Body size · LIVE

Body roundness index

BRI

Compute Thomas 2013 body roundness index from height and waist by modeling the body as an ellipse.

LIVE $0.005 USDC GET /api/calc/bri

Markdown: /docs/bri.md · Canonical: https://magentlab.com/docs/bri

Not a medical device. Not a diagnosis, dose, or listing recommendation.

What it computes

Compute Thomas 2013 body roundness index from height and waist by modeling the body as an ellipse.

When to use

When an agent needs the published Thomas 2013 BRI and must not invent a body-fat or VAT percentage.

When not to use

• Not a medical device. magent does not measure the patient.
• Not a VAT or body-fat diagnosis. Thomas 2013 relates BRI to adipose tissue; this response is BRI only.
• Does not apply all-cause-mortality quintiles.

Formula

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

Citation

Title

Relationships between body roundness with body fat and visceral adipose tissue emerging from a new geometrical model

Authors

Thomas DM, Bredlau C, Bosy-Westphal A, Mueller MJ, Shen W, Gallagher D, McDougall A, Peterson CM, Ravussin E, Heymsfield SB

Source

Obesity (Silver Spring). 2013;21(11):2264-2271

DOI

10.1002/oby.20408

Worked example

Also searched as

• body roundness index
• Thomas BRI
• waist height ellipse
• body eccentricity index
• BRI Thomas 2013
• visceral adipose roundness

Try

Opens the live endpoint. Unpaid browser requests show the paywall; agents should send Accept: application/json.

/api/calc/bri?height_cm=170&waist_cm=80

Full URL: https://api.magentlab.com/api/calc/bri?height_cm=170&waist_cm=80

Call

Expect HTTP 402 until you retry with PAYMENT-SIGNATURE. Incomplete query params return HTTP 400 before any quote or charge.

curl -i -H "Accept: application/json" "https://api.magentlab.com/api/calc/bri?height_cm=170&waist_cm=80"

Parameters

Bulk (POST)

POST the same path with a JSON items array. The first item is the GET unit; each additional item is $0.002. Invalid items return HTTP 400 before settlement.

POST /api/calc/bri Max 25 unit_amount + extra_item_amount * (n - 1) extra $0.002 PREVIEW

• 1 to 25 items. Each item uses the same keys as the GET query parameters.
• POST of 1 item costs the same as GET. Lists longer than 25: chunk into multiple POSTs. Extra items still execute; do not pad dummy rows.
• The first invalid item fails the whole request (index in the 400 JSON). You are not charged.
• HTTP 200 is {count, path, items}. Each items[i] is the GET 200 body for that row.
• Catalog misses (empty matches, found=false) stay paid 200s inside that slot.
• x402 resource URL is this path plus n and body_sha256. Browsers that prefer text/html get the same paywall as GET; Pay retries POST with the same items.

Example request (fixture)

{
  "items": [
    {
      "height_cm": "170",
      "waist_cm": "80"
    },
    {
      "height_cm": "170",
      "waist_cm": "80"
    }
  ]
}

Open bulk paywall →

Opens a two-item fixture on the API host. Unpaid browsers get the same MetaMask paywall as GET; Pay retries POST with those items.

Example 200 (fixture)

{
  "count": 2,
  "path": "/api/calc/bri",
  "items": [
    {
      "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
      "citation": {
        "authors": "Thomas DM, Bredlau C, Bosy-Westphal A, Mueller MJ, Shen W, Gallagher D, McDougall A, Peterson CM, Ravussin E, Heymsfield SB",
        "doi": "10.1002/oby.20408",
        "id": "thomas-2013",
        "pmid": "23519954",
        "source": "Obesity (Silver Spring). 2013;21(11):2264-2271",
        "title": "Relationships between body roundness with body fat and visceral adipose tissue emerging from a new geometrical model"
      },
      "formula": "bri",
      "formula_expression": "BRI = 364.2 - 365.5 * sqrt(1 - (waist_cm / (pi * height_cm))^2)",
      "height_cm": 170.0,
      "bri": 2.82,
      "waist_cm": 80.0
    },
    {
      "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
      "citation": {
        "authors": "Thomas DM, Bredlau C, Bosy-Westphal A, Mueller MJ, Shen W, Gallagher D, McDougall A, Peterson CM, Ravussin E, Heymsfield SB",
        "doi": "10.1002/oby.20408",
        "id": "thomas-2013",
        "pmid": "23519954",
        "source": "Obesity (Silver Spring). 2013;21(11):2264-2271",
        "title": "Relationships between body roundness with body fat and visceral adipose tissue emerging from a new geometrical model"
      },
      "formula": "bri",
      "formula_expression": "BRI = 364.2 - 365.5 * sqrt(1 - (waist_cm / (pi * height_cm))^2)",
      "height_cm": 170.0,
      "bri": 2.82,
      "waist_cm": 80.0
    }
  ]
}

Response

Example JSON

Machine form of the same example. Frozen fixture. Not a live lookup.

{
  "disclaimer": "Not a medical device. Deterministic published-formula or published-code output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
  "citation": {
    "authors": "Thomas DM, Bredlau C, Bosy-Westphal A, Mueller MJ, Shen W, Gallagher D, McDougall A, Peterson CM, Ravussin E, Heymsfield SB",
    "doi": "10.1002/oby.20408",
    "id": "thomas-2013",
    "pmid": "23519954",
    "source": "Obesity (Silver Spring). 2013;21(11):2264-2271",
    "title": "Relationships between body roundness with body fat and visceral adipose tissue emerging from a new geometrical model"
  },
  "formula": "bri",
  "formula_expression": "BRI = 364.2 - 365.5 * sqrt(1 - (waist_cm / (pi * height_cm))^2)",
  "height_cm": 170.0,
  "bri": 2.82,
  "waist_cm": 80.0
}

Client errors (HTTP 400)

Invalid params return 400 without charge. Shared HTTP 402 and 503 meanings: Payments.

Related tools

• BMI — Compute Keys/Quetelet body-mass index from height and weight, plus a WHO adult band.
• RFM — Compute Woolcott 2018 relative fat mass (RFM) from height, waist circumference, and sex as an estimator of whole-body fat percentage.

Payment

Unpaid requests return HTTP 402 even if query parameters or POST items are missing or invalid, so CDP and agents can index the path. After a PAYMENT-SIGNATURE, invalid params return HTTP 400 JSON before settlement. magent does not charge. Fix the params, then request a new 402 quote for that complete URL. Catalog misses (empty matches, found=false) are valid paid 200s. Unpaid valid requests return HTTP 402 with a base64 PAYMENT-REQUIRED header. HTTP 503 is not a new quote: retry the same PAYMENT-SIGNATURE. Full handshake and shared payment errors: Payments. Stdio MCP: /docs/mcp.

Guarantees

• HTTP 402 is unpaid, including a missing query. After PAYMENT-SIGNATURE, invalid parameters return HTTP 400 before settlement. You are not charged. HTTP 402 never includes the tool JSON.
• exact: settlement finishes before the tool (paymentFlow upfront). batch-settlement: verify/deposit before the tool; chargedCumulativeAmount commits after HTTP 2xx. Uncertain or failed settlement fails closed (HTTP 503). Retry the same PAYMENT-SIGNATURE.
• HTTP 402 is unpaid only. Do not sign a second authorization because of a 503.
• Execution is timeout-bounded and concurrency-capped.
• Calculator inputs are stored encrypted for allowlisted operators (Magent Console). They are not in public logs, SSH lookups, catalog, or rollups. Request logs store path without query.