Body Roundness Index (BRI) Calculator
Calculate the Thomas 2013 geometric Body Roundness Index from height and waist circumference in centimeters or inches, with measurement and interpretation limits.
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About
This page reproduces the Thomas et al. 2013 dimensionless geometric Body Roundness Index (BRI) from standing height and waist circumference. The original model approximates a body cross-section as an ellipse and maps an eccentricity-related geometric term to BRI; the result is not the ellipse eccentricity itself or an anatomical measurement. [1]
Waist-based anthropometric indices can be studied alongside body composition and outcomes, but a calculated BRI is not a direct body-fat percentage, visceral-adipose-tissue volume, diagnosis, personal mortality probability, or treatment target. [1, 6, 8]
Formula
Interpretation
What the original geometric model represents
The Thomas model uses an ellipse approximation to describe one aspect of body shape. It does not claim that the torso is a measured anatomical ellipse. Height, waist, and the published constants produce a dimensionless geometric index. Body weight is not a raw input, and age and sex are also absent from the raw equation. [1]
BRI and other anthropometric measures are not interchangeable
| Measure | Inputs | Output | Why it is not interchangeable |
|---|---|---|---|
| BRI | Height, waist | Geometric anthropometric index | Not body-fat percentage or a risk probability |
| BMI | Height, weight | Weight-for-height index | Does not directly describe fat distribution |
| Waist circumference | Waist | Single external circumference | Does not standardize by height |
| WHtR | Waist, height | Simple ratio | Not the Thomas ellipse mapping |
| RFM | Height, waist, published sex variable | Regression estimate of body-fat percentage | Different model and output target |
A 2020 meta-analysis found pooled BRI discrimination for metabolic syndrome similar to waist circumference and lower than WHtR. Some differences from BMI, waist circumference, and WHtR were not statistically significant. That evidence does not establish BRI as universally superior across populations, endpoints, or uses. [5, 6, 7]
Why this page has no “normal BRI” or risk zones
Distributions observed in Thomas 2013 were research observations, not a universal clinical normal range. Later quantiles, cutoffs, and outcome associations depend on the population, endpoint, measurement protocol, and analysis. [1, 7]
The corrected 2024 JAMA Network Open article analyzed an NHANES adult cohort and reported a U-shaped population association with all-cause mortality. It was not a personal mortality-probability model, and the authors stated that application awaited consistent validation by other independent studies. This page therefore does not turn study quantiles or values such as 3.41, 4.45, 5.46, or 6.91 into dynamic low, normal, high, or treatment categories. [8]
Waist measurement protocols differ
WHO midpoint
WHO describes the midpoint between the lowest palpable rib and the top of the iliac crest. [2]
NHANES/NIH iliac crest
NHANES uses a horizontal measurement at the uppermost lateral border of the right ilium. [3]
These are different anatomical sites. Navel, narrowest waist, midpoint, and iliac crest are not synonyms. This page does not claim one method is uniquely correct for every BRI study. For repeated measurements, document and retain the same site, standing posture, respiratory phase, tape position, and tension. [2, 4, 5]
Population and measurement limits
The cited adult evidence does not establish direct interpretation for children or adolescents, pregnancy, ascites, marked abdominal distension, edema, an abdominal mass, inability to stand in a standardized position, unusual body shape or composition, or measurements taken at changing waist sites. These are interpretation limits, not a generated diagnosis or a universal list of medical contraindications. [1, 2, 3, 5]
Worked arithmetic and model-boundary examples
170 cm height, 90 cm waist: raw BRI ≈ 3.9271077200, displayed as 3.93.
Exact US equivalent: 66.9291338583 in height and 35.4330708661 in waist normalize to the same centimeter values and produce the same raw BRI.
180 cm height, 90 cm waist: raw BRI ≈ 3.3588030217, displayed as 3.36.
100 cm height, 315 cm waist: the ellipse square-root term is outside its mathematical domain, so no BRI is reported.
200 cm height, 50 cm waist: the square-root term is defined, but the mapped BRI is nonpositive, so this calculator withholds the extrapolated value.
These examples distinguish unrounded calculation, two-decimal display, and model rejection. They do not create a health category, personal risk estimate, or treatment target. [1, 8]
References
- 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. PMID 23519954. PMCID PMC3692604. doi:10.1002/oby.20408.
