Ideal Body Weight Formulas Compared: Why Four Equations Give Four Answers

Feed a height of 178 cm into the four ideal body weight equations in common use and you get 73.2 kg from Devine, 71.1 from Robinson, 70.4 from Miller and 75.2 from Hamwi. Nearly five kilograms separate the highest from the lowest, for the same man, on the same day.

The disagreement is not a sign that three of them are broken. It is a sign that the question they were built to answer is not the question most people are asking them. None of these equations was derived from health outcomes, none was validated against mortality or morbidity data, and the oldest and most influential of them was written to standardise a pharmacy calculation.

Where the equations came from

Devine published his formula in Drug Intell Clin Pharm (1974), and its purpose was drug dosing. Certain medications, gentamicin among them, distribute mainly through lean tissue rather than fat, so a dose calculated from total body weight will overshoot in a patient carrying substantial adipose mass. Devine needed a standardised weight-for-height figure to normalise the calculation. He did not derive it from a study of healthy weight, and he did not claim it described one.

Robinson and colleagues (1983) and Miller and colleagues (1983) both published revisions in the same year, adjusting the constants against different reference data and producing systematically different results. Hamwi's version dates to 1964 and came out of clinical dietetics, where it was used to set weight targets in diabetes management. It is still the one many dietitians reach for first, largely through institutional habit.

All four share a structure. Each specifies a base weight at 5 feet, or 152.4 cm, then adds a fixed increment per inch above that. The Devine formula for men is the canonical example: 50 kg plus 2.3 kg for each inch over 5 feet. What differs between the four is the base and the increment, and those two constants are the entire source of the disagreement.

Read the increments and the pattern of disagreement becomes predictable. Hamwi has the lowest base and the steepest slope; Miller has the highest base and the shallowest. They must cross somewhere near 5 feet and diverge in both directions from there.

The divergence grows with height

At exactly 152.4 cm, the increment terms vanish and only the bases remain. Our ideal weight calculator returns 48.0 kg from Hamwi, 50.0 from Devine, 52.0 from Robinson and 56.2 from Miller for a man of that height. The spread is 8.2 kg, and Miller is the highest of the four.

At 178 cm, the ordering has already reshuffled: Miller has fallen to the lowest at 70.4 kg and Hamwi has risen to the highest at 75.2, a spread of 4.8 kg. At 193 cm the same tool gives 78.7 kg from Miller and 91.2 from Hamwi, a spread of 12.5 kg. The equation that ran highest for a short man runs lowest for a tall one by a wide margin.

For women the pattern is similar but the crossover sits differently. At 150 cm the calculator gives 45.5 kg from both Devine and Hamwi against 53.1 from Miller, a spread of 7.6 kg. At 173 cm the four converge remarkably tightly, at 62.8, 63.3, 64.1 and 64.2 kg, a spread of under a kilogram and a half. That convergence is coincidence rather than agreement. Four lines with different slopes will intersect somewhere, and near 173 cm is where these happen to.

The practical reading is that the closer you are to 5 feet or to the incidental crossover points, the more the equations agree, and the further from them, the less. Agreement between them at your particular height is not evidence that they are right.

What these numbers cannot tell you

Every ideal body weight equation takes exactly two inputs: height and sex. That is the whole of its knowledge about you.

It does not know your body composition. Two men of 178 cm and 82 kg sit equally far above the Devine figure of 73.2 kg, whether one is at 9% body fat and the other at 25%. Our body fat calculator separates them; the ideal weight equations cannot, because there is no term in which the difference could appear.

It does not know your frame. Skeletal dimensions vary substantially between adults of the same height, and a broader frame carries more bone and more supporting tissue at any body composition. Some older clinical practice applied a rough adjustment of roughly ten per cent up or down based on wrist circumference or elbow breadth, which acknowledges the problem without solving it particularly well.

It does not know your age, your ethnicity, your training history or anything about your health. And its treatment of sex is a single constant difference in the base weight, which is a crude summary of a genuine average difference in body composition rather than a description of any individual.

