BRI Calculator (Body Roundness Index from waist and height)

Understanding the body roundness index (BRI) calculator — concept and principle

This calculator works out the body roundness index (BRI) from waist circumference and height, together with the underlying ellipse eccentricity and the waist-to-height ratio. People tracking body shape and students of anthropometry use it as an alternative to body-mass index.

The body as an ellipse — with the default inputs: BRI 3.7.

How it is calculated

Short axis = waist ÷ 2π; long axis = 0.5 × height
Eccentricity e = √(1 − (waist ÷ 2π)² ÷ (0.5 × height)²)
BRI = 364.2 − 365.5 × e

Waist and height must be in the same unit. Waist is measured midway between the lowest rib and the top of the hip bone.

The principle

Thomas and colleagues (2013) modelled the body as an ellipse whose long axis is half the height and whose short axis comes from the waist. A very slim body has an ellipse close to a line, with eccentricity near 1; a rounder body has a lower eccentricity. Converting eccentricity to BRI gives a number that rises as the body gets rounder. Because e depends only on the waist-to-height ratio, BRI carries the same information as that ratio on a different scale. The authors reported that BRI related to body fat and visceral fat.

Worked example

Defaults: waist 88 cm, height 170 cm.

Short axis = 88 ÷ 2π = 14.01 cm; long axis = 85 cm.
e = √(1 − (14.01 ÷ 85)²) = √(1 − 0.0272) = 0.9863.
BRI = 364.2 − 365.5 × 0.9863 = 3.7.
Waist-to-height ratio = 88 ÷ 170 = 0.52.

How to read the result

There are no official BRI categories. Compare your value over time, or read it with the waist-to-height ratio, for which a common public-health message is to keep the waist below half of height. Studies after 2013 have linked higher BRI to health risks in some populations, but cut-offs vary.

Common mistakes

Measuring the waist at the navel or over clothes.
Using different units for waist and height.
Expecting BRI to differ in meaning from waist-to-height ratio.
Treating a single value as a diagnosis.

Keep in mind: Not a diagnosis. Body measures are screening tools; discuss health risks with a doctor.

Frequently asked questions

What is a normal BRI?

There are no official categories; compare over time and with waist-to-height ratio.

How is BRI different from BMI?

BMI uses weight and height; BRI uses waist and height, reflecting central body shape.

Why is eccentricity used?

It describes how elongated or round the body ellipse is.

Sources: Thomas DM, Bredlau C, Bosy-Westphal A et al., "Relationships between body roundness with body fat and visceral adipose tissue emerging from a new geometrical model", Obesity 2013;21(11):2264–2271

Checked 9 Nov 2026. Thomas DM, Bredlau C, Bosy-Westphal A et al., “Relationships between body roundness with body fat and visceral adipose tissue emerging from a new geometrical model”, Obesity 2013;21(11):2264–2271 (formula as reproduced in Frontiers in Nutrition 2025, doi:10.3389/fnut.2025.1538766).

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