Where the ideal body weight formulas came from
Ideal body weight formulas were not invented for dieters. They were built so clinicians could scale drug doses and ventilator settings to body size. All four classics share the same shape: a base weight at 5 feet plus a fixed amount for every inch above it. Devine (1974), the one most often used for drug dosing, gives 50 kg + 2.3 kg per inch over 5 ft for men and 45.5 kg + 2.3 kg per inch for women. Robinson (1983) uses 52 kg + 1.9 kg per inch for men and 49 kg + 1.7 kg for women. Miller (1983) uses 56.2 kg + 1.41 kg per inch for men and 53.1 kg + 1.36 kg for women. Hamwi (1964), the oldest, is stated in US units: 106 lb + 6 lb per inch for men, 100 lb + 5 lb per inch for women.
The calculator adds a fifth reference point that is not a historic formula at all: the weight that produces a BMI of 22, near the middle of the healthy 18.5-24.9 band. It scales with the square of height rather than linearly, so it tracks better at the extremes where the old formulas drift.
A worked example at 5 ft 9 in
A man who is 5 ft 9 in stands 9 inches over 5 feet and 175.3 cm tall. Devine gives 50 + 2.3 x 9 = 70.7 kg, or 155.9 lb. Robinson gives 52 + 1.9 x 9 = 69.1 kg (152.3 lb). Miller gives 56.2 + 1.41 x 9 = 68.9 kg (151.9 lb). Hamwi gives 106 + 6 x 9 = 160 lb (72.6 kg). A BMI of 22 at 1.753 m is 22 x 1.7532 = 67.6 kg, or 149.0 lb. The five results span 149 to 160 lb and average 153.8 lb, about 69.8 kg.
A woman of the same height gets a lower set: Devine 66.2 kg (145.9 lb), Robinson 64.3 kg (141.8 lb), Miller 65.3 kg (144.1 lb), Hamwi 145 lb (65.8 kg) and BMI 22 unchanged at 149.0 lb, since BMI does not use sex. For reference, the whole healthy BMI range at 5 ft 9 in runs from about 125 to 169 lb, so every formula lands comfortably inside it.
How much attention the number deserves
Not much, on its own. These equations were fitted to mid-twentieth-century insurance and hospital data, they take no account of frame size, muscle mass, age or ancestry, and they disagree with each other by 10 pounds at an ordinary height. Below 5 feet they extrapolate below their base weight and become unreliable; well above 6 ft 3 in they spread apart. Two people at the same height and the same weight can have very different amounts of body fat.
A more useful way to read the output is as the center of a range. If your weight falls within the healthy BMI band for your height, and your waist is under 40 inches (men) or 35 inches (women), the exact formula you pick makes no practical difference. If you want a target for body composition rather than a bathroom scale number, measure body fat percentage and waist circumference and watch those trend over months. Drug dosing, ventilator tidal volume and similar clinical uses are the one place where picking the right formula genuinely matters, and there the choice is made by the protocol, not by the patient.