# Serum osmolality

Status: LIVE
Price: $0.005 USDC
`GET /api/calc/serum_osmolality`
HTML: https://magentlab.com/docs/serum-osmolality
Markdown: https://magentlab.com/docs/serum-osmolality.md

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

For calculating osmolality, the simplest formula is the best
Worthley LI, Guerin M, Pain RW
Anaesth Intensive Care. 1987;15(2):199-202
DOI: [10.1177/0310057X8701500214](https://doi.org/10.1177/0310057X8701500214)

## Worked example

### Na 140, glucose 90, BUN 14

Given: `bun_mg_dl=14, glucose_mg_dl=90, sodium_mmol_l=140`

1. 2 × 140 = 280
2. 90 / 18 = 5
3. 14 / 2.8 = 5
4. calculated osm = 280 + 5 + 5 = 290 mOsm/kg


## Parameters

- `sodium_mmol_l` (number, required): Serum sodium in mmol/L (110-160).
- `glucose_mg_dl` (number, optional): Plasma glucose in mg/dL (50-1000). Provide this or glucose_mmol_l.
- `glucose_mmol_l` (number, optional): Plasma glucose in mmol/L (2.8-55.5). Converted as mg/dL = mmol/L * 18.015.
- `bun_mg_dl` (number, required): Blood urea nitrogen in mg/dL (1-200).
- `measured_osm_mosm_kg` (number, optional): Measured serum osmolality in mOsm/kg (200-400). When supplied, osm_gap_mosm_kg is returned.

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

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

Example 200:

```json
{
  "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 fields

- `formula` (string): worthley
- `formula_expression` (string): Exact expression used
- `sodium_mmol_l` (number): Input sodium in mmol/L
- `glucose_mg_dl` (number): Normalized glucose in mg/dL
- `bun_mg_dl` (number): Input BUN in mg/dL
- `calculated_osm_mosm_kg` (number): Worthley calculated osmolality in mOsm/kg, 1 decimal
- `osm_gap_mosm_kg` (number): measured_osm_mosm_kg minus calculated_osm_mosm_kg, 1 decimal. Omitted when measured osm is not supplied.
- `citation` (object): Worthley 1987 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": "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

- HTTP 400 `invalid_sodium`: sodium_mmol_l must be a number from 110 to 160 Returned before settlement; you are not charged.
- 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_bun`: bun_mg_dl must be a number from 1 to 200. Returned before settlement; you are not charged.
- HTTP 400 `invalid_measured_osmolality`: measured_osm_mosm_kg must be a number from 200 to 400. 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

- [Corrected sodium](https://magentlab.com/docs/corrected-sodium) — Compute expected sodium in hyperglycemia using Katz 1.6 or Hillier 2.4. The formula argument is required.
- [Corrected calcium](https://magentlab.com/docs/corrected-calcium) — Compute Payne albumin-corrected calcium from total calcium and albumin.
- [Bicarbonate deficit](https://magentlab.com/docs/bicarbonate-deficit) — Estimate bicarbonate deficit from weight and measured plasma HCO3 using a 50 percent body-weight apparent space.
- [Sodium deficit](https://magentlab.com/docs/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.

- 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).

## 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.