The consequence is a systematic failure with muscular bodies. A man of 183 cm and 88 kg carrying 12% body fat exceeds his Devine figure of 77.7 kg by more than ten kilograms while being, by any reasonable reading of his composition, lean. The number is arithmetically correct and substantively meaningless.

The height floor, and what happens below it

All four equations are constructed from 5 feet upward. Below 152.4 cm there is no defined increment to subtract, and the equations simply do not apply. Some implementations extrapolate downward by continuing the slope into negative inches, which produces a number without producing a meaningful one, since nothing in the derivation supports it.

Our ideal weight calculator clamps the increment at zero rather than extrapolating, so a height below 5 feet returns the base weights. Those figures should be read as the floor of the equations rather than as an estimate for that person. For adults shorter than 152.4 cm, a healthy BMI range computed from actual height is the more defensible reference, and clinical dosing in that group is a matter for a pharmacist or physician working from established paediatric and adult adjustment practice rather than a consumer tool.

The range that does the job better

The reason these equations persist is that they produce a single number, and a single number feels actionable. That is also precisely their weakness, because the evidence does not support a point target.

A healthy BMI range does. The WHO thresholds in Technical Report Series 894 (2000) place the healthy band between 18.5 and 25.0, and inverting that for a height gives a weight range rather than a value. For 178 cm, our calculator reports 58.6 to 78.9 kg. All four ideal weight figures for that height fall inside it, which is reassuring about the equations and revealing about their precision: they are locating a point within a span twenty kilograms wide and disagreeing by five in the process.

The range has an evidence base the equations lack. The Prospective Studies Collaboration pooled fifty-seven studies covering close to 900,000 adults in the Lancet (2009) and found all-cause mortality lowest between roughly 22.5 and 25.0, and the Global BMI Mortality Collaboration replicated the shape across more than ten million participants in the Lancet (2016). No comparable literature underwrites any ideal weight equation, because none was built to be tested that way.

The range needs its own qualification. The WHO Expert Consultation reported in the Lancet 363:157-163 (2004) that people of Asian descent carry higher body fat and greater cardiometabolic risk at any given BMI, recommending additional action points near 23.0 and 27.5. Our BMI calculator reports both threshold sets side by side for that reason. And a BMI range inherits BMI's blindness to composition, which is the subject of body fat percentage vs BMI.

Where these formulas are still the right tool

Dropping them entirely would be an overcorrection, because the original use case is unchanged and still important.

Clinical drug dosing continues to rely on them. For medications with narrow therapeutic windows that distribute through lean tissue, dosing on total body weight risks toxicity in patients carrying substantial fat mass, and ideal body weight or an adjusted body weight derived from it remains standard practice. Ventilator tidal volume settings are calculated from predicted body weight for a related reason: lung volume scales with height and sex, not with adiposity. Renal function estimates and some chemotherapy protocols use similar adjustments.

In each of those cases the equation is doing what Devine designed it for, which is standardising a physiological quantity against height. Nobody using it that way believes it describes a patient's healthy weight, and the fact that four versions disagree by a few kilograms matters much less when the output feeds a dose calculation with its own tolerances.

What to use instead if you want a target

If you are trying to decide what you should weigh, three things are more useful than any of these four numbers.

Start with the healthy BMI range for your height, treating it as a wide band rather than a target, and note that its upper portion is where much of the mortality data sits most favourably. Then add a waist measurement, because where fat sits carries risk that weight cannot capture; keeping waist under half your height is the simplest version, set out in waist-to-height ratio explained. Finally, if you train, use body composition rather than weight as the thing you are steering, since a weight that holds steady while composition improves is a good outcome that any weight target would score as failure. That situation is common enough to have its own name, covered in body recomposition explained.

The honest summary is that there is no ideal body weight for an individual, and the four equations are best understood as historical artefacts that happen to remain useful in pharmacy. Presenting all four together, as our calculator does, is the only responsible way to show them: seeing them disagree by five kilograms is the most informative thing about them. Where the question is genuinely clinical, whether about a target weight or a medication dose, it belongs with a clinician who can see far more than height and sex.