- World Health Organization. Waist Circumference and Waist-Hip Ratio: Report of a WHO Expert Consultation. Geneva, 8–11 December 2008. Published 2011. ISBN 9789241501491.
- CDC/NCHS. National Health and Nutrition Examination Survey: 2021 Anthropometry Procedures Manual.
- CDC/NCHS. Waist Circumference Measurement Methodology Study: National Health and Nutrition Examination Survey, 2016. Vital Health Stat 2. 2019;(182):1–20.
- Ross R, Neeland IJ, Yamashita S, et al. Waist circumference as a vital sign in clinical practice: a consensus statement from the IAS and ICCR Working Group on Visceral Obesity. Nat Rev Endocrinol. 2020;16(3):177–189. PMID 32020062. doi:10.1038/s41574-019-0310-7.
- Klein S, Allison DB, Heymsfield SB, et al. Waist circumference and cardiometabolic risk: a consensus statement. Diabetes Care. 2007;30(6):1647–1652. PMID 17360974. doi:10.2337/dc07-9921.
- Rico-Martín S, Calderón-García JF, Sánchez-Rey P, et al. Effectiveness of body roundness index in predicting metabolic syndrome: a systematic review and meta-analysis. Obes Rev. 2020;21(7):e13023. PMID 32267621. doi:10.1111/obr.13023.
- Zhang X, Ma N, Lin Q, et al. Body Roundness Index and All-Cause Mortality Among US Adults. JAMA Netw Open. 2024;7(6):e2415051. PMID 38837158. doi:10.1001/jamanetworkopen.2024.15051. The article was corrected July 11, 2024, to fix the BRI formula and clarify that height and waist use the same unit.
FAQ
The Thomas 2013 equation is BRI = 364.2 − 365.5 × √[1 − ((waist ÷ 2π)² ÷ (0.5 × height)²)]. Height and waist must use the same length unit, and BRI is dimensionless.
Sources: [1]
No. The model first forms an eccentricity-related geometric term from an ellipse approximation, then maps that term with the published constants 364.2 and 365.5. BRI is the mapped index, not eccentricity itself or an anatomical ellipse measurement.
Sources: [1]
The original geometric equation was defined from standing height and waist circumference. Body weight is not a raw input, so this page does not add it to the Thomas model.
Sources: [1]
Waist circumference is one external measurement, while WHtR is waist divided by height. BRI applies the nonlinear Thomas ellipse mapping. A meta-analysis found BRI discrimination for metabolic syndrome similar to waist circumference and lower than WHtR, with some differences not statistically significant.
BRI is the Thomas geometric index from height and waist. RFM is a separate regression estimate of body-fat percentage that uses height, waist, and a published sex variable. Their model targets and outputs are different.
Sources: [1]
No. The original research studied modeled relationships with body fat, but the BRI itself is an anthropometric geometric index and not DXA, BIA, or another direct or reference body-composition measurement.
Sources: [1]
The 2024 study reported a U-shaped population association in an NHANES adult cohort; it did not publish a personal mortality-probability calculator. Its authors stated that application awaited consistent validation by independent studies, so this page does not convert study quantiles into personal risk zones.
Sources: [8]
The cited adult evidence does not establish direct interpretation for children or adolescents, pregnancy, ascites, marked distension, edema, an abdominal mass, inability to stand consistently, or unusual body shape or composition. Those states can limit comparability without becoming an automatic diagnosis or universal contraindication here.
A domain error means the ellipse square-root term is not mathematically defined for the submitted geometry. A nonpositive extrapolation means that term is defined but the published mapping produces zero or a negative BRI. This calculator reports neither result and does not clamp it into a study range.
Sources: [1]
Related Calculators
WHR
Calculate adult waist-to-hip ratio from standardized waist and hip circumferences in metric or US units.
RFM
Estimate adult whole-body fat percentage from height and waist circumference using the published Woolcott–Bergman RFM equation.
BMI
Calculate adult BMI from metric or US customary inputs and view the CDC adult screening category with non-diagnostic interpretation limits.
Disclaimer
Educational and informational reference only. Not intended to replace professional medical advice, diagnosis, treatment, or independent verification.