# HOMA-IR (Matthews 1985)

HOMA-IR

Status: LIVE
Price: $0.005 USDC
`GET /api/calc/homa_ir`
HTML: https://magentlab.com/docs/homa-ir
Markdown: https://magentlab.com/docs/homa-ir.md

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

[Homeostasis model assessment: insulin resistance and beta-cell function from fasting plasma glucose and insulin concentrations in man](https://doi.org/10.1007/BF00280883)
Matthews DR, Hosker JP, Rudenski AS, Naylor BA, Treacher DF, Turner RC
Diabetologia. 1985;28(7):412-419
DOI: [10.1007/BF00280883](https://doi.org/10.1007/BF00280883)

## Worked example

### Glucose 90 mg/dL, insulin 10 µU/mL

Given: `glucose_mg_dl=90, insulin_uu_ml=10`

1. mmol/L = 90 / 18.0 = 5.0
2. homa_ir = (5.0 * 10) / 22.5 = 2.22


### Glucose 5.0 mmol/L, insulin 10 µU/mL

Given: `glucose_mmol_l=5.0, insulin_uu_ml=10`

1. homa_ir = (5.0 * 10) / 22.5 = 2.22


## Also searched as

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

## Parameters

- `glucose_mg_dl` (number, optional): Fasting plasma glucose in mg/dL (50-1000). Converted as mmol/L = mg/dL / 18. Provide this or glucose_mmol_l, not both.
- `glucose_mmol_l` (number, optional): Fasting plasma glucose in mmol/L (2.8-55.5). Provide this or glucose_mg_dl, not both.
- `insulin_uu_ml` (number, required): Fasting insulin in µU/mL (= mU/L) (0.1-500).

## 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.

Method: `POST /api/calc/homa_ir`
Max items: 25
Price: unit_amount * n (unit 5000 atomic)
Status: 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:

```json
{
  "items": [
    {
      "glucose_mg_dl": "90",
      "insulin_uu_ml": "10"
    },
    {
      "glucose_mg_dl": "90",
      "insulin_uu_ml": "10"
    }
  ]
}
```

Human paywall (two-item fixture): https://api.magentlab.com/paywall/bulk/homa-ir

Example 200:

```json
{
  "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 fields

- `formula` (string): homa_ir
- `formula_expression` (string): Exact expression used
- `glucose_mmol_l` (number): Fasting glucose in mmol/L (mg/dL / 18 when supplied as mg/dL), 2 decimals
- `insulin_uu_ml` (number): Fasting insulin in µU/mL used
- `homa_ir` (number): Matthews 1985 HOMA-IR approximation, 2 decimals
- `citation` (object): Matthews et al. 1985 citation
- `disclaimer` (string): Not-a-device notice

## Example JSON

Frozen fixture. Not a live lookup.

```json
{
  "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
}
```

## Errors

- HTTP 400 `invalid_glucose`: glucose_mg_dl (50-1000) or glucose_mmol_l (2.8-55.5) is required Returned before settlement; you are not charged.
- HTTP 400 `invalid_insulin`: insulin_uu_ml must be a number from 0.1 to 500. Returned before settlement; you are not charged.
- HTTP 400 `invalid_items`: POST body must be a JSON object with only an items array Returned before settlement; you are not charged.
- HTTP 400 `invalid_item_count`: items must be an array of 1 to 25 objects Returned before settlement; you are not charged.
- HTTP 400 `invalid_item`: each items entry must be a JSON object Returned before settlement; you are not charged.

Shared HTTP 402 and 503: https://magentlab.com/docs/payments

## Related tools

- [A1C ↔ eAG](https://magentlab.com/docs/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.

- GET the tool with Accept: application/json (do not send Accept: text/html unless you want the human paywall).
- HTTP 402 means you have not paid. Decode the base64 PAYMENT-REQUIRED header. HTTP 503 is not a new quote.
- Sign EIP-3009 (scheme exact, assetTransferMethod eip3009) with validBefore = now + accepts[0].maxTimeoutSeconds (600 seconds). That window starts when you sign and must cover wallet confirmation plus CDP verify and settle. Magent retries transient facilitator 429/5xx before answering. Do not send upto or batch-settlement payloads; magent does not offer those schemes.
- Retry the same URL with PAYMENT-SIGNATURE (base64 JSON echoing accepted, payload, and extensions when present).
- Success is HTTP 200 JSON plus PAYMENT-RESPONSE. Settlement happens before the tool runs. HTTP 503 settlement_uncertain or settle_failed: retry the same PAYMENT-SIGNATURE. Mint a new nonce only after a new HTTP 402.

- offered `exact` on eip155:8453: Fixed-price USDC on Base. The buyer authorizes the advertised amount (EIP-3009). magent settles before the tool runs (paymentFlow upfront). extra.assetTransferMethod=eip3009 extra.paymentFlow=upfront.

- not offered `upto`: Not offered. Usage-based: buyer authorizes a ceiling, seller settles the actual amount after work. Reserved for a future metered tool. Not for current calculators or code search.
- not offered `batch-settlement`: Not offered. Payment-channel vouchers claimed later in batches. Not the same as POST {items} bulk (that is still exact).

Same-path POST {items} is still scheme exact: one EIP-3009 authorization for n times the GET unit. That is not x402 batch-settlement (payment channels / vouchers).

Shared HTTP 402 and 503 table: https://magentlab.com/docs/payments

Stdio MCP (one process per host): https://magentlab.com/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.