# Estimated ethanol concentration Estimated ethanol Status: LIVE Price: $0.005 USDC `GET /api/calc/estimated_ethanol` HTML: https://magentlab.com/docs/estimated-ethanol Markdown: https://magentlab.com/docs/estimated-ethanol.md 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 [Prediction of blood alcohol concentrations in human subjects. Updating the Widmark Equation](https://doi.org/10.15288/jsa.1981.42.547) Watson PE, Watson ID, Batt RD J Stud Alcohol. 1981;42(7):547-556 DOI: [10.15288/jsa.1981.42.547](https://doi.org/10.15288/jsa.1981.42.547) ## Worked example ### Male 30 y, 175 cm, 70 kg, 14 g ethanol Given: `age=30, ethanol_g=14, height_cm=175, sex=male, weight_kg=70` 1. TBW_L = 2.447 - 0.09516*30 + 0.1074*175 + 0.3362*70 = 41.9212 L 2. Co_g_l = 1 * 14 * 0.80 / 41.9212 = 0.267 g/L (26.7 mg/dL) ### Female 30 y, 175 cm, 70 kg, 14 g ethanol Given: `age=30, ethanol_g=14, height_cm=175, sex=female, weight_kg=70` 1. TBW_L = -2.097 + 0.1069*175 + 0.2466*70 = 33.8725 L (age unused) 2. Co_g_l = 1 * 14 * 0.80 / 33.8725 = 0.331 g/L (33.1 mg/dL) ## Also searched as - estimated ethanol - blood alcohol concentration - Widmark equation - Watson TBW ethanol - fasting Co ethanol - serum ethanol from ingestion - total body water alcohol ## Parameters - `sex` (string, required): Sex for Watson 1980 TBW: male uses age, height, and weight; female uses height and weight only. - `age` (integer, required): Age in years (18-120). Used in male TBW; required for both sexes. - `height_cm` (number, optional): Height in centimeters (50-250). Provide height_cm or height_in. - `height_in` (number, optional): Height in inches (20-98). Converted as cm = in * 2.54. - `weight_kg` (number, optional): Weight in kilograms (1-500). Provide weight_kg or weight_lb. - `weight_lb` (number, optional): Weight in pounds (2-1100). Converted as kg = lb * 0.45359237. - `ethanol_g` (number, required): Ingested ethanol mass in grams (0-500). Watson 1981 does not publish a mass clamp; one US standard drink is about 14 g. ## 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/estimated_ethanol` 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": "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" } ] } ``` Human paywall (two-item fixture): https://api.magentlab.com/paywall/bulk/estimated-ethanol Example 200: ```json { "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.", "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)", "age_years": 30, "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.", "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)", "age_years": 30, "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 fields - `formula` (string): watson_1981 - `formula_expression` (string): Exact TBW and Co expressions - `sex` (string): female or male used for TBW - `age_years` (integer): Age in years used - `height_cm` (number): Normalized height in cm - `weight_kg` (number): Normalized weight in kg - `ethanol_g` (number): Ingested ethanol mass in grams - `tbw_l` (number): Watson 1980 total body water in L, 2 decimals - `absorbed_fraction` (number): Fasting absorbed fraction from Watson 1981 (1.0) - `blood_water_fraction` (number): Watson 1981 blood-water fraction (0.80 w/w) - `co_g_l` (number): Theoretical fasting Co in g/L, 3 decimals - `co_mg_dl` (number): Same Co as mg/dL (g/L × 100), 1 decimal - `citation` (object): Watson 1981 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": "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)", "age_years": 30, "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 } ``` ## Errors - HTTP 400 `invalid_sex`: sex must be female or male Returned before settlement; you are not charged. - HTTP 400 `invalid_age`: age must be an integer from 18 to 120 Returned before settlement; you are not charged. - HTTP 400 `invalid_height`: height_cm (50-250) or height_in (20-98) is required Returned before settlement; you are not charged. - HTTP 400 `invalid_weight`: weight_kg (1-500) or weight_lb (2-1100) is required Returned before settlement; you are not charged. - HTTP 400 `invalid_ethanol`: Ethanol ingestion inputs must match Watson 1981 sex, age, height, weight, and alcohol mass from that paper. 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 - [Anion gap](https://magentlab.com/docs/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](https://magentlab.com/docs/winters) — Compute expected arterial PCO2 in metabolic acidosis from plasma bicarbonate using the Albert–Winters 1967 formula. - [Free water deficit](https://magentlab.com/docs/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. - 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 of accepted and payload). Magent attaches canonical extensions.bazaar on CDP verify/settle; echoing 402 bazaar is optional. - 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. 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.