Ideal Body Weight: History, Formulas, and Limitations
From Broca's 19th-century index to BMI-based calculations—how we estimate healthy weight and why every formula is wrong in its own way
1. The Broca Index: The First Major Formula
Women: Height (cm) − 105 = IBW
Belgian mathematician Adolphe Quetelet and French physician Paul Broca independently developed early IBW formulas in the 1800s. Broca's index was simple: subtract 100 cm from height for men, 105 for women. The formula was revolutionary for its time but assumes a"normal" body frame and doesn't account for age, muscle mass, or gender differences beyond a flat 5 kg adjustment.
2. Devine and Hamwi: The 1970s Medical Applications
Hamwi: 48 + 2.7 × (height in inches − 60) [men] / 45.5 + 2.2 × (height in inches − 60) [women]
Dr. BJ Devine published his formula in 1974 specifically for calculating drug dosing. It wasn't intended as a health weight guideline—it became used that way anyway. The Hamwi formula, also from the same era, was developed for similar clinical applications. Both formulas tend to give higher weight values for taller individuals and are less accurate outside certain height ranges.
3. BMI-Based Ideal Weight
A BMI of 22 is traditionally cited as the"ideal" for cardiovascular health in medical literature. This translates to IBW = 22 × height(m)². The range of 18.5-24.9 BMI represents"normal" weight, which gives you a weight range rather than a single number.
Range: 18.5 × height(m)² to 24.9 × height(m)²
BMI-based formulas are population-level tools: they predict health outcomes well at scale but fail individually because they don't measure body composition. A bodybuilder at 5'10" and 200 lbs has a BMI of 28.7 (overweight) but 8% body fat (athletic).
4. Robinson and Miller: Refinements of Devine
Miller: 56.2 + 1.41 × (height in inches − 60) [men] / 53.1 + 1.41 × (height in inches − 60) [women]
Both formulas are refinements of Devine, developed using different population samples in the 1980s. Robinson's formula typically produces slightly lower values than Devine for shorter individuals. Miller's formula gives the lowest values among common formulas, which some argue more closely matches modern body composition norms.
5. Why Frame Size Matters
Frame size acknowledges that bone structure varies. A person with wide shoulders and large bones naturally weighs more than someone of the same height with narrow bones at the same body fat percentage. In clinical practice, frame size is estimated by wrist circumference relative to height, or by elbow breadth measurement.
Small Frame
× 0.9 adjustment
Narrow shoulders, thin wrists
Medium Frame
× 1.0 (baseline)
Average bone structure
Large Frame
× 1.1 adjustment
Wide shoulders, thick bones
6. The Limitations Nobody Talks About
- No muscle measurement: Muscle weighs more than fat. An athletic person with 15% body fat may weigh well above every formula's result while being exceptionally healthy.
- No bone density adjustment: Osteoporosis reduces bone weight; some populations have denser bones than others genetically.
- Age ignored: Muscle mass naturally declines after 30. The"ideal" for a 70-year-old is different than for a 30-year-old of the same height.
- Ethnicity variations: Different ethnic groups have different body compositions at the same BMI. Asian populations show health risks at lower BMI; some African populations have higher average muscle mass.
- Height range limits: Most formulas were derived from data in the 5'0"-6'0" range and become increasingly inaccurate outside it.
Conclusion
Ideal weight formulas are useful as starting points, not destinations. Use this calculator to get a general range, then forget the number. Focus instead on sustainable habits: regular physical activity, balanced nutrition, adequate sleep, and stress management. If you're concerned about your weight or body composition, a healthcare provider can offer personalized guidance that no formula can replace.