# About arithmetic formulas for calculating ideal body weight

The history of the formulas for calculating ideal body weight began in 1871 when Dr. P.P. Broca4 (a French surgeon) created this formula ( known as Broca's index):

Weight (in kg) should equal Height( in cm) - 100, plus or minus 15% for women or 10% for men.

An unknown person translated Broca's formula into pounds and inches, and modified it to create this improved simple rule:

"For women, allow 100 lbs for the first 5 feet and 5lbs for each additional inch. For men, allow 110 lbs for the first 5 feet and 5 lbs for each additional inch"1.

These formulas pre-dated and probably influenced development of the Metropolitan Life tables of height and weight. As discussed on another page, the Met Life tables were created in 1943, and were commonly used by the 1970s as a surrogate indicator of desirable or "ideal" body weight. Thus, the Met life tables strongly influenced the subsequent development of other formulas.

Dr. BJ Devine published the following formula in 1974, which basically converted the above simple rule from pounds to kilograms, for medical use:

men: Ideal Body Weight (in kilograms) = 50 + 2.3 kg per inch over 5 feet.
women: Ideal Body Weight (in kilograms) = 45.5 + 2.3 kg per inch over 5 feet.

This "Devine formula" was intended to be used to calculate the dosage of certain medications such as gentamicin, digoxin and theophylline. But after its publication, the formula became much more widely used.. In fact, the Devine formula is the most commonly used formula on the internet for ideal body weight. It appears on MANY HUNDREDS of javascript calculator pages!

Later in 1983, Dr. JD Robinson discovered through correpondence with Dr. Devine, that the Devine equations were not based on any defined population data. Instead, they were apparently based on estimates from Dr. M. McCarron, who was Dr. Devine's mentor1.

Now, in modern times, we can examine the Devine formulas more scientifically, and compare them to current knowledge. The following charts show the Devine formula compared to the average weight2 and lean body mass3 of the American population.

The "Lean Body Weight" refers to the weight of all of the body's organs, bone and muscles, WITHOUT FAT. As you can see, the women's formula gets too close to the Lean Body Weight, in short women.

The Devine formula suggests an ideal weight, which would create an average Body Mass Index of 23.0 kg/m2 in the adult Male population, (which is appropriate), but for women, it suggests an ideal weight that would create an average Body Mass Index of 20.8 kg/m2 in the adult Female population, which is too low.

In 1983, Dr. JD Robinson published a modification of the formula5, and Dr. DR Miller published a different modification.

 Robinson: Men: Ideal Body Weight (in kilograms) = 52 kg + 1.9 kg for each inch over 5 feet Women: Ideal Body Weight (in kilograms) = 49 kg + 1.7 kg for each inch over 5 feet Miller Men: Ideal Body Weight (in kilgrams) = 56.2 kg + 1.41 kg for each inch over 5 feet Women: Ideal Body Weight (in kilograms) = 53.1 kg + 1.36 kg for each inch over 5 feet.

### Problems with the Devine Formula for Ideal Body Weight

As descibed above, the Devine IBW formula suggests ideal body weight values that are too low in women generally and impossibly low in short women. Since the Devine formula is used by hundreds (perhaps thousands) of websites to suggest goals for weight loss, it is important to point out its limitations. The other formulas are rarely (if ever) seen on websites.

The Robinson and Miller formulas would perform poorly for tall men. The best compromise, in my opinion, is to use the Devine formula for Men, and use the Robinson formula for Women. In Men, the average suggested weight by the Devine formula, would give a BMI of 23.0. In Women, the average suggested weight by the Robinson formula, would give a BMI of 21.1.

However, these formulas have no method to compensate for Age and Current Weight. They are only based on Height. For people who are very overweight or obese, the Devine, Robinson and Miller formulas would suggest an ideal weight that is virtually impossible to achieve or maintain through dieting.

### The Hamwi formula

The Hamwi formula6 is yet another variation on the above. I don't know much about it, other than it has uses in some drug dosage calculations. It is quite similar to the Devine forumla.

 Hamwi: Men: Ideal Body Weight (in kilograms) = 48 kg + 2.7 kg for each inch over 5 feet Women: Ideal Body Weight (in kilograms) = 45.5 kg + 2.2 kg for each inch over 5 feet

References

1. Pai MP, Paloucek FP, The origin of the "Ideal" body weight equations. Ann Pharmacol 2000; 34:1066-69
2. NHANES III. Third National Health and Nutrition Examination Survey. 1988-1994 data from USA.
3. Formulas for Lean Body Weight (men) = (1.10 x Weight(kg)) - 128 ( Weight2/(100 x Height(m))2)
Lean Body Weight (women) = (1.07 x Weight(kg)) - 148 ( Weight2/(100 x Height(m))2)
4. Mémoires d’anthropologie. Paris, 1871/1877
5. Robinson JD, Lupkiewicz SM, Palenik L, Lopez LM, Ariet M, Determination of ideal body weight for drug dosage calculations. Am J Hosp Parm 1983 40:1016-9.
6. Hamwi GJ. Therapy: changing dietary concepts. In: Diabetes Mellitus: Diagnosis and Treatment (vol. 1). Danowski TS (ed). American Diabetes Association. New York. 1964, pp73-8.