Electrolytes / glucose · LIVE

Free water deficit in hypernatremia (Adrogué–Madias)

Free water deficit

Estimate free water deficit from weight, sex-specific TBW, and measured serum Na versus a chosen target.

LIVE $0.005 USDC GET /api/calc/free_water_deficit

Markdown: /docs/free-water-deficit.md · Canonical: https://magentlab.com/docs/free-water-deficit

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

What it computes

Estimate free water deficit from weight, sex-specific TBW, and measured serum Na versus a chosen target.

When to use

When an agent needs Adrogué–Madias hypernatremia deficit arithmetic and must not invent TBW or a replacement volume.

When not to use

• Not a treatment order and not an infusion protocol. The result is an estimate of free water deficit versus a target sodium, not a dosing or correction-rate order.
• Sex-only TBW fractions (0.6 male, 0.5 female); no extra elderly coefficient. Does not model ongoing losses or the safe rate of correction.

Formula

TBW_L = 0.6 * weight_kg (male) or 0.5 * weight_kg (female); free_water_deficit_l = TBW_L * (sodium_mmol_l / desired_na_mmol_l - 1)

Citation

Title

Hypernatremia

Authors

Adrogué HJ, Madias NE

Source

N Engl J Med. 2000;342(20):1493-1499

DOI

10.1056/NEJM200005183422006

Worked example

Also searched as

• free water deficit
• hypernatremia free water
• Adrogue Madias hypernatremia
• water deficit hypernatremia
• TBW free water deficit

Try

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

/api/calc/free_water_deficit?weight_kg=70&sex=male&sodium_mmol_l=160&desired_na_mmol_l=140

Full URL: https://api.magentlab.com/api/calc/free_water_deficit?weight_kg=70&sex=male&sodium_mmol_l=160&desired_na_mmol_l=140

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/free_water_deficit?weight_kg=70&sex=male&sodium_mmol_l=160&desired_na_mmol_l=140"

Parameters

Bulk (POST)

POST the same path with a JSON items array. The first item is the GET unit; each additional item is $0.002. Invalid items return HTTP 400 before settlement.

POST /api/calc/free_water_deficit Max 25 unit_amount + extra_item_amount * (n - 1) extra $0.002 PREVIEW

• 1 to 25 items. Each item uses the same keys as the GET query parameters.
• POST of 1 item costs the same as GET. Lists longer than 25: chunk into multiple POSTs. Extra items still execute; do not pad dummy rows.
• 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": [
    {
      "desired_na_mmol_l": "140",
      "sex": "male",
      "sodium_mmol_l": "160",
      "weight_kg": "70"
    },
    {
      "desired_na_mmol_l": "140",
      "sex": "male",
      "sodium_mmol_l": "160",
      "weight_kg": "70"
    }
  ]
}

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/free_water_deficit",
  "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": "Adrogué HJ, Madias NE",
        "doi": "10.1056/NEJM200005183422006",
        "id": "adrogue-madias-hypernatremia-2000",
        "source": "N Engl J Med. 2000;342(20):1493-1499",
        "title": "Hypernatremia"
      },
      "formula": "adrogue_madias",
      "formula_expression": "TBW_L = 0.6 * weight_kg (male) or 0.5 * weight_kg (female); free_water_deficit_l = TBW_L * (sodium_mmol_l / desired_na_mmol_l - 1)",
      "sodium_mmol_l": 160.0,
      "weight_kg": 70.0,
      "sex": "male",
      "tbw_l": 42.0,
      "desired_na_mmol_l": 140.0,
      "free_water_deficit_l": 6.0
    },
    {
      "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": "Adrogué HJ, Madias NE",
        "doi": "10.1056/NEJM200005183422006",
        "id": "adrogue-madias-hypernatremia-2000",
        "source": "N Engl J Med. 2000;342(20):1493-1499",
        "title": "Hypernatremia"
      },
      "formula": "adrogue_madias",
      "formula_expression": "TBW_L = 0.6 * weight_kg (male) or 0.5 * weight_kg (female); free_water_deficit_l = TBW_L * (sodium_mmol_l / desired_na_mmol_l - 1)",
      "sodium_mmol_l": 160.0,
      "weight_kg": 70.0,
      "sex": "male",
      "tbw_l": 42.0,
      "desired_na_mmol_l": 140.0,
      "free_water_deficit_l": 6.0
    }
  ]
}

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": "Adrogué HJ, Madias NE",
    "doi": "10.1056/NEJM200005183422006",
    "id": "adrogue-madias-hypernatremia-2000",
    "source": "N Engl J Med. 2000;342(20):1493-1499",
    "title": "Hypernatremia"
  },
  "formula": "adrogue_madias",
  "formula_expression": "TBW_L = 0.6 * weight_kg (male) or 0.5 * weight_kg (female); free_water_deficit_l = TBW_L * (sodium_mmol_l / desired_na_mmol_l - 1)",
  "sodium_mmol_l": 160.0,
  "weight_kg": 70.0,
  "sex": "male",
  "tbw_l": 42.0,
  "desired_na_mmol_l": 140.0,
  "free_water_deficit_l": 6.0
}

Client errors (HTTP 400)

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

Related tools

• Sodium deficit — Estimate sodium (cation) deficit from weight, sex-specific TBW, and measured serum Na versus a chosen target.
• Corrected sodium — Compute expected sodium in hyperglycemia using Katz 1.6 or Hillier 2.4. The formula argument is required.
• Serum osmolality — Compute Worthley calculated serum osmolality from sodium, glucose, and BUN, plus an optional osmolar gap when a measured osm is supplied.

Payment

Unpaid requests return HTTP 402 even if query parameters or POST items are missing or invalid, so CDP and agents can index the path. After a PAYMENT-SIGNATURE, 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

• HTTP 402 is unpaid, including a missing query. After PAYMENT-SIGNATURE, invalid parameters return HTTP 400 before settlement. You are not charged. HTTP 402 never includes the tool JSON.
• exact: settlement finishes before the tool (paymentFlow upfront). batch-settlement: verify/deposit before the tool; chargedCumulativeAmount commits after HTTP 2xx. 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.