LIVE

A-a O2 gradient

Compute the alveolar–arterial oxygen gradient from arterial blood-gas values using the simplified ideal alveolar-gas equation.

LIVE $0.005 USDC GET /api/calc/aa_gradient

Markdown: /docs/aa-gradient.md · Canonical: https://magentlab.com/docs/aa-gradient

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

What it computes

Compute the alveolar–arterial oxygen gradient from arterial blood-gas values using the simplified ideal alveolar-gas equation.

When to use

When an agent needs PAO2 minus PaO2 from FiO2, barometric pressure, PaCO2, and PaO2 and must not invent an A-a gradient or an age-expected rule of thumb.

When not to use

• Not a diagnosis. Uses the simplified alveolar-gas equation with PH2O = 47 mm Hg at body temperature.
• Does not apply age-expected A-a rules of thumb.
• FiO2 is a fraction (0.21–1.0), not a percent.

Formula

PAO2_mm_hg = fio2 * (pb_mm_hg - 47) - paco2_mm_hg / rq; aa_gradient_mm_hg = PAO2_mm_hg - pao2_mm_hg

Citation

Title

"Ideal" alveolar air and the analysis of ventilation-perfusion relationships in the lungs

Authors

Riley RL, Cournand A

Source

J Appl Physiol. 1949;1(12):825-847

DOI

10.1152/jappl.1949.1.12.825

Worked example

Try

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

/api/calc/aa_gradient?paco2_mm_hg=40&pao2_mm_hg=95

Full URL: https://api.magentlab.com/api/calc/aa_gradient?paco2_mm_hg=40&pao2_mm_hg=95

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/aa_gradient?paco2_mm_hg=40&pao2_mm_hg=95"

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/aa_gradient 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": [
    {
      "paco2_mm_hg": "40",
      "pao2_mm_hg": "95"
    },
    {
      "paco2_mm_hg": "40",
      "pao2_mm_hg": "95"
    }
  ]
}

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/aa_gradient",
  "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.",
      "aa_gradient_mm_hg": 4.7,
      "citation": {
        "authors": "Riley RL, Cournand A",
        "doi": "10.1152/jappl.1949.1.12.825",
        "id": "riley-cournand-1949",
        "source": "J Appl Physiol. 1949;1(12):825-847",
        "title": "\"Ideal\" alveolar air and the analysis of ventilation-perfusion relationships in the lungs"
      },
      "fio2": 0.21,
      "formula": "aa_gradient",
      "formula_expression": "PAO2_mm_hg = fio2 * (pb_mm_hg - 47) - paco2_mm_hg / rq; aa_gradient_mm_hg = PAO2_mm_hg - pao2_mm_hg",
      "paco2_mm_hg": 40.0,
      "pao2_alveolar_mm_hg": 99.7,
      "pao2_mm_hg": 95.0,
      "pb_mm_hg": 760.0,
      "rq": 0.8,
      "water_vapor_mm_hg": 47.0
    },
    {
      "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.",
      "aa_gradient_mm_hg": 4.7,
      "citation": {
        "authors": "Riley RL, Cournand A",
        "doi": "10.1152/jappl.1949.1.12.825",
        "id": "riley-cournand-1949",
        "source": "J Appl Physiol. 1949;1(12):825-847",
        "title": "\"Ideal\" alveolar air and the analysis of ventilation-perfusion relationships in the lungs"
      },
      "fio2": 0.21,
      "formula": "aa_gradient",
      "formula_expression": "PAO2_mm_hg = fio2 * (pb_mm_hg - 47) - paco2_mm_hg / rq; aa_gradient_mm_hg = PAO2_mm_hg - pao2_mm_hg",
      "paco2_mm_hg": 40.0,
      "pao2_alveolar_mm_hg": 99.7,
      "pao2_mm_hg": 95.0,
      "pb_mm_hg": 760.0,
      "rq": 0.8,
      "water_vapor_mm_hg": 47.0
    }
  ]
}

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.",
  "aa_gradient_mm_hg": 4.7,
  "citation": {
    "authors": "Riley RL, Cournand A",
    "doi": "10.1152/jappl.1949.1.12.825",
    "id": "riley-cournand-1949",
    "source": "J Appl Physiol. 1949;1(12):825-847",
    "title": "\"Ideal\" alveolar air and the analysis of ventilation-perfusion relationships in the lungs"
  },
  "fio2": 0.21,
  "formula": "aa_gradient",
  "formula_expression": "PAO2_mm_hg = fio2 * (pb_mm_hg - 47) - paco2_mm_hg / rq; aa_gradient_mm_hg = PAO2_mm_hg - pao2_mm_hg",
  "paco2_mm_hg": 40.0,
  "pao2_alveolar_mm_hg": 99.7,
  "pao2_mm_hg": 95.0,
  "pb_mm_hg": 760.0,
  "rq": 0.8,
  "water_vapor_mm_hg": 47.0
}

Errors

Related tools

• MAP — Compute conventional estimated mean arterial pressure from cuff systolic and diastolic pressures.
• Oxygenation index — Compute the oxygenation index from inspired oxygen fraction, mean airway pressure in cm H2O, and arterial PO2.

Also searched as

• A-a gradient
• A-a O2
• alveolar-arterial oxygen gradient
• alveolar gas equation
• PAO2 minus PaO2
• A-a O2 gradient

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.