Broca, 1871
height in cm − 100
The oldest and the coarsest. It does not read sex, and its gap with the other two widens as height moves away from the nineteenth-century average it was drawn on.
The tool
Ideal weight calculator
There is no ideal weight, there is a range. The calculation returns the interval that matches a normal build for a height, then the three historical formulas side by side, with their dates, and the gap that separates them.
No account, no sign-up, no cap. Measurements go in as pounds and feet or as kilos and centimeters, and they stay in the browser: nothing is sent, nothing is stored.
The measurements, then the result
The formulas
Three methods, three answers, and not one of them validated
They are almost always shown alone, without their name and without their date. Put side by side, they contradict each other plainly, and that is the most useful thing this question has to offer.
Lorentz, 1929
height − 100 − (height − 150) / 4 for men, / 2 for women
Broca corrected by a term that depends on sex. This is the number most calculators print under the words ideal weight, usually without naming the formula or giving its date.
Devine, 1974
50 kg for men, 45.5 kg for women, plus 2.3 kg per inch over five feet
The only one of the three with a real use, and it is not this one: in pharmacology it sets doses on a theoretical ideal body weight, for drugs that do not spread into fat tissue. It was never established to tell anyone what to weigh.
The case of Devine
The only one of these formulas that really serves does not serve this
The Devine formula was published in 1974 in a pharmacology paper, to work out a gentamicin dose. It is still used for that: some drugs do not spread into fat tissue, and their dosing is set on a theoretical ideal body weight rather than on measured weight.
It was never established to tell anyone what they should weigh, and the paper that publishes it makes no such claim. That is the best summary of this whole family of formulas: they have a use, and it is not the one they are found under online.
A height is not enough to settle a weight.
These formulas read one measurement, sometimes two. They ignore muscle mass, frame, age, weight history and everything a doctor looks at before talking about a target. Two people of the same height get the same number, whoever they are.
What does get measured is the trend: weight over several weeks, read next to what has been logged. That is the work Zemiam does, and it is why this page opens a question rather than closing one.
Questions
What comes up most often
How do you calculate an ideal weight?
There is no authoritative calculation, and that is the first thing to know. The three historical formulas return three different numbers for the same profile: for a man of 1.75 m, 5 ft 9 in, the gap between the highest and the lowest passes six kilos, around thirteen pounds.
The defensible answer is an interval: the one that puts body mass index between 18.5 and 25 for the given height. It is commonly twenty kilos wide, and it contains all three formula results.
What is the Lorentz formula?
Height in centimeters minus one hundred, minus a quarter of the gap to 150 in men, half of it in women. It dates from 1929 and corrects the Broca formula, published in 1871.
Below 1.50 m, 4 ft 11 in, its correcting term changes sign and the formula inverts: it then returns a higher weight than Broca, which it is supposed to pull down. This page still shows it, and flags that the height falls outside the ground the formula was established on.
Why do calculators disagree?
Because they apply different formulas without saying so. A site showing Lorentz and one showing Broca will be six kilos apart for the same person, each under the words your ideal weight.
None of them is wrong as arithmetic: they simply compute different things, all of them established on populations and periods that are not the reader's.
Is there an ideal weight for a woman, and one for a man?
The Lorentz and Devine formulas carry a separate term by sex, which gives lower results in women at equal height. Broca takes no account of it at all.
That distinction reflects an average difference in body composition observed at the scale of a population, not a personal target. The normal build range depends on height alone: body mass index does not read sex.
Does ideal weight account for muscle?
No, none of these formulas. They read height, and sometimes sex. A very muscular person and a sedentary one of the same height get exactly the same number.
It is the same limit as body mass index, and it is corrected the same way: by waist circumference, which says where the mass sits, and by a body composition measurement when one is available.
Is this calculation medical advice?
No. It applies published formulas to a typed height, and it shows how far apart they are. A desirable weight is discussed with a doctor, who accounts for age, weight history, body composition and medical background.
These formulas suit neither children, nor teenagers, nor pregnancy, and were never established in older adults.
Sources
- The origin of the Devine formula, published to adjust a drug dose. Devine BJ. “Gentamicin therapy”. Drug Intelligence and Clinical Pharmacy, 1974, volume 8, pages 650 to 655.
- The review that traces where these equations came from, and the absence of clinical validation. Pai MP, Paloucek FP. “The origin of the ‘ideal’ body weight equations”. The Annals of Pharmacotherapy, 2000, volume 34, pages 1066 to 1069.
- The classification the normal build range is drawn from. World Health Organization. “Obesity: preventing and managing the global epidemic”. WHO Technical Report Series 894, Geneva, 2000.
This page applies published formulas to a typed height and shows how far apart they land. It replaces neither a doctor nor a dietitian, and it suits neither children, nor teenagers, nor pregnancy.
Next
The two questions, better asked
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A day's calorie needs and how they split into protein, carbs and fat, for losing weight, holding steady, or gaining.
OpenBMI calculator
Body mass index, the WHO category it falls into, and the weight range that matches a normal build for a given height.
OpenA weight is measured as a trend, not as a formula.
In Zemiam, weight is followed over several weeks next to what has been logged, and the target resets on measured expenditure rather than on an equation.