Four Formulas Give Four Different Answers for Ideal Weight. None of Them Were Designed for Fitness.
What does a 5-foot-9 man weigh at his ideal body weight? The answer depends entirely on which formula you ask.
The Hamwi formula, developed by Dr. G. J. Hamwi in 1964, says 172 pounds. The Devine formula, published by B. J. Devine in 1974, says 167 pounds. The Robinson formula from 1983 says 163 pounds. The Miller formula, also from 1983, says 159 pounds. Four formulas, four answers, a 13-pound spread between the highest and lowest, and not one of them was originally designed to tell you what you should weigh.
That last point is the one that tends to surprise people. These formulas appear on health websites, gym apps, and nutrition calculators described as targets. Their origins are entirely different. Understanding where they came from explains what they are measuring and why the range they produce is a rough orientation rather than a precise individual target.
The Clinical Origins of Ideal Body Weight Formulas
The Hamwi formula was developed by Dr. G. J. Hamwi, an endocrinologist, and published in 1964 in a journal on diabetes management. His intent was to give physicians a quick way to estimate appropriate weight for hospitalized patients so that drug doses, fluid volumes, and nutritional requirements could be calculated from a standardized baseline. The formula, which starts at 100 pounds for a woman 5 feet tall and adds 5 pounds per inch above 5 feet (106 pounds for a man, adding 6 pounds per inch), was never validated as a health target. It was a convenient approximation for a dosing reference.
The Devine formula was published in 1974 by Dr. B. J. Devine in an article specifically about gentamicin dosing. Gentamicin is an antibiotic whose effective dose is highly sensitive to body size. A dosage calibrated for a 200-pound patient that is administered to a 140-pound patient can cause kidney toxicity. Devine needed a formula that could be quickly applied to body size for pharmacokinetic calculations. The formula he published (45.5 kg plus 2.3 kg per inch above 5 feet for women, 50 kg plus 2.3 kg per inch for men) was adopted in hospital pharmacy practice and then migrated into health calculators with the original context stripped away.
The Robinson and Miller formulas, both published in 1983, drew from actuarial data in the Metropolitan Life Insurance tables. Metropolitan Life had published height-weight tables in 1943 and revised them in 1959 and 1983, based on mortality statistics from their policyholders. The tables showed which weight ranges were associated with longer life among insured individuals. Robinson et al. and Miller et al. used this actuarial data to derive formulas producing similar outputs. The question those formulas answered was not "what weight is optimal for health" but rather "at what weight do MetLife policyholders statistically survive longer."
The MetLife policyholders of the mid-twentieth century were not representative of the general population. They were disproportionately white, educated, and economically stable, all of which correlate independently with longevity. The mortality associations in the data reflect the demographics of who bought life insurance from a specific company in specific decades, not universal biological optima.
What the Formulas Ignore
All four formulas use only two inputs: height and sex. They ignore muscle mass, bone density, age, adipose tissue distribution, and metabolic health markers. This means a 165-pound man who is a competitive swimmer with 8 percent body fat and a 165-pound man who is sedentary with 30 percent body fat receive identical results from every formula. Their physiology is dramatically different; their ideal body weight number is the same.
The limitation is inherent to the design intent. In a hospital pharmacy setting, you need a formula that a technician can apply in thirty seconds from data already in the patient's chart. Height and sex are recorded on admission. Dexa scans and body composition measurements are not. The simplicity of the two-input formula is not a flaw for its intended use case. It becomes a problem when the output is recontextualized as a personal fitness target.
Body mass index, which is weight in kilograms divided by height in meters squared, was developed by Belgian mathematician Adolphe Quetelet in the 1830s as a tool for population statistics, not individual health assessment. Quetelet explicitly intended it as a measure of the "average man" for social science purposes. The BMI was later adopted by insurance companies and public health agencies as a population screening tool. Its limitations for individual assessment, including its failure to distinguish fat mass from muscle mass and its poor performance across different ethnic groups, have been extensively documented in the medical literature since the 1990s.
Comparing the Four Formulas at Different Heights
The formulas agree most closely at average heights and diverge as height increases. For a 5-foot-6 woman, the four formulas produce a range of approximately 130 to 140 pounds. For a 6-foot-2 man, they diverge by nearly 20 pounds.
The divergence comes from different per-inch increments. Devine adds 2.3 pounds per inch above 5 feet. Robinson adds 1.7 pounds. Miller adds 1.8 pounds. Hamwi adds 5 or 6 pounds per inch, which produces the highest estimate at every height above average. At 5 feet, the formulas agree exactly because they are all anchored to the same starting point. At 6 feet and above, the different increments compound.
For clinical use, the formulas remain appropriate because they are standardized and fast to calculate. A hospital pharmacist computing a creatinine clearance or an antibiotic dose does not need the most accurate possible estimate of ideal weight; they need a consistent calculation that produces defensible, reproducible results. All four formulas meet that standard.
What Current Clinical Guidelines Say
The World Health Organization's weight classification system uses BMI ranges (18.5 to 24.9 for normal weight) as a population health screening tool and explicitly acknowledges that these ranges do not account for the health effects of varying fat distributions, particularly the difference between abdominal fat and peripheral fat. The WHO notes that the same BMI can represent meaningfully different health risks depending on where fat is distributed.
More recent clinical guidance has moved toward waist circumference and waist-to-height ratio as better individual metabolic risk predictors than weight or BMI alone. A waist circumference above 102 centimeters in men and 88 centimeters in women is associated with increased cardiovascular risk independent of total weight. The waist-to-height ratio below 0.5 is a simple threshold used in several national health guidelines as a screening criterion for metabolic syndrome risk.
Neither the ideal body weight formulas nor BMI captures this information. They measure size but not shape, and current evidence suggests that shape is the more predictive variable for individual metabolic health.
How to Use the Results
The ideal weight calculator showing results across all four formulas is not producing four competing answers that disagree. It is showing the range of a parameter that has always been an approximation rather than a precise measurement. The spread between formulas gives you a range to interpret rather than a target to hit.
Conclusion
For someone using these numbers for general health context, the relevant information is whether their current weight is substantially above or below the entire range, not whether it hits a specific formula's output. A person 80 pounds above the highest formula output and a person 2 pounds above the lowest are not in the same situation, and treating both as "above ideal weight" misses that distinction.
The formulas are most useful as a starting point for a conversation with a clinician who can add the information the formulas cannot capture: body composition, metabolic markers, family history, and the specific health goals that make a weight target meaningful for a particular person.
Frequently Asked Questions
Which ideal weight formula is most accurate?
None was designed for fitness accuracy. Devine and Hamwi were for drug dosing. Robinson and Miller used insurance mortality tables. They are useful as clinical references, not personal weight targets.
Why do ideal weight formulas only use height and sex?
They were built for quick clinical calculations where only height and sex are readily available. They do not account for muscle mass, bone density, age, or body composition.
How much do the four ideal weight formulas differ?
For a 5-foot-9 man, the spread between the highest and lowest formula is about 13 pounds. The gap grows larger for taller individuals because each formula uses a different per-inch increment.