BRI Calculator — Body Roundness Index

Background.

Two people can share a height, a weight and a BMI and still carry their fat very differently — one mostly under the skin of the hips and thighs, the other packed around the organs of the abdomen. That second pattern, visceral fat, is the one most closely tied to metabolic disease, and body mass index cannot see it. A tape measure around the waist gets closer, which is why several indices try to turn waist and height into a reading of body shape.

The body roundness index, published by Diana Thomas and colleagues in 2013, does it with geometry. It pictures the body as an ellipse whose long axis is your height and whose short axis is the diameter of a circle with your waist's circumference. A tall, slim person makes a long, narrow ellipse with an eccentricity close to 1; as the waist grows relative to height, the ellipse fattens and the eccentricity falls. BRI rescales that eccentricity so adults land on small positive numbers that rise as the body gets rounder, and the authors related it to measured body fat and visceral fat.

One consequence of the geometry is worth knowing. Only the ratio of waist to height enters the ellipse, so BRI is a one-to-one translation of your waist-to-height ratio. A 160 cm person with an 80 cm waist and a 175 cm person with an 87.5 cm waist both have a ratio of 0.5 and a BRI of about 3.36. The index puts the ratio on a different scale; it does not add new information about you.

Nor does it deliver a verdict. The index is reported without risk bands, it is not a body-fat percentage, and it is not a diagnosis. Where the waist is measured, pregnancy, fluid retention and the population a reference value came from all change what a given number means, and interpreting it belongs with a clinician.

What is bri calculator — body roundness index?

The body roundness index is a dimensionless number derived from waist circumference and height. It treats the body as an ellipse whose semi-major axis is half the height and whose semi-minor axis is the waist circumference divided by 2π, the radius of a circle with that perimeter. The ellipse's eccentricity runs from 0 for a circle towards 1 for a thin line, and BRI equals 364.2 minus 365.5 times that eccentricity, so a rounder body gives a higher value. It is an anthropometric indicator, not a measurement of fat.

How to use this calculator.

1. 01Measure the waist with a flexible tape held level and snug without compressing the skin, at the end of a normal breath out. Protocols disagree on the site — the top of the hip bone in some surveys, midway between the lowest rib and the hip bone in others — so choose one and keep to it.
2. 02Enter the waist circumference in centimetres. Inches also work if the height is in inches too, because only the ratio of the two affects the result.
3. 03Enter your height without shoes, in the same unit as the waist.
4. 04Read the index together with the scope note beside it, and compare your own readings over time rather than against a cut-off drawn from a population unlike yours.

The formula.

BRI = 364.2 − 365.5 × √(1 − (WC/2π)² ÷ (0.5H)²). WC/2π turns the waist circumference into the radius of a circle with that perimeter, which serves as the ellipse's semi-minor axis; 0.5H, half the height, is the semi-major axis. The square-root term is the ellipse's eccentricity. The constants 364.2 and 365.5 are the scaling Thomas and colleagues chose so that adults fall on a convenient range of small positive numbers; because 365.5 is the larger, an implausibly narrow ellipse would actually score slightly below zero. Since (WC/2π) ÷ (0.5H) simplifies to WC ÷ (πH), the answer depends on the waist-to-height ratio alone. The curve steepens as the waist grows: at 175 cm tall, going from an 80 to a 90 cm waist adds about 1.04, while going from 100 to 110 cm adds about 1.29. A waist of π times the height or more cannot form the ellipse, so the page refuses it.

A worked example.

Frequently asked questions.

References& sources.

1. [1]Thomas DM et al. Relationships Between Body Roundness with Body Fat and Visceral Adipose Tissue. Obesity. 2013;21(11):2264-2271.
2. [2]Stefanescu A et al. A New and Simple Method to Estimate Visceral Adipose Tissue Volume in Adults. PLoS ONE. 2014.
3. [3]BIPM, The International System of Units (SI Brochure), 9th ed., version 3.01, coherent derived units and quantity equations.