Calculate your ideal body weight with the Broca Index — one of the oldest and simplest height-to-weight formulas. Free online tool with sex adjustments.
The Broca Index Calculator uses one of medicine's oldest ideal-body-weight formulas, published by French surgeon Paul Broca in 1871. The original formula is elegantly simple: ideal weight (kg) = height (cm) − 100. Over the decades clinicians refined it with sex-based adjustments — subtracting 10% for men and 15% for women — to better reflect differences in body composition.
Although modern evidence-based formulas like Devine, Robinson, and Miller have largely replaced the Broca Index in clinical dosing, it remains widely taught in medical schools around the world and is still referenced in European and Asian clinical guidelines as a quick mental estimate. Its greatest strength is its ease of memorization: no calculator needed, just subtract 100 from your height in centimeters.
This tool computes the original Broca value, the sex-adjusted version, and a common modified form, then compares them with your actual weight so you can see at a glance how you measure up against this historic benchmark.
The Broca Index offers an instantly memorable rule of thumb that requires no technology — useful in emergency rooms, field clinics, and situations where quick estimates are needed. While it lacks the precision of modern formulas, its simplicity makes it a helpful sanity check. Comparing Broca's estimate alongside more refined formulas helps you understand the range of "ideal weight" predictions and why no single number is definitive.
Original Broca Index: Ideal Weight (kg) = Height (cm) − 100 Sex-Adjusted Broca: Male: Ideal Weight = (Height − 100) × 0.90 Female: Ideal Weight = (Height − 100) × 0.85 Modified Broca (Brugsch variant): Height < 165 cm: Ideal = Height − 100 Height 165–175 cm: Ideal = Height − 105 Height > 175 cm: Ideal = Height − 110 Deviation = (Actual Weight − Ideal Weight) / Ideal Weight × 100%
Result: Original: 75.0 kg | Adjusted: 67.5 kg | Modified: 70.0 kg
A 175 cm male has an original Broca ideal weight of 175 − 100 = 75.0 kg. The sex-adjusted (male) value is 75.0 × 0.90 = 67.5 kg. The modified Brugsch variant for heights 165–175 cm gives 175 − 105 = 70.0 kg. At 80 kg actual weight, the person is about 6.7% above the original estimate and 18.5% above the sex-adjusted estimate.
Paul Broca proposed his ideal weight formula in an era when anthropometry — the systematic measurement of the human body — was a cutting-edge science. Published in 1871, the formula "height (cm) minus 100" was among the first quantitative attempts to define a healthy body weight. It predated BMI's widespread adoption by over 100 years and served as the primary clinical weight-assessment tool through much of the 20th century.
Over the decades, numerous clinicians modified the original formula. The most notable is the Brugsch modification, which adjusts the subtracted constant based on height, and the sex adjustments (0.90 for men, 0.85 for women) that became standard in Central European clinical practice. Some Asian medical traditions subtract 105 or even 110 uniformly, reflecting differences in average body frame.
The Broca Index's greatest strength is its simplicity: it can be calculated mentally in seconds without any tools. Its main weakness is that it does not account for body frame, age, muscle mass, or ethnicity. For individuals at the extremes of the height distribution, it produces notably inaccurate estimates. Nevertheless, its cultural persistence and ease of use ensure it remains part of the medical lexicon.
Today the Broca Index is best understood as a historical benchmark rather than a clinical tool. When used alongside Devine, Robinson, Miller, and Hamwi formulas — plus BMI and body composition measurements — it provides useful context and illustrates how our understanding of ideal weight has evolved over 150 years of medical science.
Paul Broca (1824–1880) was a French physician and anthropologist best known for discovering the brain's speech production area (Broca's area). He proposed the height-minus-100 ideal weight formula in 1871 as part of his anthropometric research. It became one of the most widely used weight-height formulas in medicine for over a century.
While it has been largely replaced by evidence-based formulas (Devine, Hamwi) for drug dosing and nutritional assessment, the Broca Index is still taught in medical education and used in some European and Asian clinical guidelines as a rapid estimation tool. Its simplicity makes it valuable in resource-limited settings.
The original Broca formula gives the same ideal weight for men and women of the same height. Since women typically have a higher percentage of body fat and lower lean mass than men, the sex adjustment (0.90 for men, 0.85 for women) was introduced to give more realistic targets. The adjustments reduce the ideal weight, reflecting that even at optimal body composition, average frame and lean mass differ by sex.
BMI uses weight/height² and classifies ranges (18.5–24.9 = normal), while the Broca Index predicts a single ideal weight. For a height of 170 cm, Broca gives 70 kg ideal weight, which corresponds to a BMI of about 24.2 — near the upper boundary of normal. The two methods generally agree for average heights but diverge for very tall or short individuals.
The Brugsch modification adjusts the amount subtracted based on height range: subtract 100 for heights under 165 cm, 105 for heights 165–175 cm, and 110 for heights over 175 cm. This attempts to account for the fact that taller people carry proportionally less weight per centimeter of height, producing more realistic estimates than the flat subtraction of 100.
No. For someone 200 cm tall, the original Broca formula gives 100 kg as ideal weight, which corresponds to a BMI of 25 — borderline overweight. The modified Brugsch variant partially addresses this by subtracting 110 for tall individuals, but even 90 kg may be high. Modern formulas handle extreme heights more accurately.
The Broca Index was designed for adults. Children's ideal weights are assessed using age- and sex-specific growth charts (CDC or WHO percentile charts). Applying Broca's formula to children would produce meaningless results because children's height-weight relationships differ fundamentally from adults.
A deviation of ±10% from the Broca ideal is generally considered within normal limits. Deviations of 10–20% above suggest overweight status, while more than 20% above may indicate obesity. Below −10% suggests underweight. These are rough guidelines — actual health status depends on many factors the formula doesn't capture.