It was developed in the 19th century by the French surgeon and anthropologist Paul Broca and remains one of the most widely known and straightforward tools for assessing body weight. The formula provides a reference value used in nutritional counseling and general health promotion.

How to Calculate Ideal Weight Using the Broca Formula

The basic formula is:

Ideal weight (kg) = Height (cm) − 100

For example, a person who is 175 cm tall would have an ideal weight of 75 kg.

Corrected Broca Index

Because the original formula is considered too simplistic, a corrected version that accounts for biological sex is often used:

Men: Ideal weight = (Height in cm − 100) × 0.9
Women: Ideal weight = (Height in cm − 100) × 0.85

This adjustment reflects the fact that women typically have a higher body fat percentage, while men tend to have greater muscle mass.

Weight Categories According to the Broca Formula

Based on the Broca Formula, the following weight categories can be defined:

Normal weight: within ± 10% of the calculated ideal weight
Overweight: more than 10% above the ideal weight
Obesity: more than 20% above the ideal weight
Underweight: more than 10% below the ideal weight

Advantages of the Broca Formula

The Broca Formula is particularly popular because it:

is very easy to calculate without any tools or devices,
requires no specialized equipment,
provides a quick first estimate of body weight status.

Limitations and Criticism

Despite its simplicity, the Broca Formula has notable limitations:

It does not account for body composition (muscle mass vs. fat mass), age, or body frame size.
Athletes with high muscle mass may be classified as overweight even though their body fat percentage is low.
It is not suitable for children and adolescents, who have their own growth-specific reference ranges.
Compared to the Body Mass Index (BMI), the Broca Formula is considered less precise and less scientifically validated today.

Broca Formula vs. BMI

The Body Mass Index (BMI) is currently the most widely used international method for classifying body weight. It is calculated by dividing body weight in kilograms by the square of height in meters (kg/m²). The World Health Organization (WHO) recommends the BMI as the standard classification tool, as it allows for better comparisons across different population groups. Nevertheless, the Broca Formula continues to be used as a simple rule of thumb in everyday practice.

Clinical Relevance

Although the Broca Formula is not a diagnostic tool, it is used in general health counseling, nutrition programs, and patient education. For a thorough medical assessment of body weight, it should always be supplemented by additional measurements such as BMI, waist circumference, or body fat analysis.

References

World Health Organization (WHO) -- Obesity: preventing and managing the global epidemic. WHO Technical Report Series, No. 894. Geneva, 2000.
Lenz M. et al. -- Overweight and obesity as independent diseases. Deutsches Ärzteblatt, 2009.
Wirth A., Hauner H. -- Adipositas: Ätiologie, Folgekrankheiten, Diagnostik, Therapie. Springer Medizin Verlag, 4th edition, 2013.

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