Electrolytes / glucose · LIVE

Estimated ethanol concentration

Estimated ethanol

Estimate fasting theoretical blood ethanol (Co) from ingested ethanol grams and sex-specific Watson 1980 total body water, using the Watson 1981 Widmark update.

LIVE $0.005 USDC GET /api/calc/estimated_ethanol

Markdown: /docs/estimated-ethanol.md · Canonical: https://magentlab.com/docs/estimated-ethanol

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

What it computes

Estimate fasting theoretical blood ethanol (Co) from ingested ethanol grams and sex-specific Watson 1980 total body water, using the Watson 1981 Widmark update.

When to use

When an agent needs a published fasting Co from ethanol mass and anthropometrics and must not invent a medicolegal BAC or a treatment dose.

When not to use

• Not a medical device. A licensed clinician remains responsible for interpretation.
• Not a medicolegal BAC. Co is a fasting Widmark-type theoretical zero-time estimate, not a measured blood or breath alcohol and not evidence for impairment or legal limits.
• Fasting Widmark-type estimate only. Absorbed fraction is 1. Does not model drinking duration, food, or elimination (βt).
• Ethanol only. Not a treatment dose.

Formula

TBW_L (male) = 2.447 - 0.09516*age_years + 0.1074*height_cm + 0.3362*weight_kg; TBW_L (female) = -2.097 + 0.1069*height_cm + 0.2466*weight_kg; Co_g_l = absorbed_fraction * ethanol_g * blood_water_fraction / TBW_L (fasting absorbed_fraction = 1, blood_water_fraction = 0.80)

Citation

Title

Prediction of blood alcohol concentrations in human subjects. Updating the Widmark Equation

Authors

Watson PE, Watson ID, Batt RD

Source

J Stud Alcohol. 1981;42(7):547-556

DOI

10.15288/jsa.1981.42.547

Worked example

Also searched as

• estimated ethanol
• blood alcohol concentration
• Widmark equation
• Watson TBW ethanol
• fasting Co ethanol
• serum ethanol from ingestion
• total body water alcohol

Try

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

/api/calc/estimated_ethanol?sex=male&age=30&height_cm=175&weight_kg=70&ethanol_g=14

Full URL: https://api.magentlab.com/api/calc/estimated_ethanol?sex=male&age=30&height_cm=175&weight_kg=70&ethanol_g=14

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/estimated_ethanol?sex=male&age=30&height_cm=175&weight_kg=70&ethanol_g=14"

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/estimated_ethanol 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": [
    {
      "age": "30",
      "ethanol_g": "14",
      "height_cm": "175",
      "sex": "male",
      "weight_kg": "70"
    },
    {
      "age": "30",
      "ethanol_g": "14",
      "height_cm": "175",
      "sex": "male",
      "weight_kg": "70"
    }
  ]
}

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/estimated_ethanol",
  "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.",
      "age_years": 30,
      "citation": {
        "authors": "Watson PE, Watson ID, Batt RD",
        "doi": "10.15288/jsa.1981.42.547",
        "id": "watson-1981",
        "pmid": "7289599",
        "source": "J Stud Alcohol. 1981;42(7):547-556",
        "title": "Prediction of blood alcohol concentrations in human subjects. Updating the Widmark Equation"
      },
      "formula": "watson_1981",
      "formula_expression": "TBW_L (male) = 2.447 - 0.09516*age_years + 0.1074*height_cm + 0.3362*weight_kg; TBW_L (female) = -2.097 + 0.1069*height_cm + 0.2466*weight_kg; Co_g_l = absorbed_fraction * ethanol_g * blood_water_fraction / TBW_L (fasting absorbed_fraction = 1, blood_water_fraction = 0.80)",
      "sex": "male",
      "weight_kg": 70.0,
      "tbw_l": 41.92,
      "height_cm": 175.0,
      "absorbed_fraction": 1.0,
      "blood_water_fraction": 0.8,
      "co_g_l": 0.267,
      "co_mg_dl": 26.7,
      "ethanol_g": 14.0
    },
    {
      "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.",
      "age_years": 30,
      "citation": {
        "authors": "Watson PE, Watson ID, Batt RD",
        "doi": "10.15288/jsa.1981.42.547",
        "id": "watson-1981",
        "pmid": "7289599",
        "source": "J Stud Alcohol. 1981;42(7):547-556",
        "title": "Prediction of blood alcohol concentrations in human subjects. Updating the Widmark Equation"
      },
      "formula": "watson_1981",
      "formula_expression": "TBW_L (male) = 2.447 - 0.09516*age_years + 0.1074*height_cm + 0.3362*weight_kg; TBW_L (female) = -2.097 + 0.1069*height_cm + 0.2466*weight_kg; Co_g_l = absorbed_fraction * ethanol_g * blood_water_fraction / TBW_L (fasting absorbed_fraction = 1, blood_water_fraction = 0.80)",
      "sex": "male",
      "weight_kg": 70.0,
      "tbw_l": 41.92,
      "height_cm": 175.0,
      "absorbed_fraction": 1.0,
      "blood_water_fraction": 0.8,
      "co_g_l": 0.267,
      "co_mg_dl": 26.7,
      "ethanol_g": 14.0
    }
  ]
}

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.",
  "age_years": 30,
  "citation": {
    "authors": "Watson PE, Watson ID, Batt RD",
    "doi": "10.15288/jsa.1981.42.547",
    "id": "watson-1981",
    "pmid": "7289599",
    "source": "J Stud Alcohol. 1981;42(7):547-556",
    "title": "Prediction of blood alcohol concentrations in human subjects. Updating the Widmark Equation"
  },
  "formula": "watson_1981",
  "formula_expression": "TBW_L (male) = 2.447 - 0.09516*age_years + 0.1074*height_cm + 0.3362*weight_kg; TBW_L (female) = -2.097 + 0.1069*height_cm + 0.2466*weight_kg; Co_g_l = absorbed_fraction * ethanol_g * blood_water_fraction / TBW_L (fasting absorbed_fraction = 1, blood_water_fraction = 0.80)",
  "sex": "male",
  "weight_kg": 70.0,
  "tbw_l": 41.92,
  "height_cm": 175.0,
  "absorbed_fraction": 1.0,
  "blood_water_fraction": 0.8,
  "co_g_l": 0.267,
  "co_mg_dl": 26.7,
  "ethanol_g": 14.0
}

Client errors (HTTP 400)

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

Related tools

• Anion gap — Compute the serum anion gap from sodium, chloride, and bicarbonate, with or without potassium, using the Emmett–Narins 1977 formulas. formula is required.
• Winters' formula — Compute expected arterial PCO2 in metabolic acidosis from plasma bicarbonate using the Albert–Winters 1967 formula.
• Free water deficit — Estimate free water deficit from weight, sex-specific TBW, and measured serum Na versus a chosen target.

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.