The ideal weight calculator: where the formulas come from and what they cannot see
There is no such thing as an ideal weight: the name is given to the output of formulas derived from insurance height and weight tables, and the Devine formula was published to calculate drug doses. At 170 cm they give 60.7 to 70 kg, while a healthy BMI on the WHO scale corresponds to 53 to 72 kg.
What the calculator shows
The calculator asks for sex and a height from 140 to 220 cm. Its main answer is not a point but a range: the WHO healthy BMI limits, 18.5 and 24.9, multiplied by height squared. For 170 cm that is 53–72 kg. Below it are the formulas, each naming a single number inside the range or near it.
The result for a height of 170 cm, as the page calculates it:
| Formula | Men | Women |
|---|---|---|
| Devine (1974) | 65.9 kg (BMI 22.8) | 61.4 kg (BMI 21.2) |
| Robinson (1983) | 65.2 kg (BMI 22.6) | 60.8 kg (BMI 21.0) |
| Hamwi (1964) | 66.7 kg (BMI 23.1) | 60.7 kg (BMI 21.0) |
| Broca (1871), height minus 100 | 70 kg (BMI 24.2), one number for both sexes | |
The Miller formula (1983) is also on the page. All of them except Broca are built the same way: a base weight for a height of five feet (152.4 cm) plus an increment for each inch above. Below 152.4 cm the increment would go negative, so the calculator hides the formulas and shows only the range.
The coefficients on the page are rounded the way reference sources usually give them. In Robinson's original publication the figures are 51.65 kg plus 1.85 kg per inch for men and 48.67 kg plus 1.65 kg for women; the page uses 52 + 1.9 and 49 + 1.7. At 170 cm the difference is under a kilogram.
Where the formulas come from
The word “ideal” came from the insurance business. The review by Chichester, Holmes and Hubbard (2021) describes how US insurers collected clients' heights and weights and matched them with how long people lived. Metropolitan Life, together with the statistician L. Dublin, collected data on about four million policyholders, and its weight tables came out in 1942–1943. “Ideal” was the weight with the lowest mortality. The review's authors call the frame size used to split people in the tables arbitrarily defined. In the 1983 tables the words “ideal” and “desirable” were dropped because they were misinterpreted. In the 1959 and 1983 tables about 20% and 10% of the heights and weights were reported by the people themselves, not measured.
Tables are hard to memorize, and clinicians wanted simple formulas. Broca's “height minus 100” dates to 1871, Hamwi's to 1964: 106 pounds for a man five feet tall plus 6 pounds per inch above, and 100 pounds plus 5 for a woman. In kilograms the calculator writes this as 48 + 2.7 and 45.5 + 2.2. The Devine formula was printed in 1974 in an article on gentamicin dosing. In 1983 Robinson and colleagues derived their formula for drug dose calculations by regression on the Metropolitan Life tables. The 2021 review's authors write that Devine relied on scattered observations, while Robinson's regression gave a better-founded approach. In the same year Miller and colleagues recalculated the formula from the updated tables.
The formulas are close to each other not because they confirm each other. Pai and Paloucek (2000) explain the similarity by the fact that all were derived from the same height and weight tables. All the formulas therefore inherit the flaws of the tables.
Where the formulas part ways with BMI
The formulas do not track one BMI across heights. Broca gives a BMI of 23.4 at 160 cm, 24.7 at 180 cm and 24.9 at 190 cm: the taller the person, the closer the number to the upper limit of healthy. The women's Devine formula at the same 160 and 180 cm gives BMIs of 20.5 and 21.8. A comparison of formulas and tables with BMI by Shah and colleagues (2006) showed the same: for shorter people the formulas sit closer to a BMI of 20, for taller people closer to 25. The Robinson formula for men agreed best with BMI, while for women no formula came close to a BMI of 22. The authors conclude that BMI ranges would be more useful than formulas.
That is why the calculator puts the range above the formulas. It does not pick one of them: at 170 cm the spread between formulas is 60.7 to 70 kg, at 180 cm it is 67.5 to 80 kg, and the BMI range is wider than both (60–81 kg).
