Body roundness index calculator

The formula

BRI models the body as an oval (an ellipse) as tall as you are and as wide as your waist (Thomas 2013). Half your height is the long radius. Your waist, treated as a circle, gives the short radius: waist ÷ 2π. How stretched that oval is, its eccentricity, is then scaled to a friendlier number:

Eccentricity = √(1 − (waist ÷ 2π)² ÷ (0.5 × height)²)

BRI = 364.2 − 365.5 × eccentricity

Waist and height must be in the same unit; the paper used centimeters (Thomas 2013), and the 2024 study wrote the same formula out in centimeters (Zhang 2024). Because only the ratio matters, inches give the same answer.

The authors say the 364.2 and 365.5 were chosen only to spread eccentricity, which sits between 0 and 1, over a range of about 1 to 20 (Thomas 2013). In NHANES the lowest BRI they saw was 1 (Thomas 2013). Larger values mean a rounder body; values near 1 mean a narrow, lean shape.

For example, a person 175 cm tall with a 100 cm waist has an eccentricity of 0.9833 and a BRI of about 4.80. A person 165 cm tall with an 80 cm waist has a BRI of about 3.08, and a person 170 cm tall with a 120 cm waist about 8.05. The papers print no worked example; these are worked from the formula.

In NHANES III, which the paper used, waist was measured just above the top of the hip bone (iliac crest) (Thomas 2013).

BRI and BMI in the original study

Average BRI rose with each BMI group in the NHANES III adults, but the ranges overlapped, so people with the same BMI can have quite different BRI values (Thomas 2013):

From Table 3 of the paper (Thomas 2013). The paper also describes a healthy range of body roundness, but that range depends on age, sex and height through a formula the paper does not print, so we do not show one (Thomas 2013).

What a 2024 study found

Zhang and colleagues worked out BRI for 32,995 US adults aged 20 and over in NHANES from 1999 to 2018 and followed them for deaths through 2019, a median of about 10 years (Zhang 2024). Average BRI rose from 4.80 in 1999 to 2000 to 5.62 in 2017 to 2018 (Zhang 2024).

The study found a U-shaped link: compared with the middle fifth, both the lowest and the two highest fifths had a higher risk of death from any cause, after allowing for age, sex, race and ethnicity, education, income, smoking, drinking and family history of cardiovascular disease and diabetes (Zhang 2024):

From Table 3 of the study (Zhang 2024). The authors chose fifths because BRI has no reference range. They wrote that BRI could become a screening tool for mortality risk, pending consistent validation in other independent cohorts (Zhang 2024). The calculator shows which fifth your value falls in; that is a comparison with this group, not your own risk.

A research index, with limits

BRI uses only two tape measurements. It does not measure fat directly, and it cannot tell fat from muscle. In the original paper, BRI predicted body fat and fat around the organs only slightly better than BMI, waist or hip size (Thomas 2013), and the authors noted that predictions from circumference measures alone may have reached their limit (Thomas 2013). No guideline body sets a BRI cutoff. A high or low value is a reason to talk to your doctor about your weight, waist size and other heart and metabolic risk factors, not a diagnosis.

Related checks

The waist-to-height ratio uses the same two measurements and has guideline bands from NICE. The waist-to-hip ratio compares waist with hips, and the BMI calculator uses weight and height. The visceral adiposity index adds BMI, triglycerides and HDL to waist size, and the body shape index (ABSI) adjusts waist for both height and weight. The relative fat mass calculator turns the same waist and height into an estimated body fat percentage.