Respiratory · LIVE

Alveolar–arterial oxygen gradient (A-a O2)

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

Also searched as

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

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

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/aa_gradient?paco2_mm_hg=40&pao2_mm_hg=95"

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/aa_gradient 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": [
    {
      "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.",
      "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"
      },
      "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,
      "aa_gradient_mm_hg": 4.7,
      "fio2": 0.21,
      "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.",
      "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"
      },
      "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,
      "aa_gradient_mm_hg": 4.7,
      "fio2": 0.21,
      "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.",
  "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"
  },
  "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,
  "aa_gradient_mm_hg": 4.7,
  "fio2": 0.21,
  "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
}

Client errors (HTTP 400)

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

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.

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.