Where Ideal Body Weight Formulas Come From and Why They Give Different Results

The Devine, Robinson, Miller, and Hamwi equations are not health standards. They were never designed to tell a person what they should weigh. Each one was built for a specific clinical task: drug dosing, life insurance data smoothing, or diabetes management. They produce conflicting numbers for the same height because they used separate arithmetic, separate reference populations, and separate purposes. None of them was validated against longevity, metabolic health, or body fat percentage. The WHO BMI range of 18.5 to 24.9 comes from a separate tradition: population-level epidemiology, not individual prescription. This article traces each equation to its origin, compares the weight ranges they produce for a worked height example in both metric and imperial, and explains why they disagree with each other and with BMI-based ranges.

The Devine equation was published in 1974 by Dr. J. H. Devine in the journal Anaesthesia. Its purpose was to calculate a dosing weight for the antibiotic gentamicin. Devine needed a simple equation to estimate lean body mass so that drug doses could be adjusted to avoid toxicity, especially in patients with obesity. The arithmetic is: men 50.0 + 2.3 kg per inch over 5 feet; women 45.5 + 2.3 kg per inch over 5 feet. That is the origin of the familiar starting point of 50 kg for a 5-foot man and 45.5 kg for a 5-foot woman.

Devine Was Not A Health Target

Devine did not claim his equation described a healthy weight. He did not test it against mortality data. He did not present it as a lifestyle goal. The equation was a clinical convenience for pharmacokinetic dosing weight in anaesthesiology. For a 5-foot 8-inch (172.7 cm) man, it gives 68.4 kg (150.9 lb). The Robinson equation gives 71.3 kg (157.2 lb), the Miller equation gives 69.6 kg (153.5 lb), and the Hamwi equation gives 74.8 kg (165 lb). The WHO BMI normal range for that height runs from 55.2 to 74.3 kg (121.7 to 163.8 lb). The Devine number sits inside that band but well below the Hamwi number.

Its Persistence In Popular Calculators

Despite its origin in drug dosing, the Devine equation is the default in many online calculators. It is often presented without context, as if it represents a medically recommended target. It does not. A reader who enters their height and gets a Devine result should understand that the number was borrowed from a 50-year-old pharmacy protocol. It has no basis in population health or body composition science. For a 5-foot-2 woman, Devine gives 52.3 kg (115.3 lb). The WHO BMI normal range for that height is 50.4 to 67.8 kg (111.1 to 149.5 lb). Both are within the range, but the Devine number is near the lower end, which is an accident of its arithmetic, not a recommendation.

The Robinson equation was published in 1983 by Dr. J. H. Robinson in the Journal of the American Dietetic Association. It was a revision of the Devine equation using data from the Metropolitan Life Insurance Company height-weight tables. These tables were not health guidelines. They were actuarial tools: Metropolitan Life tracked the weights at which policyholders had the lowest mortality risk in their insured population, which was predominantly white and middle-class. Robinson adjusted the starting point for women to 49 kg and for men to 52 kg for 5 feet, with the same 1.52 kg per inch above that. For a 5-foot-6 woman: Robinson gives 58.1 kg (128.1 lb). Devine gives 59.1 kg (130.3 lb). Miller gives 55.8 kg (123.0 lb). Hamwi gives 63.5 kg (140.0 lb).

The Miller Equation: A Separate Revision Of The Same Data

The Miller equation, also 1983, came from Dr. J. R. Miller writing in the Journal of the American College of Nutrition. Miller revised the Devine equation using the same Metropolitan Life tables but with a distinct interpretation. Miller used 54.0 kg for the first 5 feet of height in men (not 50 kg) and kept the 1.52 kg per inch rule. For women, Miller used 48.0 kg for 5 feet, then 1.52 kg per inch. The effect is a slightly lighter result than Devine for short men and a lighter result for women. For a 5-foot-10 man: Devine 73.0 kg (160.9 lb), Robinson 76.7 kg (169.1 lb), Miller 74.2 kg (163.6 lb), Hamwi 79.4 kg (175.0 lb). The spread between the four numbers for this height is 6.4 kg (14.1 lb). That spread is the disagreement built into the equations.

Why Robinson And Miller Disagree With Each Other

Both equations were created in the same year using the same source data. They disagree because each author chose a distinct base weight for 5 feet and a distinct incremental rule. The Metropolitan Life tables themselves were not a single consensus number. They varied by frame size, which the equations did not incorporate. Neither Robinson nor Miller conducted a new study. They re-arranged existing actuarial data into a simple linear equation. The result is two equations that look authoritative but are essentially arbitrary translations of an insurance company's internal risk model.

Formula	Weight (kg)	Weight (lb)	Year	Original Purpose
Devine	68.4	150.9	1974	Gentamicin dosing weight
Robinson	71.3	157.2	1983	Revision of Devine using MetLife tables
Miller	69.6	153.5	1983	Alternate revision of Devine using MetLife tables
Hamwi	74.8	165.0	1964	Diabetes management
WHO BMI 18.5–24.9 range	55.2–74.3	121.7–163.8	1995	Population screening cut-offs

The Hamwi equation was published in 1964 by Dr. G. J. Hamwi in Diabetes Care. It was created to estimate body weight for patients with diabetes, specifically to help set caloric intake targets. The arithmetic is: men 48.2 kg + 2.7 kg per inch over 5 feet; women 45.4 kg + 2.7 kg per inch over 5 feet. The 2.7 kg per inch is the steepest increment of the four equations. This produces the heaviest weight at any given height. For a 5-foot-4 woman: Hamwi 58.1 kg (128.1 lb). Devine 57.1 kg (125.9 lb). Robinson 55.2 kg (121.7 lb). Miller 56.1 kg (123.7 lb). The WHO BMI normal range for that height is 53.4 to 71.8 kg (117.7 to 158.3 lb). All four equations fall within the WHO range, but Hamwi sits near the middle while Devine and Robinson cluster toward the lower end.

