# Pediatric uncuffed ETT size (Cole)

Pediatric ETT size

Status: LIVE
Price: $0.005 USDC
`GET /api/calc/pediatric_ett`
HTML: https://magentlab.com/docs/pediatric-ett
Markdown: https://magentlab.com/docs/pediatric-ett.md

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

## What it computes

Compute Cole 1957 uncuffed pediatric endotracheal tube internal diameter from age in years.

## When to use

When an agent needs the published age/4+4 millimetre arithmetic and must not invent a cuffed formula or tape length.

## When not to use

- Not a device-selection order and not a substitute for length-based tapes. Cole does not specify 0.5 mm stock rounding; magent returns 1 decimal.
- Uncuffed Cole formula only. Does not apply Khine/cuffed (age/4)+3.5. Age 0.5-12 years is an implementation clamp around typical pediatric use.

## Formula

```
ett_id_mm = age_years / 4 + 4
```

## Citation

[Pediatric formulas for the anesthesiologist](https://doi.org/10.1001/archpedi.1957.04030070084009)
Cole F
AMA Am J Dis Child. 1957;94(6):672-673
DOI: [10.1001/archpedi.1957.04030070084009](https://doi.org/10.1001/archpedi.1957.04030070084009)

## Worked example

### Age 4 years

Given: `age_years=4`

1. ID = 4/4 + 4 = 5.0 mm


### Age 1 year

Given: `age_years=1`

1. ID = 1/4 + 4 = 4.3 mm


## Also searched as

- pediatric ETT size
- Cole formula tube
- uncuffed endotracheal tube
- age over 4 plus 4
- pediatric tube diameter

## Parameters

- `age_years` (number, required): Age in years (0.5-12). Cole uncuffed ID (mm) = age/4 + 4. Not a neonatal-only formula.

## 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.

Method: `POST /api/calc/pediatric_ett`
Max items: 25
Price: unit_amount + extra_item_amount * (n - 1) (unit 5000 atomic, extra 2000 atomic)
Status: 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:

```json
{
  "items": [
    {
      "age_years": "4"
    },
    {
      "age_years": "4"
    }
  ]
}
```

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

Example 200:

```json
{
  "count": 2,
  "path": "/api/calc/pediatric_ett",
  "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": "Cole F",
        "doi": "10.1001/archpedi.1957.04030070084009",
        "id": "cole-1957",
        "source": "AMA Am J Dis Child. 1957;94(6):672-673",
        "title": "Pediatric formulas for the anesthesiologist"
      },
      "formula": "cole_1957",
      "formula_expression": "ett_id_mm = age_years / 4 + 4",
      "age_years": 4.0,
      "ett_id_mm": 5.0
    },
    {
      "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": "Cole F",
        "doi": "10.1001/archpedi.1957.04030070084009",
        "id": "cole-1957",
        "source": "AMA Am J Dis Child. 1957;94(6):672-673",
        "title": "Pediatric formulas for the anesthesiologist"
      },
      "formula": "cole_1957",
      "formula_expression": "ett_id_mm = age_years / 4 + 4",
      "age_years": 4.0,
      "ett_id_mm": 5.0
    }
  ]
}
```

## Response fields

- `formula` (string): cole_1957
- `formula_expression` (string): Exact expression used
- `age_years` (number): Age in years used
- `ett_id_mm` (number): Uncuffed internal diameter in mm, 1 decimal
- `citation` (object): Cole 1957 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": "Cole F",
    "doi": "10.1001/archpedi.1957.04030070084009",
    "id": "cole-1957",
    "source": "AMA Am J Dis Child. 1957;94(6):672-673",
    "title": "Pediatric formulas for the anesthesiologist"
  },
  "formula": "cole_1957",
  "formula_expression": "ett_id_mm = age_years / 4 + 4",
  "age_years": 4.0,
  "ett_id_mm": 5.0
}
```

## Errors

- HTTP 400 `invalid_pediatric_age`: age_years must be a number from 0.5 to 12. 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

- [Apgar score](https://magentlab.com/docs/apgar) — Compute the Apgar newborn evaluation score as the sum of five caller-assigned 0-2 signs.
- [Maintenance fluids](https://magentlab.com/docs/maintenance-fluids) — Compute Holliday–Segar 1957 daily maintenance water from weight, plus the corresponding hourly milliliters.

## 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.

- 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 accepts[0] (exact, EIP-3009) with validBefore = now + maxTimeoutSeconds (600 seconds), or accepts[1] (batch-settlement deposit/voucher) on product GET. Ping and POST {items} stay exact. Magent retries transient facilitator 429/5xx before answering.
- Retry the same URL with PAYMENT-SIGNATURE (base64 JSON echoing accepted, payload, and extensions when present).
- Success is HTTP 200 JSON plus PAYMENT-RESPONSE. exact settles before the tool. batch-settlement verifies (and deposit-settles) before the tool and commits the charge after HTTP 2xx. HTTP 503: retry the same PAYMENT-SIGNATURE. Mint a new exact 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.
- offered `batch-settlement` on eip155:8453: Payment-channel vouchers claimed later in batches. Exact stays accepts[0]. Same-path POST {items} is still exact. extra.assetTransferMethod=eip3009 extra.paymentFlow=authorization.

- 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.

Same-path POST {items} is still scheme exact: one EIP-3009 authorization for GET unit plus $0.002 per extra item. 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

- HTTP 402 is unpaid, including a missing query. After PAYMENT-SIGNATURE, invalid parameters return HTTP 400 before settlement. You are not charged.
- 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.