# Friedewald LDL-C

Status: WEDGE
Price: $0.005 USDC
`GET /api/calc/friedewald`
HTML: https://magentlab.com/docs/friedewald
Markdown: https://magentlab.com/docs/friedewald.md

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

## What it computes

Estimate LDL-C from total cholesterol, HDL, and triglycerides using Friedewald 1972.

## When to use

When an agent needs Friedewald LDL arithmetic and must not invent a VLDL factor or mix mg/dL with mmol/L.

## When not to use

- Not a diagnosis and not a statin order. Direct LDL assay is out of scope.
- Triglycerides above 400 mg/dL (or 4.5 mmol/L) are rejected. The paper's VLDL estimate of TG/5 is for typical specimens only.

## Formula

```
ldl_c_mg_dl = total_cholesterol_mg_dl - hdl_mg_dl - (triglycerides_mg_dl / 5); ldl_c_mmol_l = total_cholesterol_mmol_l - hdl_mmol_l - (triglycerides_mmol_l / 2.2)
```

## Citation

Estimation of the concentration of low-density lipoprotein cholesterol in plasma, without use of the preparative ultracentrifuge
Friedewald WT, Levy RI, Fredrickson DS
Clin Chem. 1972;18(6):499-502
DOI: [10.1093/clinchem/18.6.499](https://doi.org/10.1093/clinchem/18.6.499)

## Worked example

### TC 200, HDL 50, TG 150 mg/dL

Given: `hdl_mg_dl=50, total_cholesterol_mg_dl=200, triglycerides_mg_dl=150`

1. VLDL = 150 / 5 = 30 mg/dL
2. LDL-C = 200 - 50 - 30 = 120.0 mg/dL


## Parameters

- `total_cholesterol_mg_dl` (number, optional): Total cholesterol in mg/dL (50-500). Provide the full mg/dL set or the full mmol/L set, not mixed.
- `hdl_mg_dl` (number, optional): HDL cholesterol in mg/dL (5-150). Same unit system as the other lipids.
- `triglycerides_mg_dl` (number, optional): Triglycerides in mg/dL (10-400). Values above 400 are rejected; Friedewald VLDL is TG/5 for typical specimens only.
- `total_cholesterol_mmol_l` (number, optional): Total cholesterol in mmol/L (1.3-12.9). Converted as mg/dL = mmol/L * 38.67. Do not mix with mg/dL keys.
- `hdl_mmol_l` (number, optional): HDL cholesterol in mmol/L (0.1-3.9). Converted as mg/dL = mmol/L * 38.67.
- `triglycerides_mmol_l` (number, optional): Triglycerides in mmol/L (0.1-4.5). Cap is the SI stand-in for 400 mg/dL (mg/dL = mmol/L * 88.57). SI LDL uses TG/2.2.

## 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/friedewald`
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": [
    {
      "hdl_mg_dl": "50",
      "total_cholesterol_mg_dl": "200",
      "triglycerides_mg_dl": "150"
    },
    {
      "hdl_mg_dl": "50",
      "total_cholesterol_mg_dl": "200",
      "triglycerides_mg_dl": "150"
    }
  ]
}
```

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

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/friedewald",
  "items": [
    {
      "unit": "mg_dl",
      "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": "Friedewald WT, Levy RI, Fredrickson DS",
        "doi": "10.1093/clinchem/18.6.499",
        "id": "friedewald-1972",
        "source": "Clin Chem. 1972;18(6):499-502",
        "title": "Estimation of the concentration of low-density lipoprotein cholesterol in plasma, without use of the preparative ultracentrifuge"
      },
      "formula": "friedewald",
      "formula_expression": "ldl_c_mg_dl = total_cholesterol_mg_dl - hdl_mg_dl - (triglycerides_mg_dl / 5)",
      "hdl_mg_dl": 50.0,
      "ldl_c_mg_dl": 120.0,
      "ldl_c_mmol_l": 3.1,
      "total_cholesterol_mg_dl": 200.0,
      "triglycerides_mg_dl": 150.0
    },
    {
      "unit": "mg_dl",
      "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": "Friedewald WT, Levy RI, Fredrickson DS",
        "doi": "10.1093/clinchem/18.6.499",
        "id": "friedewald-1972",
        "source": "Clin Chem. 1972;18(6):499-502",
        "title": "Estimation of the concentration of low-density lipoprotein cholesterol in plasma, without use of the preparative ultracentrifuge"
      },
      "formula": "friedewald",
      "formula_expression": "ldl_c_mg_dl = total_cholesterol_mg_dl - hdl_mg_dl - (triglycerides_mg_dl / 5)",
      "hdl_mg_dl": 50.0,
      "ldl_c_mg_dl": 120.0,
      "ldl_c_mmol_l": 3.1,
      "total_cholesterol_mg_dl": 200.0,
      "triglycerides_mg_dl": 150.0
    }
  ]
}
```