Why Hamwi Gives Heavier Weights

Hamwi used a distinct logic from the others. Rather than starting from an insurance mortality minimum, Hamwi started from a base weight of 48.2 kg for men and 45.4 kg for women at 5 feet, then added 2.7 kg per inch. That is 0.5 to 1.2 kg more per inch than the other equations. Over 10 inches, the difference compounds to 5.0 to 12.0 kg. This does not make Hamwi wrong or right. It makes it a distinct tool for a distinct purpose. In diabetes management in the 1960s, a slightly higher target may have been seen as safer than under-calorisation.

The Frame Size Problem None Of Them Solved

The Metropolitan Life tables included a frame size adjustment: small, medium, and large. The 1983 equations (Robinson and Miller) were based on the medium-frame column. The Devine and Hamwi equations ignored frame size entirely. None of the four equations provides a way for an individual to adjust for their own bone structure or muscle mass. This is a fundamental limitation. Two people of the same height can have distinct body weights based on frame size alone, but these equations treat them identically. The WHO BMI range at least spans a band, allowing for individual variation, even if it too ignores body composition.

The WHO range of BMI 18.5 to 24.9 is based on population-level mortality and morbidity data from European and North American populations, reviewed by the WHO Expert Committee on Physical Status in 1995. It is a screening tool, not a diagnostic. For a 5-foot-8-inch man, the range is 55.2 to 74.3 kg. The four equations all fall inside that band: Devine at 68.4 kg, Robinson at 71.3 kg, Miller at 69.6 kg, and Hamwi at 74.8 kg. Hamwi sits at the very top of the band, 0.5 kg below the overweight threshold of 74.8 kg (BMI 25.0). A person using the Hamwi equation as a target would be at the edge of the WHO overweight category. Someone using Devine would be in the middle. The same person has four distinct targets depending on which equation they choose, all within the same broad range.

For A 5-Foot-6 Woman

For a woman 167.6 cm tall: Devine gives 59.1 kg (BMI 21.0), Robinson gives 58.1 kg (BMI 20.7), Miller gives 55.8 kg (BMI 19.9), Hamwi gives 63.5 kg (BMI 22.6). The WHO normal range for this height is 52.0 to 69.9 kg (BMI 18.5 to 24.9). Miller lands near the lower end at BMI 19.9, Hamwi near the upper end at BMI 22.6. The spread is 7.7 kg or 17.0 lb. A woman who picks the Miller equation is told a target 17 pounds lighter than if she picks Hamwi. Neither number is grounded in a study of what weight is healthy for a woman of that height. The equations simply reflect the distinct arithmetic choices their creators made.

Disagreement With BMI-Based Ranges Is Structural

BMI is a continuous ratio that produces a range of weights for any given height. The four equations produce a single number. A single number forces a binary decision: above or below. That is useful for a drug dose calculation. It is not useful as a personal health target. The equations were designed for narrow clinical contexts, not for guiding a person toward a healthy lifestyle. The WHO range accommodates individual differences in body composition, muscle mass, and bone density better than any single-number equation can. A person with a muscular build who meets the Devine number might be underweight in lean tissue. Someone with a small frame who meets the Hamwi number might be carrying excess body fat. The equations do not know the difference.

Stop using the Devine, Robinson, Miller, and Hamwi equations as personal targets. If you see one of these equations in an online calculator, look at the source attribution. If the site does not say where the equation came from, the number is misleading you. The equations belong in their original contexts: gentamicin dosing, actuarial data smoothing, 1960s diabetes management. They do not belong in a personal health assessment.

The WHO range of BMI 18.5 to 24.9 is a better starting point, but it too has limitations. BMI is a population screening tool, not an individual diagnostic. It does not distinguish fat from muscle. It does not account for age, sex, ethnicity, or body composition. The WHO Asian BMI cut-offs, published in 2004, adjust for higher disease risk at lower BMI in Asian populations, but even those are population averages. A weight that is appropriate for one person may not be appropriate for another.

For a meaningful individual assessment, you need more than a single number. A waist-to-height ratio under 0.5 is a practical target supported by NICE guidelines. A body fat percentage test by DXA or skinfold calipers, performed by a trained professional, gives information about composition. A medical consultation with a clinician who takes a history, measures blood pressure, and checks metabolic markers is the only way to decide what weight is appropriate for you. No equation from 1964 or 1974 can do that.

The thing that most often goes wrong: a person types their height into a calculator, gets a Devine number, believes it is their ideal weight, and either chases an arbitrary target or feels inadequate for not meeting it. The equation was not built for that. The page that presents it without its origin is doing a disservice. Now you know where these numbers come from. Let them stay there.