How ideal weight formulas work (and why they are not targets)

Where these formulas come from

'Ideal' weight formulas look scientific, but their history is more modest. A historical review in The Annals of Pharmacotherapy traces them to height-weight tables that insurers built, in which the weights were found to correlate with mortality, which is how the words 'desirable' and 'ideal' came to be attached to them. Over time ideal body weight (IBW) was interpreted as a stand-in for fat-free or lean weight, and pharmacists noticed that the way some drugs are cleared correlated with IBW. The equation published by Devine in 1974 for dosing, which the review describes as consistent with an older rule of thumb derived from those tables, became the standard.

The practical takeaway is in the review's own conclusion: the equations are similar to each other because they all derive from the general agreement among the same kinds of height-weight tables. They are close cousins, not independent measurements. None of them was designed to say what you should weigh to be healthy, and none was validated as a personal health goal.

The four formulas, and which ones the tool uses

All four common formulas share one structure: a base weight at 5 feet for men and for women, plus a fixed number of kilograms for each inch over 5 feet. Only the constants differ. The first two below are in the EveryFix calculator, which averages them. The last two are widely published alternatives. The Miller and Hamwi constants below are the values published consistently by several calculator and reference sites; they were not checked against the original papers, so treat them as reported values.

• Devine (1974): men 50 kg + 2.3 kg per inch over 5 ft; women 45.5 kg + 2.3 kg per inch. In the calculator.
• Robinson (1983): men 52 kg + 1.9 kg per inch; women 49 kg + 1.7 kg per inch. In the calculator.
• Miller (1983): men 56.2 kg + 1.41 kg per inch; women 53.1 kg + 1.36 kg per inch. Not in the calculator.
• Hamwi (1964): men 48 kg + 2.7 kg per inch; women 45.5 kg + 2.2 kg per inch. Not in the calculator.
• Origins, as reported by calculator and reference sites: Hamwi is described as a quick estimate for clinicians and dietitians; Robinson and Miller as later revisions fit to insurance-style height-weight data; Devine as a dosing formula.

Worked examples with all four formulas

Example 1, a man 70 inches tall, which is 10 inches over 5 feet. Devine: 50 + 2.3 x 10 = 73.0 kg. Robinson: 52 + 1.9 x 10 = 71.0 kg. The calculator averages those to 72.0 kg, which is 158.7 lb and appears as about 159 lb. For comparison, Miller gives 56.2 + 1.41 x 10 = 70.3 kg (155 lb) and Hamwi gives 48 + 2.7 x 10 = 75.0 kg (165 lb). The tool shows the healthy BMI range for his height as roughly 129 to 174 lb.

Example 2, a woman 64 inches tall, 4 inches over 5 feet. Devine: 45.5 + 2.3 x 4 = 54.7 kg. Robinson: 49 + 1.7 x 4 = 55.8 kg. Average: about 55 kg, or 122 lb. Miller gives 53.1 + 1.36 x 4 = 58.5 kg (129 lb) and Hamwi gives 45.5 + 2.2 x 4 = 54.3 kg (120 lb). Her healthy BMI range is about 108 to 145 lb.

Example 3, a man 6 feet tall, 12 inches over: Devine gives 77.6 kg, Robinson 74.8 kg, and the tool averages them to 76.2 kg, about 168 lb, beside a BMI range of roughly 136 to 184 lb.

Why the formulas disagree

Look at the 70-inch man: four formulas, four answers from 70.3 to 75.0 kg, a gap of 4.7 kg or about 10 lb. The gap exists because each formula pairs a different base with a different slope. Devine and Hamwi have steep slopes (2.3 and 2.7 kg per inch for men) but low bases. Miller has a high base and a gentle slope (1.41). Robinson's slope sits between those two.

Because slopes differ, the lines cross and fan apart as height changes. For men, Devine and Robinson give the same answer at exactly 65 inches (5 ft 5 in), because the 2 kg base difference is made up at 0.4 kg per inch over 5 inches. Taller than that, Devine pulls ahead. By 76 inches, the four formulas run from 78.8 kg (Miller) to 91.2 kg (Hamwi), a spread of 12.4 kg or about 27 lb. For women at 66 inches the four land within 2.6 kg of each other, but at 5 feet they range from 45.5 kg (Hamwi and Devine) to 53.1 kg (Miller), 7.6 kg or about 17 lb apart.

There is a second effect built into the calculator. Both formulas anchor at 5 feet and add nothing below it, so anyone at or under 60 inches gets the same base result no matter how short. A woman 58 inches tall and a woman 60 inches tall both see about 104 lb, even though the BMI range at 58 inches starts about 6 lb lower than at 60. The formulas were not built to extrapolate downward.

Why none of these numbers is a target

The formulas use two inputs, height and sex. They have no way to see muscle mass, bone structure, frame size, age, body fat distribution, pregnancy, or health conditions. A person with a lot of muscle can sit well above the 'ideal' figure and be metabolically healthy; a person with low muscle can sit exactly on it and not be. The formulas also date from decades ago and were never refined for individual health goals.

That is why the calculator shows a second number beside the estimate: the weight range for a BMI from 18.5 to 24.9. For context, the CDC defines the healthy weight BMI range for adults as 18.5 to less than 25 and describes BMI as a screening measure and one potential health indicator that should be considered with other factors. The BMI range is much wider than the formula's single value, for example roughly 108 to 145 lb for the 64-inch woman. A single number like 122 lb is simply a point within, or near, that range. Neither is a pass-fail line.

If you want something closer to composition than a height-weight rule can offer, a body fat estimate (such as the Body Fat Calculator on this site) adds information, though it comes with its own error. For personal decisions about weight, a healthcare provider can account for the things a formula cannot.

Reading the estimate next to the BMI range

The calculator reports two things, and they answer different questions. The formula estimate is one point derived from height and sex. The BMI range is the span of weights that would put your BMI between 18.5 and 24.9 at your height, calculated as 18.5 x height in meters squared up to 24.9 x height in meters squared. For the 70-inch man that span is about 58.5 to 78.7 kg, and the formula estimate of 72.0 kg sits in the upper-middle of it.

The estimate does not sit in the middle of the BMI range as height changes. For the 64-inch woman the BMI range is about 48.9 to 65.8 kg and the estimate of 55 kg is a little below the middle. For a man 76 inches tall the range is 68.9 to 92.8 kg, and the estimate of 84.6 kg sits in the upper part. These are simply different rules, so the position changes. If the estimate and the range seem to conflict, that is the formulas disagreeing with each other, which is normal, and not a sign that you entered something wrong.

Using the results sensibly, and common mistakes

The best use of an ideal-weight estimate is as a loose reference point alongside the BMI range, not as a goal weight.

• Treating the single number as a goal. The formulas disagree with each other by several kilograms, so the honest answer is a range.
• Ignoring the unit of the increment. The slopes are in kilograms per inch, not pounds, so applying a kilogram slope to pounds would inflate the answer by a factor of about 2.2.
• Using it for children, teens or pregnant adults. These formulas were built for adults.
• Assuming a heavier muscular build means something is wrong. The formulas cannot see muscle.
• Comparing different calculators without checking which formula they use. Some use only Devine, some use Hamwi or Miller, and some average several, so the same height can give different answers.
• Using the result for drug dosing. Clinicians apply these equations under specific protocols; a web calculator is not a dosing tool.