Broca, Devine and BMI: The Ideal-Weight Formulas Compared
Three formulas, three results — and all claim to calculate "ideal weight". No wonder the confusion is great. In this article we place Broca, Devine and the BMI healthy-weight range side by side: how do they calculate, where do they come from and when does each method make sense?
You will see the difference fastest by entering your own measurements in the <a href="/en/ideal-weight-body-fat-calculator">ideal weight and body fat calculator</a> — all three methods appear at once there, along with body fat percentage.
Broca: The Mental-Arithmetic Formula
Broca is the simplest of the three: normal weight equals height in centimetres minus 100. From normal weight you subtract about 10 percent for men and about 15 percent for women to get the ideal weight. The formula is over 150 years old and comes from a time without calculators — its strength is simplicity, its weakness imprecision. Beyond roughly 160 to 185 cm it quickly becomes unrealistic.
Devine: Sounds Precise, Meant for Medicine
The Devine formula seems more exact because it works with decimals and inches. For men it begins at 50 kg for 152 cm and adds 2.3 kg per inch above that; for women at 45.5 kg. It was developed in 1974 for drug dosing, not as a life ideal. That explains why it is popular in pharmacology, but as a personal goal it calculates past muscle and stature just as Broca does.
The BMI Range: A Band Instead of a Number
The BMI method takes a different path. Instead of a single figure it gives a range: all weights that lead to a BMI between 18.5 and 24.9 count as normal weight. For 175 cm that is about 57 to 76 kg. This band is the internationally recognised reference of the World Health Organization and the reason the calculator highlights it as the recommended value.
The Direct Comparison of Numbers
Take a person of 175 cm. Broca calculates a normal weight of 75 kg and an ideal weight of about 67.5 kg (man) or 63.8 kg (woman). Devine gives about 71 kg for a man. The BMI range runs from 57 to 76 kg. This single example already shows: the formulas can be ten kilos apart — and none is objectively "more correct" than the others. They answer different questions.
Which Method When?
For healthy everyday guidance the BMI range is the best choice, because it marks out a realistic band. Devine has its place in medicine. Broca is at most suitable as a rough mental calculation. For all of them: muscle mass, build and health cannot be captured by any of these formulas — for that you need body fat percentage or a medical assessment.
Conclusion
Broca, Devine and BMI are not competitors with a clear winner but tools with different purposes. Seeing them side by side, you quickly understand that "ideal weight" is not a fixed quantity. Try the comparison with your own values in the <a href="/en/ideal-weight-body-fat-calculator">ideal weight and body fat calculator</a> and use the result as a reference point, not a verdict.