LIVE

Serum osmolality

Compute Worthley calculated serum osmolality from sodium, glucose, and BUN, plus an optional osmolar gap when a measured osm is supplied.

LIVE $0.005 USDC GET /api/calc/serum_osmolality

Markdown: /docs/serum-osmolality.md · Canonical: https://magentlab.com/docs/serum-osmolality

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

What it computes

Compute Worthley calculated serum osmolality from sodium, glucose, and BUN, plus an optional osmolar gap when a measured osm is supplied.

When to use

When an agent needs a published 2×Na calculated osmolality and must not invent an ethanol, mannitol, or 1.86×Na+9 formula.

When not to use

• Worthley argued the simple 2×Na formula is the best. This is a calculated osmolarity/osmolality estimate from sodium, glucose, and BUN only — not a measured freezing-point osmometer.
• Does not include ethanol, mannitol, or a 1.86×Na+9 (Dorwart–Chalmers) term. Not a diagnosis of a toxic alcohol or an osmolar-gap workup.

Formula

calculated_osm_mosm_kg = 2 * sodium_mmol_l + glucose_mg_dl / 18 + bun_mg_dl / 2.8

Citation

Title

For calculating osmolality, the simplest formula is the best

Authors

Worthley LI, Guerin M, Pain RW

Source

Anaesth Intensive Care. 1987;15(2):199-202

DOI

10.1177/0310057X8701500214

Worked example

Try

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

/api/calc/serum_osmolality?sodium_mmol_l=140&glucose_mg_dl=90&bun_mg_dl=14

Full URL: https://api.magentlab.com/api/calc/serum_osmolality?sodium_mmol_l=140&glucose_mg_dl=90&bun_mg_dl=14

x402 V2 curl

Expect HTTP 402 and a PAYMENT-REQUIRED header until you retry with PAYMENT-SIGNATURE. Incomplete query params return HTTP 400 before any quote or charge. HTTP 503 after a signature: retry the same PAYMENT-SIGNATURE — that is not a new 402.

curl -i -H "Accept: application/json" "https://api.magentlab.com/api/calc/serum_osmolality?sodium_mmol_l=140&glucose_mg_dl=90&bun_mg_dl=14"

Cursor mcp.json

Intended config for @magent/mcp. This is not npm @x402/fetch (a payment fetch wrapper).

{
  "mcpServers": {
    "magent": {
      "args": [
        "-y",
        "@magent/mcp"
      ],
      "command": "npx",
      "env": {
        "X402_PRIVATE_KEY": "0xYOUR_SPENDING_KEY"
      }
    }
  }
}

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/serum_osmolality 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": [
    {
      "bun_mg_dl": "14",
      "glucose_mg_dl": "90",
      "sodium_mmol_l": "140"
    },
    {
      "bun_mg_dl": "14",
      "glucose_mg_dl": "90",
      "sodium_mmol_l": "140"
    }
  ]
}

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/serum_osmolality",
  "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": "Worthley LI, Guerin M, Pain RW",
        "doi": "10.1177/0310057X8701500214",
        "id": "worthley-1987",
        "source": "Anaesth Intensive Care. 1987;15(2):199-202",
        "title": "For calculating osmolality, the simplest formula is the best"
      },
      "formula": "worthley",
      "formula_expression": "calculated_osm_mosm_kg = 2 * sodium_mmol_l + glucose_mg_dl / 18 + bun_mg_dl / 2.8",
      "glucose_mg_dl": 90.0,
      "sodium_mmol_l": 140.0,
      "bun_mg_dl": 14.0,
      "calculated_osm_mosm_kg": 290.0
    },
    {
      "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": "Worthley LI, Guerin M, Pain RW",
        "doi": "10.1177/0310057X8701500214",
        "id": "worthley-1987",
        "source": "Anaesth Intensive Care. 1987;15(2):199-202",
        "title": "For calculating osmolality, the simplest formula is the best"
      },
      "formula": "worthley",
      "formula_expression": "calculated_osm_mosm_kg = 2 * sodium_mmol_l + glucose_mg_dl / 18 + bun_mg_dl / 2.8",
      "glucose_mg_dl": 90.0,
      "sodium_mmol_l": 140.0,
      "bun_mg_dl": 14.0,
      "calculated_osm_mosm_kg": 290.0
    }
  ]
}

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": "Worthley LI, Guerin M, Pain RW",
    "doi": "10.1177/0310057X8701500214",
    "id": "worthley-1987",
    "source": "Anaesth Intensive Care. 1987;15(2):199-202",
    "title": "For calculating osmolality, the simplest formula is the best"
  },
  "formula": "worthley",
  "formula_expression": "calculated_osm_mosm_kg = 2 * sodium_mmol_l + glucose_mg_dl / 18 + bun_mg_dl / 2.8",
  "glucose_mg_dl": 90.0,
  "sodium_mmol_l": 140.0,
  "bun_mg_dl": 14.0,
  "calculated_osm_mosm_kg": 290.0
}

Errors

Related tools

• Corrected sodium — Compute expected sodium in hyperglycemia using Katz 1.6 or Hillier 2.4. The formula argument is required.
• Corrected calcium — Compute Payne albumin-corrected calcium from total calcium and albumin.
• Bicarbonate deficit — Estimate bicarbonate deficit from weight and measured plasma HCO3 using a 50 percent body-weight apparent space.
• Sodium deficit — Estimate sodium (cation) deficit from weight, sex-specific TBW, and measured serum Na versus a chosen target.

Also searched as

• serum osmolality
• calculated osmolarity
• osmolar gap
• Worthley osmolality
• 2Na glucose BUN

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.

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.