What the body roundness index is
The body roundness index (BRI) was proposed by mathematician Diana Thomas and colleagues in 2013. It models the human body as an ellipse whose long axis is your height and whose width is set by your waist. The rounder the ellipse, the more weight is carried around the middle, and the higher the BRI.
The formula
BRI = 364.2 − 365.5 × √(1 − (waist ÷ 2π)² ÷ (0.5 × height)²)
Waist and height must be in the same unit. The square-root term is the eccentricity of the ellipse: close to 1 for a slim, elongated shape, lower for a rounder one. Most adults have a BRI between about 3 and 7.
Worked example
A person 69 in (5 ft 9 in) tall with a 36 in waist:
- Waist ÷ 2π = 5.73 in; half the height = 34.5 in
- Eccentricity = √(1 − (5.73 ÷ 34.5)²) ≈ 0.9861
- BRI = 364.2 − 365.5 × 0.9861 ≈ 3.78
- Waist-to-height ratio = 36 ÷ 69 = 0.522
The BRI sits in the lower-risk middle range, while the waist-to-height ratio is just above 0.5, a hint that the waist deserves attention.
What the research shows
A 2024 study in JAMA Network Open followed about 33,000 US adults for up to 20 years. Mortality followed a U-shaped curve:
| BRI | Mortality compared with the middle group |
|---|---|
| Below about 3.4 | about 25% higher |
| About 3.4–5.5 | lowest |
| About 5.5–6.9 | similar to slightly higher |
| About 6.9 or more | about 50% higher |
Higher BRI is also linked to diabetes, high blood pressure, fatty liver disease and heart disease. The higher risk at very low values probably reflects illness and frailty rather than slimness itself.
BRI, BMI and waist-to-height ratio
- BMI uses weight and height only. It cannot tell muscle from fat or show where fat sits.
- Waist-to-height ratio is simple and well validated: keep your waist to less than half your height.
- BRI carries the same information as the waist-to-height ratio, rescaled into a shape index that is easier to compare across studies.
How to measure
Stand straight, breathe out normally and measure around the waist at the level of the navel, with the tape horizontal and snug but not tight. Measure height without shoes.
This calculator is for general information and education. It is not medical advice and does not replace the judgment of a doctor, nurse or pharmacist who knows the full clinical picture.