Understanding "ideal weight"
Four formulas, none of them right.
Where the Robinson, Miller, Devine and Hamwi formulas came from, why they disagree by 10 kg, and the medical use case they were actually built for.
The four formulas, with dates.
Devine (1974): the original, developed to dose pharmaceuticals — many drugs are administered per-kg of lean body mass, so a single estimate was useful even for very tall or very short patients. 50 kg + 2.3 kg per inch over 5 ft (men); 45.5 kg + 2.3 kg per inch (women). Robinson (1983), Miller (1983), Hamwi (1964): subsequent revisions, each tweaking the base weight and per-inch increment slightly. The constants come from population statistics, not from any deep biological principle.
Why they disagree.
Each formula was fit to a different population at a different time. Hamwi (1964) used hospitalised diabetic patients; Devine (1974) used patients presenting at a hospital pharmacy; Robinson (1983) used a different clinical cohort. The "ideal" was implicit: each formula predicts the average weight of people who happened to be that height in the studied cohort. The differences (sometimes 5-10 kg between formulas at the same height) reflect the differences between those populations, not different definitions of "ideal".
The pharmaceutical origin matters.
These formulas exist because some drug dosages (aminoglycoside antibiotics most famously) depend on lean body mass, not total weight. Dose by actual weight on an obese patient and you over-dose; dose by ideal weight and you approximate the lean mass. The "ideal" was a clinical proxy for "what the patient's lean mass would be if they were a typical patient at this height". It was never meant as a lifestyle target.
BMI does this better.
A modern reading: "ideal weight" is whatever produces a BMI of 22 (the midpoint of the WHO normal range, 18.5-24.9). For a 175 cm person: 22 × 1.75² = 67.4 kg. Bands: BMI 18.5 (57 kg) to BMI 24.9 (76 kg) — a 19 kg range, all considered normal. The ideal-weight formulas produce single numbers; BMI produces ranges. The range is closer to reality.
Bodies have legitimate variation.
Frame size matters (broad-shouldered vs slight build). Muscle mass matters (an athlete can weigh well above any formula's "ideal" and be objectively healthy). Age matters (the body re-composes across decades). Ancestry matters (population averages differ). Reproductive history matters. Any single-number target ignores all of this. The right use of these formulas: a rough starting question, not an answer. The right body-related target: measurements of body composition (waist circumference, body-fat percentage) and metabolic markers (blood pressure, fasting glucose), not the weight on the scale.
Why these calculators still exist.
Medical contexts where lean-mass dosing matters keep them in use. Athletic contexts where weight-category sports (boxing, wrestling, rowing) need target weights use them. Insurance underwriting, military fitness assessments, some legal contexts (workplace fitness-for-duty). For an individual at home wondering "what should I weigh", they're nearly useless; for the institutional contexts that originally needed them, they remain functional. Use them where they fit; ignore them where they don't.