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 is a historical ideal-body-weight formula that subtracts a fixed amount from height in centimeters. It is simple to calculate and still appears in some clinical and educational references, but it is best treated as a rough benchmark rather than a modern standard.
This page shows the original formula, common sex-adjusted variants, and a modified version so you can compare how the historical estimates differ.
The Broca Index is useful as a quick historical reference. Comparing it with newer formulas helps show how much ideal-body-weight estimates can vary.
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.
The Broca Index is one of several historical height-based ideal-weight rules. It is best understood as a simple benchmark from an earlier era of anthropometry.
Over time, clinicians introduced sex and height adjustments to make the basic rule a little more usable, but the formula remains a rough estimate rather than a definitive standard.
Its main strength is simplicity. Its main weakness is that it does not account for frame size, body composition, or many other factors that affect weight.
Today the Broca Index is most useful when compared with newer formulas, not when treated as a standalone target.
Last updated:
This calculator applies the original Broca height-minus-100 rule and shows common sex-adjusted and height-band variants as historical reference forms. The page is intended to compare formulas, not to claim that one of them precisely defines a healthy weight.
Because Broca is a simple anthropometric rule, the result should be read as a rough estimate that can vary meaningfully from later formulas like Devine, Robinson, Miller, and Hamwi.
Broca is one of the oldest height-based ideal-weight formulas and is typically cited as a historical reference rather than a current standard.
Broca is still useful as a historical comparison because of its simplicity, but newer formulas are usually preferred for practical use.
Sex-adjusted variants were introduced to make the original fixed-height rule a little closer to common clinical expectations, but they remain rough adjustments rather than validated targets.
BMI and Broca answer different questions. BMI classifies weight-for-height ranges, while Broca produces a single reference weight.
The Brugsch variant changes the amount subtracted by height band. It is a historical modification, not a universally accepted standard.
No. The formula becomes less useful at very tall or very short heights, which is one reason modern equations are often preferred.
It was designed for adults. Children should be assessed with age- and sex-specific growth references instead.
A small deviation from any historical ideal-body-weight formula is common. Broca should be interpreted as a rough reference rather than a strict threshold.