# PaO2/FiO2 ratio

PaO2/FiO2 ratio

Status: LIVE
Price: $0.005 USDC
`GET /api/calc/pf_ratio`
HTML: https://magentlab.com/docs/pf-ratio
Markdown: https://magentlab.com/docs/pf-ratio.md

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

## What it computes

Compute the PaO2/FiO2 ratio as arterial PO2 in mm Hg divided by inspired oxygen fraction.

## When to use

When an agent needs PaO2 divided by FiO2 and must not invent ARDS severity bands or the oxygenation index.

## When not to use

- Not a diagnosis. Magent does not apply ARDS severity cutoffs.
- This is not the oxygenation index (FiO2 × MAP × 100 / PaO2).
- FiO2 is required as a fraction (0.21–1.0), not a percent, and is not defaulted to room air.

## Formula

```
pf_ratio = pao2_mm_hg / fio2
```

## Citation

[Pulmonary response to major injury](https://doi.org/10.1001/archsurg.1974.01350270079014)
Horovitz JH, Carrico CJ, Shires GT
Arch Surg. 1974;108(3):349-355
DOI: [10.1001/archsurg.1974.01350270079014](https://doi.org/10.1001/archsurg.1974.01350270079014)

## Worked example

### PaO2 95, FiO2 0.21

Given: `fio2=0.21, pao2_mm_hg=95`

1. pf_ratio = 95 / 0.21 = 452.381… → 452.4


### PaO2 60, FiO2 1.0

Given: `fio2=1.0, pao2_mm_hg=60`

1. pf_ratio = 60 / 1.0 = 60.0


## Also searched as

- P/F ratio
- PaO2 over FiO2
- PaO2/FiO2
- PaO2 FiO2 ratio
- PF ratio
- arterial PaO2 FiO2

## Parameters

- `pao2_mm_hg` (number, required): Arterial PO2 in mm Hg (20-700).
- `fio2` (number, required): Inspired oxygen as a fraction (0.21-1.0), not a percent. Required.

## 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/pf_ratio`
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": [
    {
      "fio2": "0.21",
      "pao2_mm_hg": "95"
    },
    {
      "fio2": "0.21",
      "pao2_mm_hg": "95"
    }
  ]
}
```

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

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/pf_ratio",
  "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": "Horovitz JH, Carrico CJ, Shires GT",
        "doi": "10.1001/archsurg.1974.01350270079014",
        "id": "horovitz-1974",
        "source": "Arch Surg. 1974;108(3):349-355",
        "title": "Pulmonary response to major injury"
      },
      "formula": "pf_ratio",
      "formula_expression": "pf_ratio = pao2_mm_hg / fio2",
      "fio2": 0.21,
      "pao2_mm_hg": 95.0,
      "pf_ratio": 452.4
    },
    {
      "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": "Horovitz JH, Carrico CJ, Shires GT",
        "doi": "10.1001/archsurg.1974.01350270079014",
        "id": "horovitz-1974",
        "source": "Arch Surg. 1974;108(3):349-355",
        "title": "Pulmonary response to major injury"
      },
      "formula": "pf_ratio",
      "formula_expression": "pf_ratio = pao2_mm_hg / fio2",
      "fio2": 0.21,
      "pao2_mm_hg": 95.0,
      "pf_ratio": 452.4
    }
  ]
}
```

## Response fields

- `formula` (string): pf_ratio
- `formula_expression` (string): Exact expression used
- `pao2_mm_hg` (number): Arterial PO2 used, mm Hg
- `fio2` (number): Inspired oxygen fraction used
- `pf_ratio` (number): PaO2 divided by FiO2, 1 decimal
- `citation` (object): Horovitz, Carrico, and Shires 1974 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": "Horovitz JH, Carrico CJ, Shires GT",
    "doi": "10.1001/archsurg.1974.01350270079014",
    "id": "horovitz-1974",
    "source": "Arch Surg. 1974;108(3):349-355",
    "title": "Pulmonary response to major injury"
  },
  "formula": "pf_ratio",
  "formula_expression": "pf_ratio = pao2_mm_hg / fio2",
  "fio2": 0.21,
  "pao2_mm_hg": 95.0,
  "pf_ratio": 452.4
}
```

## Errors

- HTTP 400 `invalid_pao2`: pao2_mm_hg must be a number from 20 to 700. Returned before settlement; you are not charged.
- HTTP 400 `invalid_fio2`: fio2 must be a fraction from 0.21 to 1.0. 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.

Shared HTTP 402 and 503: https://magentlab.com/docs/payments

## Related tools

- [A-a O2 gradient](https://magentlab.com/docs/aa-gradient) — Compute the alveolar–arterial oxygen gradient from arterial blood-gas values using the simplified ideal alveolar-gas equation.
- [Oxygenation index](https://magentlab.com/docs/oxygenation-index) — Compute the oxygenation index from inspired oxygen fraction, mean airway pressure in cm H2O, and arterial PO2.

## 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).

Shared HTTP 402 and 503 table: https://magentlab.com/docs/payments

Stdio MCP (one process per host): https://magentlab.com/docs/mcp

## 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.