Ideal Weight Calculator

This is general information, not medical advice

This page does arithmetic and explains where the arithmetic came from. It is general educational information about four historical formulas. It is not medical advice, it is not a diagnosis, and it cannot take account of anything about you that a height and a sex do not capture — which is nearly everything that matters.

None of the four formulas was fitted to health outcomes. Devine (1974) was published for antibiotic dosing. Robinson and Miller (both 1983) are regressions against the Metropolitan Life height-weight tables, whose underlying population was insurance applicants in the United States — self-selected, overwhelmingly white, and screened for insurability rather than sampled for health. Hamwi (1964) was a bedside shortcut for planning diabetic diets. If any of those populations does not sound like you, that is the point: none of them was chosen to represent anyone.

If you are thinking about changing your weight, or you have been handed a target by a form, an app, or an insurer and do not know what to make of it, talk to a doctor, nurse, or registered dietitian. If you are pregnant, under 20, an older adult, recovering from illness, or living with an eating disorder, these formulas were not drawn with you in mind and are especially likely to mislead. Please do not use this page as a reason to act alone.

How the four numbers are worked out

Every one of these formulas has the same two-part shape: a base weight at exactly five feet, plus a fixed number of kilograms for each inch above it. They differ only in where the line starts and how steeply it climbs.

Metric heights are converted at exactly 2.54 cm per inch, and imperial results are converted back at exactly 0.45359237 kg per pound (NIST SP 811), rather than through the rounded factors that circulate with these formulas. Nothing is averaged, nothing is weighted, and no formula is preferred: all four come back and the spread between them is reported as a figure in its own right.

The healthy BMI range is the one output here that is not a historical curiosity. It is the same arithmetic as the BMI calculator, run backwards — the weights that would put your BMI between 18.5 and 24.9 at the height you entered.

A man at 175 cm, step by step

Start by converting: 175 cm ÷ 2.54 = 68.90 inches, which is 8.90 inches above the five-foot anchor. Now run the four lines. Devine: 50 + 2.3 × 8.90 = 70.5 kg. Robinson: 52 + 1.9 × 8.90 = 68.9 kg. Miller: 56.2 + 1.41 × 8.90 = 68.7 kg. Hamwi: 48 + 2.7 × 8.90 = 72.0 kg.

Four answers from one height, spanning 3.3 kg. The healthy BMI range at 1.75 m is 18.5 × 3.0625 = 56.7 kg through 24.9 × 3.0625 = 76.3 kg, so all four estimates sit comfortably inside a band that is 19.6 kg wide. They are arguing over a third of a kilogram per formula inside a range that does not care which of them wins.

Push the height up and the argument gets louder, because the slopes differ. At 190 cm the same man gets 77.1 kg from Miller and 88.0 kg from Hamwi — 10.9 kg apart, more than three times the spread at 175 cm. Nothing about the person changed; only the distance from an anchor that four authors happened to plant in the same place.

Push it down instead and the formulas leave their evidence entirely. At 145 cm a woman gets 38.8 kg from Devine, against a healthy BMI floor of 38.9 kg for that height. The formula has extrapolated below the region it was fitted in and produced a weight that BMI would classify as underweight.

Why none of these is a health target

The most useful thing to know about ideal body weight formulas is what they were made for, because it was not this.

• Devine was a drug dosing rule. It appeared in a 1974 note on gentamicin therapy, where the problem was that dosing an obese patient on total body weight overshoots for a drug that does not distribute into fat tissue. Pharmacists needed a reproducible size estimate; Devine gave them one. Pai and Paloucek went looking for the derivation in 2000 and found that the constants had no supporting data behind them at all. The formula is still excellent at the job it was built for and has never been shown to be good at this one.
• Robinson and Miller are regressions on insurance tables. Both 1983 papers fitted lines to the Metropolitan Life height-weight tables, which were built from the mortality experience of people who bought life insurance in the United States. That population was self-selected and not representative, the heights and weights were often self-reported, and the tables carried frame-size categories that were never defined by measurement. A regression is only ever as good as what it was regressed on.
• Hamwi was a bedside shortcut. The 1964 rule was published for estimating calorie and protein needs when planning diets for people with diabetes — a clinical convenience designed to be done in your head, in pounds, at the bedside. It was never a claim about what anyone should weigh.
• The slopes have no evidence behind them. There is no study showing that a person gains 2.3 kg of optimal weight per inch of height rather than 1.41. The four numbers are simply different, and their difference is the honest measure of how much any of them is worth.
• None of them can see you. No frame size, no body composition, no age, no ancestry, no medical history. Two people of the same height and sex get identical numbers from all four formulas regardless of every other fact about them.

The healthy BMI range is different in kind, not just in quality. It comes from population health data, it is published by the World Health Organization and reviewed, and it is stated as a range because the evidence supports a range. It has its own real limits — it cannot see body composition either, and its cut-points were drawn largely from European-ancestry populations — which the BMI calculator sets out in full. But it is the only figure on this page that was ever about health.

What this calculator assumes

• You are an adult. All four formulas were written for adults and none has a growth term; they mean nothing for children or teenagers.
• Your height is at least five feet, or you have read the flag. All four lines are anchored at 60 inches and extrapolate below it into a region where they were never fitted.
• Sex is binary here because the source formulas are. Each was published with one set of constants for men and one for women, and there is no third set to offer without inventing it.
• Height is measured without shoes. An inch of error moves the estimates by 1.4 to 2.7 kg depending on the formula, which is most of the spread between them.
• The published constants are used exactly as written, with no frame-size adjustment. The common ±10% small and large frame rule is a convention applied to Hamwi, not a measurement.
• Metric heights convert at exactly 2.54 cm per inch and imperial results at exactly 0.45359237 kg per pound, so the two unit systems always agree to within a rounding step.
• The healthy BMI range is the arithmetic span of BMI 18.5 to 24.9 at your height. It is not a prescription and nobody has issued it to you.

Ideal weight FAQ

Sources and review notes

1. World Health Organization — Obesity and overweight fact sheet, the source of the 18.5 to 24.9 healthy BMI band this page puts beside the four formulas
2. Pai MP, Paloucek FP. “The origin of the ‘ideal’ body weight equations.” Annals of Pharmacotherapy, 2000 — the paper that traced Devine, Robinson, Miller and Hamwi back to their sources and found no derivation behind the constants
3. NIST Special Publication 811 — the exact inch and pound definitions used for both unit conversions

The four formulas are historical constants and cannot go stale; they are quoted here exactly as published. The healthy BMI band can change, because it is a public-health convention revised by committee, and the WHO fact sheet above is the version this page reports. Where a clinician or a national guideline uses different thresholds, theirs are the ones that apply to you.