The “lowest mortality” criterion is disputed too
Even the original criterion remains a matter of debate. In the Global BMI Mortality Collaboration analysis (239 studies, 10.6 million participants; the main analysis covered never-smokers without chronic disease), mortality was lowest at a BMI of 20–25. The Flegal meta-analysis (2013) found a hazard ratio of 0.94 for a BMI of 25–30 relative to the 18.5–25 norm (95% CI 0.91–0.96). These describe groups. What to do about a particular person's build, muscle and illnesses does not follow from them. For the limits of BMI itself see the BMI calculator article and body mass index.
What the formulas cannot see
- Muscle and fat. People of the same height and weight differ in body composition. Waist circumference, body fat percentage and bioimpedance help estimate it; the site has a body fat calculator.
- Age. Age was removed from the Metropolitan Life tables: Dublin held that weight should not change once growth has ceased. The formulas inherited this. The calculator is for adults, and in older people weight is assessed together with a doctor.
- Background. A 2004 WHO consultation noted that in several Asian populations the risk of type 2 diabetes and heart disease is noticeable already below a BMI of 25. The 2021 review's authors cite work in which frame size differed markedly between people of European and African American descent.
- Health. Weight depends on more than height: medication, the thyroid and illness all affect it.
How to use the result
- Look at the range, not the point. WHO counts any weight inside it as healthy for adults, and where exactly depends on build and body composition.
- Read the formulas as history and as estimates used in other people's calculations: pharmacists and dietitians use them for dosing and feeding plans. They are not a goal for yourself.
- Do not fit your eating to a number. If your weight is far from the range, or a number from a formula has become a reason to change your food sharply, discuss it with a doctor first. The calculator says so itself.
- Watch the trend. A rise or fall over months says more than one weighing, and weight swings through the day.
When to see a doctor
- Your weight is falling although your eating and activity have not changed. The NHS advises seeing a doctor in that case.
- Your weight is well below or above the range and you do not know why.
- You are pregnant, or this is a teenager or a child: the calculator is not meant for them.
- Thoughts about the “right” number and about food have taken up too much room. That is a reason to see a doctor or a psychotherapist.
The calculator: ideal weight by height and sex. Alongside it are the BMI calculator and the article on daily calorie needs.
Frequently asked questions
- Which ideal weight formula is the most accurate?
- None measures health. All were derived from height and weight tables, which is why they resemble each other. In the 2006 comparison by Shah and colleagues, the Robinson formula for men agreed best with BMI, and for women no formula came close to a BMI of 22.
- Who came up with the Devine formula, and why?
- B. Devine published it in 1974 in an article on gentamicin dosing, for drugs dosed by “ideal” body mass. It was not created as a weight loss target. For men it is 50 kg plus 2.3 kg per inch above five feet, for women 45.5 kg plus 2.3 kg.
- Why do the formulas give different numbers?
- They were derived by different authors from different editions of the tables, and in the calculator the Broca formula is one for both sexes. At 170 cm the calculator gives values from 60.7 to 70 kg, while the healthy BMI range is wider: 53–72 kg.
- What is a healthy weight in the calculator?
- The BMI range of 18.5 to 24.9 on the WHO classification, converted to kilograms for your height. Any value inside it is healthy for an adult.
- Is the calculator suitable for athletes and older people?
- No, the formulas do not see muscle mass or age. In older people weight is assessed with a doctor; in athletes, body composition matters.
Read next
- The FoodGPT BMI calculator: how it works and what to do with the result — The BMI calculator divides weight in kilograms by height in meters squared and names a category from the WHO scale.
- Body mass index: how to calculate it and where it goes wrong — Body mass index takes ten seconds to calculate and is therefore used where it shouldn't be: for an individual.
- Excess weight and health: what risks are confirmed — This topic is usually presented in a way meant to induce fear.
- Smart scales: what bioimpedance actually measures — Smart scales display body fat percentage, water percentage, muscle mass, bone mass, and "metabolic age.
- Daily calorie intake — There is no universal norm: it depends on weight, height, age, sex, and activity level.
This article is for general information. It is not medical advice, a diagnosis, or a prescription for treatment or a diet, and it does not replace a consultation with your doctor. If you have a health condition, are pregnant, take medication, or follow a diet prescribed to you, decisions about food belong with your doctor.
Figures from regulations, guidelines and studies are given as they stood when this article was prepared and may since have changed; check them against the primary sources. This article is not advertising, an offer, or individual advice, and neither the author nor the site owner is responsible for decisions taken on the basis of it.