Broca's formula

Related Terms

Broca's formula, Broca's index, Devine formula, Hamwi formula, IBW, Miller formula, Robinson formula, simple rule.

Background

Ideal body weight (IBW) is the weight that people are expected to weigh based on age, sex, and height. The ideal body weight today is used as a tool to calculate the dosage of most medications. There are two different formulas to determine ideal body weight; one formula for men and another for women.
The history of the formulas for calculating ideal body weight began in 1871 when Dr. Broca (a French surgeon) created the formula known as Broca's index. An unknown person translated Broca's formula into pounds and inches and modified it to create a formula called the simple rule. In 1974, Dr. Devine converted the simple rule from pounds to kilograms and published that formula for medical use. The Devine formula was intended for use to calculate the dosage of certain medications such as gentamicin, digoxin and theophylline. However, after its publication, the formula became much more widely used and became the most commonly used formula. In 1983, Dr. Robinson published a modification of the Devine formula; this contemporary modification is still in use today to calculate the dosage of most medications.
The ideal body weight calculator was discredited by all major medical institutions as a tool for measuring obesity and malnourishment in the last quarter of the 20thCentury. The tool did not account for the nutritional needs of patients, especially women, when it was devised. The Devine IBW formula suggests ideal body weight values that may be too low in women, and impossibly low in shorter women. A limitation of the Robinson and Miller formulas are that they give low calculations in taller men.
Today Dr. Robinson's ideal body weight calculator is used for medication dosing. The tool is not used to measure rates of obesity or for a clinical diagnosis of obesity. Other tools of medication dosing may surpass the ideal body weight calculator in the future.

Theory / Evidence

Ideal body weight is frequently confused with body mass index. However, ideal body weight is used to calculate the dosage of medications, whereas body mass index calculates the healthy weight of an individual.
It is important to note that the IBW took what was considered an attractive height and weight at the time it was developed as its primary consideration.
Calculations of medications using the ideal body weight have become increasingly complex in recent years as physicians and pharmacists account for the flaws in the design of the ideal body weight ratio. Body composition, genetics, and diet are all factors influencing the body's absorption of drugs that the ideal body weight calculator does not take into account. Additional modifications in dosing may be required for individuals who are over or underweight according to the body mass index.

Author information

This information has been edited and peer-reviewed by contributors to the Natural Standard Research Collaboration (www.naturalstandard.com).

Bibliography

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Robinson JD, Lupkiewicz SM, Palenik L, et al. Determination of ideal body weight for drug dosage calculations. Am J Hosp Parm 1983 40:1016-9.

Charts and calculators

Though doctors and nurses have used ideal body weight charts to measure doses in the past, this technique is no longer in use. Today, doctors and nurses typically use an equation based on the ideal body weight formula to determine dosing. The below describes some of the simpler formulas that have been used.
Broca formula
Men: Ideal Body Weight (kilograms) = [Height (cm) - 100] - ([Height (cm) - 100] x 10%)
Women: Ideal Body Weight (kilograms) = [Height (cm) - 100] + ([Height (cm) - 100] x 15%)
Devine formula
Men: Ideal Body Weight (kilograms) = 50 + 2.3kg per inch over 5 feet
Women: Ideal Body Weight (kilograms) = 45.5 + 2.3kg per inch over 5 feet
Hamwi formula
Men: Ideal Body Weight kilograms) = 48kg + 2.7kg for each inch over 5 feet
Women: Ideal Body Weight (in kilograms) = 45.5kg + 2.2kg for each inch over 5 feet
Miller formula
Men: Ideal Body Weight kilograms) = 56.2kg + 1.41kg for each inch over 5 feet
Women:Ideal Body Weight (kilograms) = 53.1kg + 1.36kg for each inch over 5 feet
Robinson formula
Men: Ideal Body Weight (kilograms) = 52kg + 1.9kg for each inch over 5 feet
Women:Ideal Body Weight (kilograms) = 49kg + 1.7kg for each inch over 5 feet
Simple rule
Men: Allow 110lbs for the first 5 feet and 5lbs for each additional inch.
Women: Allow 100lbs for the first 5 feet and 5lbs for each additional inch.
Other formulas
Men: Ideal Body Weight (kilograms) = 50kg + 2.3kg for each inch of height over 5 feet
Women: Ideal Body Weight (kilograms) = 45.5kg + 2.3kg for each inch of height over 5 feet
Note: 1 kilogram (kg) = 2.2 pounds (lb)