Electrolytes / glucose · LIVE

HOMA-IR (Matthews 1985)

HOMA-IR

Compute the Matthews 1985 HOMA-IR approximation from fasting plasma glucose and insulin.

LIVE $0.005 USDC GET /api/calc/homa_ir

Markdown: /docs/homa-ir.md · Canonical: https://magentlab.com/docs/homa-ir

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

What it computes

Compute the Matthews 1985 HOMA-IR approximation from fasting plasma glucose and insulin.

When to use

When an agent needs the published Matthews 1985 HOMA-IR approximation and must not invent HOMA2, HOMA-B, or an insulin-resistance cutoff.

When not to use

• Not a diagnosis of diabetes. Matthews 1985 HOMA approximation only; magent does not emit an insulin-resistance cutoff.
• Does not compute HOMA-B (beta-cell function) and is not the HOMA2 computer model.

Formula

homa_ir = (glucose_mmol_l * insulin_uu_ml) / 22.5

Citation

Title

Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man

Authors

Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC

Source

Diabetologia. 1985;28(7):412-419

DOI

10.1007/BF00280883

Worked example

Also searched as

• HOMA-IR
• homeostasis model assessment
• insulin resistance HOMA
• Matthews HOMA
• fasting insulin glucose
• HOMA IR approximation
• homeostatic model assessment IR

Try

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

/api/calc/homa_ir?glucose_mg_dl=90&insulin_uu_ml=10

Full URL: https://api.magentlab.com/api/calc/homa_ir?glucose_mg_dl=90&insulin_uu_ml=10

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/homa_ir?glucose_mg_dl=90&insulin_uu_ml=10"

Parameters

Bulk (POST)

POST the same path with a JSON items array. Price is n times the GET unit. Invalid items return HTTP 400 before settlement.

POST /api/calc/homa_ir Max 25 unit_amount * n PREVIEW

• 1 to 25 items. Each item uses the same keys as the GET query parameters.
• 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": [
    {
      "glucose_mg_dl": "90",
      "insulin_uu_ml": "10"
    },
    {
      "glucose_mg_dl": "90",
      "insulin_uu_ml": "10"
    }
  ]
}

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/homa_ir",
  "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": "Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC",
        "doi": "10.1007/BF00280883",
        "id": "matthews-1985",
        "source": "Diabetologia. 1985;28(7):412-419",
        "title": "Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man"
      },
      "formula": "homa_ir",
      "formula_expression": "homa_ir = (glucose_mmol_l * insulin_uu_ml) / 22.5",
      "glucose_mmol_l": 5.0,
      "homa_ir": 2.22,
      "insulin_uu_ml": 10.0
    },
    {
      "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": "Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC",
        "doi": "10.1007/BF00280883",
        "id": "matthews-1985",
        "source": "Diabetologia. 1985;28(7):412-419",
        "title": "Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man"
      },
      "formula": "homa_ir",
      "formula_expression": "homa_ir = (glucose_mmol_l * insulin_uu_ml) / 22.5",
      "glucose_mmol_l": 5.0,
      "homa_ir": 2.22,
      "insulin_uu_ml": 10.0
    }
  ]
}

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": "Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC",
    "doi": "10.1007/BF00280883",
    "id": "matthews-1985",
    "source": "Diabetologia. 1985;28(7):412-419",
    "title": "Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man"
  },
  "formula": "homa_ir",
  "formula_expression": "homa_ir = (glucose_mmol_l * insulin_uu_ml) / 22.5",
  "glucose_mmol_l": 5.0,
  "homa_ir": 2.22,
  "insulin_uu_ml": 10.0
}

Client errors (HTTP 400)

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

Related tools

• A1C ↔ eAG — Convert A1C percent to estimated average glucose, or the reverse, using Nathan/ADAG.

Payment

Required query parameters must be present and valid. 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

• Invalid query parameters return HTTP 400 before settlement. You are not charged.
• Settlement finishes before the tool executes (paymentFlow upfront). 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.