The Math of Ideal Body Weight (IBW) Formulas
Calculate your medically suggested weight ranges instantly using our Ideal Weight Calculator, or read on to understand the scientific formulas used by the medical community.
The concept of an "Ideal Body Weight" (IBW) was not originally created by doctors to ensure health. It was created in the 19th century by life insurance companies trying to mathematically calculate statistical mortality risks to set premium prices.
Today, while doctors acknowledge that health cannot be reduced to a single number, IBW formulas are still heavily used in medicine, particularly in anesthesiology and pharmacology, to determine safe drug dosages.
The Problem with BMI
The most famous weight metric is the Body Mass Index (BMI). BMI is a simple formula that divides your weight by your height squared.
The problem with BMI is that it provides a massive, generalized "healthy" range. For a 5'10" adult, a healthy BMI allows for a weight anywhere between 130 lbs and 173 lbs. That is a 43-pound variance!
IBW formulas attempt to pinpoint a much more specific, statistically optimal target weight within that broad BMI range.
The 4 Major IBW Formulas
Over the last 150 years, scientists have developed four primary mathematical formulas to calculate Ideal Body Weight. They all rely strictly on two variables: Height and Biological Sex.
(Note: These formulas were developed using adult data and are not mathematically valid for children).
1. The Broca Index (1871)
Developed by French surgeon Paul Broca, this is the oldest and simplest formula.
- Men:
Height (in cm) - 100= IBW in kg. - Women:
Height (in cm) - 100 - (15%)= IBW in kg. Flaw: This formula breaks down mathematically for very tall or very short people.
2. The Devine Formula (1974)
Created by Dr. Ben Devine originally for calculating drug dosages, this is currently the most widely used medical formula in the world.
- Men:
50.0 kg + 2.3 kg for every inch over 5 feet. - Women:
45.5 kg + 2.3 kg for every inch over 5 feet.
3. The Robinson Formula (1983)
A slight modification of the Devine formula to create a more realistic target for women.
- Men:
52.0 kg + 1.9 kg for every inch over 5 feet. - Women:
49.0 kg + 1.7 kg for every inch over 5 feet.
4. The Miller Formula (1983)
Another modification that slightly adjusts the mathematical weight gain per inch of height.
- Men:
56.2 kg + 1.41 kg for every inch over 5 feet. - Women:
53.1 kg + 1.36 kg for every inch over 5 feet.
The Flaws of Mathematical Ideal Weight
While mathematically precise, all IBW formulas share a massive biological flaw: they completely ignore body composition.
Because the formulas only ask for your height, they assume every human skeleton is exactly the same width, and they assume a standard ratio of fat to muscle.
Muscle is roughly 18% denser than fat. A professional bodybuilder who is 5'10" and heavily muscled will mathematically register as "morbidly obese" on an IBW calculator, despite having a single-digit body fat percentage.
Therefore, modern medicine uses IBW as a statistical baseline, not a strict health mandate. Metrics like Body Fat Percentage and Waist-to-Hip Ratio are much better mathematical indicators of actual metabolic health.
FAQ
Why do all the formulas start at 5 feet tall? These formulas were developed based on standard deviation models of adult height distributions in the 20th century. Because they use a linear equation (adding a flat weight for every inch), the math completely breaks if the person is under 5 feet tall (60 inches), often returning dangerously low or negative target weights.
Compare your exact metrics across all four medical formulas instantly using the CalcUnit Ideal Weight Calculator.