An ideal body weight formula turns height and sex into a single weight: a fixed figure at five feet (152.4 cm) plus so much for every inch above it. Four are in common use, named for Devine, Robinson, Miller and Hamwi. Three came out of drug-dosing work; Hamwi's comes from a 1964 diabetes diet text. We ran all four at every whole centimetre from 153 to 195 cm, with the rounded constants most calculators print. For men they come within 1.2 kg of each other at 168 cm and end 13.9 kg apart at 195 cm. For women the closest point is 173 cm, at 1.4 kg, and the widest gap is 8.2 kg at 195 cm. Below 152.4 cm none is stated to apply, yet each still returns a number.
Around 165 cm the Robinson, Devine and Hamwi lines cross for men
Every figure here uses the constants in Table 3 of Peterson and colleagues' 2016 paper. With them, Robinson's men's line (52 kg plus 1.9 kg per inch) and Devine's (50 kg plus 2.3 kg) meet at 165.1 cm and 61.5 kg. Hamwi's, published in pounds (106 lb plus 6 lb per inch), crosses Devine at 164.0 cm and Robinson at 164.5 cm.
The near-meeting belongs to the rounding. Robinson's own abstract gives 51.65 kg plus 1.85 kg per inch for men, and with that the three lines share no point. For women, Devine and Hamwi run almost side by side, 0.1 to 0.7 kg apart. The gap below is the highest of the four formulas minus the lowest.
| Height (cm) | Gap for men (kg) | Gap for women (kg) |
|---|---|---|
| 153 | 7.8 | 7.5 |
| 160 | 4.2 | 5.0 |
| 168 | 1.2 | 2.2 |
| 173 | 2.7 | 1.4 |
| 180 | 6.1 | 3.0 |
| 195 | 13.9 | 8.2 |
Below five feet the formulas still produce a number
Peterson states the 60-inch limit for Devine and Hamwi, Robinson's slope is per inch "greater than 5 feet", and Sawyer and colleagues found in 1983 that IBW was "not appropriate in patients less than 60 inches tall". The arithmetic does not stop there. Extended down, Devine's women's formula gives 34.3 kg at 140 cm, a BMI of 17.5, under the 18.5 line where WHO's normal range begins. At 50 cm the lines go negative. MDCalc gives a modification for patients under five feet, subtracting 2 to 5 lb per inch, which it sources to a 2018 written communication.
Until 18 October 2026 our ideal weight calculator extended them, printing that 34.3 kg for a 140 cm woman and a negative range at 50 cm. Its "ideal range", the four formulas' average plus or minus 5%, had a top edge above BMI 23 for men at every height from 149 cm, and its worked example gave Robinson 66.5 kg for a 170 cm man. The revision made that day refuses heights under 100 cm, shows only the BMI band below 152.4 cm, and lists the four results as reference figures with the gap between them and no verdict on anyone's weight. At 170 cm it gives Robinson's 65.2 kg for men and 60.8 kg for women.
In life-insurance tables an ideal weight meant the longest expected life
Peterson and colleagues write that IBW "or desirable weight was originally defined as the weight associated with the greatest life expectancy at each height". Pai and Paloucek's 2000 review traces the terms desirable and ideal to height-weight tables whose weights "were found to correlate with mortality".
The dosing use came later. "Devine 1974" is a case study, "Case Number 25 Gentamicin Therapy", in Drug Intelligence & Clinical Pharmacy, with Margaret McCarron as first author and Ben Devine second; we could not open it. Robinson and colleagues titled their 1983 paper "Determination of ideal body weight for drug dosage calculations" and built it on Metropolitan Life Insurance tables, the 1959 edition according to Peterson. Miller's constants come from a 1983 letters exchange in the same journal, and Hamwi's from a 1964 American Diabetes Association book. We read neither; their constants rest on Peterson's table.
On the BMI scale Devine and Hamwi imply leaner short women and heavier tall men
A formula's weight divided by height squared gives the BMI it implies. From 153 to 195 cm, by our arithmetic, Devine's men's line rises from BMI 21.6 to 23.3 and Hamwi's from 20.8 to 24.6. For women both start near 19.6 and reach about 22. Robinson stays between 22.1 and 22.6 for men. Miller runs the other way for men, from 24.2 down to 21.0.
Shah, Sucher and Hollenbeck reported the pattern in 2006: "for shorter heights the formulas were closer to BMI 20 kg/m2 and for taller heights, were closer to BMI 25". Peterson's Table 4 gives each formula's best-fit BMI, which our figures reproduce.
Within Singapore's health survey the moderate-risk line is a BMI of 23
The Ministry of Health's National Population Health Survey 2022 uses WHO's "Normal weight 18.5 – 24.9" and, in a second table, labels 18.5 to 22.9 "Low risk", 23.0 to 27.4 "Moderate risk" and 27.5 and above "High risk", citing the WHO expert consultation of 2004. That consultation found the cut-off for observed risk "varies from 22 kg/m2 to 25 kg/m2 in different Asian populations". Its history is in our guide to BMI, BMR and TDEE with Asian cut-offs.
The average of the four formulas implies BMI 22.2 to 22.9 for men and 20.8 to 21.3 for women from 153 to 195 cm, by our arithmetic, inside the survey's "Low risk" band. Single men's formulas pass 23 at some heights; no women's formula reaches it.
Near modelled average heights women see the widest gap between formulas
We found no Singapore or Malaysia survey publishing a mean adult height. The NCD-RisC collaboration's 2020 Lancet dataset gives modelled estimates for 19-year-olds in 2019. They are model outputs for one age group rather than survey means.
| Modelled 19-year-olds, 2019 | Height (95% interval) | Gap between the four formulas |
|---|---|---|
| Singapore, men | 173.5 cm (171.4–175.8) | 2.9 kg |
| Malaysia, men | 169.2 cm (167.7–170.7) | 1.5 kg |
| Singapore, women | 161.3 cm (159.5–163.2) | 4.6 kg |
| Malaysia, women | 157.1 cm (155.9–158.3) | 6.1 kg |
The Malaysian women's modelled 157.1 cm sits less than 5 cm above the five-foot floor, where the women's gap is already 7.7 kg.
Across every height the formulas read nothing but height and sex
None of the four asks about frame, age, muscle or fat; Robinson's abstract gives its equations "for men of all frame sizes" and likewise for women. Pai and Paloucek concluded that "the similarity between the IBW equations was a result of the general agreement among the various height-weight tables from which they were derived", and went on: "Therefore, any one of these equations may be used to estimate IBW." That verdict appeared in a pharmacy journal, where IBW is a dosing quantity, and the equations it calls interchangeable share the same two inputs.
These are published equations and survey categories, given as general information. Nothing here is medical or dietary advice, and no figure in it is offered as a target.
View author profile → · Editorial policy
