LIVE

QTc

Compute heart-rate-corrected QT using Bazett or Fridericia. The formula argument is required.

LIVE $0.005 USDC GET /api/calc/qtc

Markdown: /docs/qtc.md · Canonical: https://magentlab.com/docs/qtc

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

What it computes

Compute heart-rate-corrected QT using Bazett or Fridericia. The formula argument is required.

When to use

When an agent must not apply Bazett silently. Callers must choose formula=bazett or formula=fridericia.

When not to use

Not a diagnosis and not a drug-safety recommendation.
formula is required. magent does not pick Bazett or Fridericia.
Fridericia has no verified DOI in this record; citation is the 1920 Acta Med Scand paper.

Formula

QTc_ms = QT_ms / sqrt(RR_s)

Citation

Title: An analysis of the time-relations of electrocardiograms
Authors: Bazett HC
Source: Heart. 1920;7:353-370
DOI: none

Worked example

QT 400 ms, HR 80, Bazett

Given: formula=bazettheart_rate_bpm=80qt_ms=400

RR_s = 60 / 80 = 0.75
QTc = 400 / sqrt(0.75) = 461.9 ms

Try

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

/api/calc/qtc?qt_ms=400&heart_rate_bpm=80&formula=bazett

Full URL: https://api.magentlab.com/api/calc/qtc?qt_ms=400&heart_rate_bpm=80&formula=bazett

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.

curl -i -H "Accept: application/json" "https://api.magentlab.com/api/calc/qtc?qt_ms=400&heart_rate_bpm=80&formula=bazett"

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

Name	Type	Required	Description
`qt_ms`	number	required	Measured QT interval in milliseconds (200-800).
`heart_rate_bpm`	integer	required	Heart rate in beats per minute (30-220). RR_s = 60 / HR.
`formula`	string	required · bazett, fridericia	Correction formula. Required; magent does not pick one silently.

Response

Field	Type	Description
`formula`	string	bazett or fridericia
`formula_expression`	string	Exact expression used
`qt_ms`	number	Input QT in ms
`heart_rate_bpm`	integer	Input heart rate
`rr_s`	number	RR interval in seconds (60/HR)
`qtc_ms`	number	Corrected QT in ms, 1 decimal
`citation`	object	Bazett 1920 or Fridericia 1920
`disclaimer`	string	Not-a-device notice

Example JSON

Machine form of the same example. Frozen fixture. Not a live lookup.

{
  "disclaimer": "Not a medical device. Deterministic published-formula or coded-ontology output for autonomous agents. A licensed clinician remains responsible for patient care and billing submissions.",
  "citation": {
    "authors": "Bazett HC",
    "doi": null,
    "id": "bazett-1920",
    "source": "Heart. 1920;7:353-370",
    "title": "An analysis of the time-relations of electrocardiograms"
  },
  "formula": "bazett",
  "formula_expression": "QTc_ms = QT_ms / sqrt(RR_s)",
  "heart_rate_bpm": 80,
  "qt_ms": 400.0,
  "qtc_ms": 461.9,
  "rr_s": 0.75
}

Errors

HTTP	Code	When
400	`invalid_qt`	qt_ms must be a number from 200 to 800 Returned before settlement; you are not charged.
400	`invalid_heart_rate`	heart_rate_bpm must be an integer from 30 to 220 Returned before settlement; you are not charged.
400	`invalid_formula`	formula must be bazett or fridericia Returned before settlement; you are not charged.
402	`payment_required`	Missing or invalid PAYMENT-SIGNATURE; decode the PAYMENT-REQUIRED header
409	`payment_in_progress`	The same authorization nonce is already being settled; retry shortly
429	`rate_limited`	Too many requests from this client
503	`settlement_uncertain`	Settlement is unconfirmed; retry with the same PAYMENT-SIGNATURE
503	`facilitator_unavailable`	Payment facilitator unavailable
503	`facilitator_misconfigured`	Payment facilitator is not configured
503	`facilitator_unauthorized`	Payment facilitator rejected credentials
503	`ledger_unavailable`	Payment ledger unavailable
503	`payment_unavailable`	Payment processing unavailable

Related tools

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Also searched as

QTc Bazett vs Fridericia
Bazett formula
Fridericia QTc
corrected QT

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. Retry the same URL with PAYMENT-SIGNATURE. Settlement completes before the tool runs. 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. Uncertain settlement fails closed (HTTP 503).
Execution is timeout-bounded and concurrency-capped.
Calculator inputs are not persisted. Request logs store path without query.