## Response fields

- `formula` (string): friedewald
- `formula_expression` (string): Exact expression used
- `unit` (string): mg_dl or mmol_l, the unit system supplied
- `total_cholesterol_mg_dl` (number): Total cholesterol in mg/dL (converted when SI inputs are used)
- `hdl_mg_dl` (number): HDL cholesterol in mg/dL (converted when SI inputs are used)
- `triglycerides_mg_dl` (number): Triglycerides in mg/dL (converted when SI inputs are used)
- `ldl_c_mg_dl` (number): Estimated LDL-C in mg/dL, 1 decimal
- `ldl_c_mmol_l` (number): Estimated LDL-C in mmol/L, 1 decimal
- `citation` (object): Friedewald Clin Chem 1972 citation
- `disclaimer` (string): Not-a-device notice

## Example JSON

Frozen fixture. Not a live lookup.

```json
{
  "unit": "mg_dl",
  "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": "Friedewald WT, Levy RI, Fredrickson DS",
    "doi": "10.1093/clinchem/18.6.499",
    "id": "friedewald-1972",
    "source": "Clin Chem. 1972;18(6):499-502",
    "title": "Estimation of the concentration of low-density lipoprotein cholesterol in plasma, without use of the preparative ultracentrifuge"
  },
  "formula": "friedewald",
  "formula_expression": "ldl_c_mg_dl = total_cholesterol_mg_dl - hdl_mg_dl - (triglycerides_mg_dl / 5)",
  "hdl_mg_dl": 50.0,
  "ldl_c_mg_dl": 120.0,
  "ldl_c_mmol_l": 3.1,
  "total_cholesterol_mg_dl": 200.0,
  "triglycerides_mg_dl": 150.0
}
```

## Errors

- HTTP 400 `invalid_cholesterol`: provide all of total_cholesterol_mg_dl (50-500), hdl_mg_dl (5-150), and triglycerides_mg_dl, or all of total_cholesterol_mmol_l (1.3-12.9), hdl_mmol_l (0.1-3.9), and triglycerides_mmol_l, not mixed. Returned before settlement; you are not charged.
- HTTP 400 `invalid_triglyceride`: triglycerides_mg_dl must be 10-400; triglycerides_mmol_l must be 0.1-4.5 (~400 mg/dL). Friedewald is not applied above 400 mg/dL. Returned before settlement; you are not charged.
- HTTP 400 `invalid_lipid_inputs`: computed LDL-C would be negative; check total cholesterol, HDL, and triglycerides. 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.
- HTTP 402 `payment_required`: Missing or invalid PAYMENT-SIGNATURE; decode the PAYMENT-REQUIRED header
- HTTP 409 `payment_in_progress`: The same authorization nonce is already being settled; retry shortly
- HTTP 429 `rate_limited`: Too many requests from this client
- HTTP 503 `settlement_uncertain`: Settlement is unconfirmed; retry with the same PAYMENT-SIGNATURE
- HTTP 503 `settle_failed`: Settlement failed; retry with the same PAYMENT-SIGNATURE shortly
- HTTP 503 `facilitator_unavailable`: Payment facilitator unavailable
- HTTP 503 `facilitator_misconfigured`: Payment facilitator is not configured
- HTTP 503 `facilitator_unauthorized`: Payment facilitator rejected credentials
- HTTP 503 `ledger_unavailable`: Payment ledger unavailable
- HTTP 503 `payment_unavailable`: Payment processing unavailable

## Related tools

- [A1C ↔ eAG](https://magentlab.com/docs/a1c-eag) — Convert A1C percent to estimated average glucose, or the reverse, using Nathan/ADAG.

## Also searched as

- Friedewald equation
- LDL-C estimate
- calculated LDL cholesterol
- VLDL triglycerides/5
- Friedewald 1972
- estimated LDL-C

## 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 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.
- 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.

## Guarantees

- Invalid query parameters return HTTP 400 before settlement. You are not charged.
- Settlement finishes before the tool executes. 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 not persisted. Request logs store path without query.