MAGENT

BRI calculator: the body roundness index formula (Thomas 2013)

The body roundness index (BRI) describes body shape with one number, using waist circumference and height. It treats the body as an ellipse: the rounder the ellipse for a given height, the higher the BRI. This BRI calculator applies the Thomas 2013 formula and returns the index to two decimals.

Not a medical device. Not a diagnosis or dosing recommendation.

Use this calculator via API

What is the body roundness index?

Thomas and colleagues proposed the BRI as a geometric model linking body roundness with body fat and visceral fat. Height sets the long axis of the ellipse and waist circumference sets how round it is. The formula turns that into the ellipse's eccentricity and rescales it.

The calculator doesn't take measurements. Both values are supplied by the caller.

The BRI formula

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

BRI = 364.2 − 365.5 × eccentricity

waist and height in cm; result to 2 decimals

Exact expression the calculator uses:

BRI = 364.2 - 365.5 * sqrt(1 - (waist_cm / (pi * height_cm))^2)

Inputs

InputMeaningUnit
height_cmHeightcm
height_inHeight, if you'd rather give inches (converted as inches × 2.54)in
waist_cmWaist circumference, 40 to 200cm

Give one of the two height inputs.

How the calculation works

  1. Put height in cm. Inches are multiplied by 2.54.
  2. Divide the waist by π times the height.
  3. Square that, subtract it from 1 and take the square root. This is the eccentricity of the ellipse.
  4. Multiply by 365.5 and subtract from 364.2.
  5. Round to two decimals.

A larger waist for the same height lowers the eccentricity, which raises the BRI. The calculator returns the index with no categories.

Worked examples

These use Magent's own expected values for the calculator.

Example 1: height 170 cm, waist 80 cm

  1. Divide 80 by π × 170, square the result, subtract it from 1 and take the square root.
  2. Multiply that eccentricity by 365.5 and subtract from 364.2.
  3. BRI 2.82.

Example 2: height 170 cm, waist 120 cm

  1. The same height with a larger waist gives a rounder ellipse.
  2. BRI 8.05.

Example 3: height 67 in, waist 80 cm

  1. 67 × 2.54 = 170.18 cm.
  2. That's almost the same as Example 1.
  3. BRI 2.82.

History of the body roundness index

Thomas and colleagues published "Relationships between body roundness with body fat and visceral adipose tissue emerging from a new geometrical model" in Obesity (Silver Spring) in 2013. The constants the calculator uses come from that paper.

When it's used

When someone wants a shape measure that uses waist circumference as well as height.

Where it's used

Research on body composition, and clinics and health checks that record waist and height.

Who uses it

Researchers, clinicians and dietitians. The calculator handles the geometry.

Limits of the calculation

  • It depends on an accurate waist measurement, which varies with where and how it's taken.
  • The calculator returns the index with no categories or cutoffs.
  • A BRI value doesn't measure body fat directly.
  • If the waist is too large for the height, the ellipse model breaks down and the calculator rejects the input.
  • This page doesn't say what a value means for a particular person.

Clinical decisions belong to a qualified clinician who knows the patient.

Other body size calculators use weight as well as height. The BRI uses waist circumference and height, with no weight.

Glossary

  • Ellipse: an oval shape.
  • Eccentricity: how far an ellipse is from a circle.
  • Visceral fat: fat around the internal organs.

Common mistakes

  • Mixing units. Waist is in cm; height in cm, or in inches through height_in.
  • Using hip instead of waist. The formula uses waist circumference.
  • Looking for a cutoff. The calculator doesn't give one.

Source

Thomas DM, et al. Relationships between body roundness with body fat and visceral adipose tissue emerging from a new geometrical model. Obesity (Silver Spring). 2013;21(11):2264-2271. DOI: 10.1002/oby.20408. PMID: 23519954

Frequently asked questions

How is the body roundness index calculated?

Divide the waist by π times the height, square it, subtract from 1, take the square root, multiply by 365.5 and subtract from 364.2.

Does BRI use weight?

No. It uses waist circumference and height.

Can I enter height in inches?

Yes, through height_in. It's converted at 2.54 cm per inch.

Does the calculator say whether a BRI is high?

No. It returns the index without categories.