# Winters' Formula PCO2 Calculator (Metabolic Acidosis Compensation)

> Winters' Formula PCO2 Calculator (Metabolic Acidosis Compensation) is a paid API for AI agents from api.magentlab.com, paid per call via x402, $0.005/call, status unknown (last checked 2026-09-15).

Calculates expected PaCO2 using Winters' formula (1.5 × HCO3 + 8 ±2 mmHg) and optionally compares a measured PaCO2 to determine if respiratory compensation is adequate, excessive, or insufficient.

## Facts

- Endpoint: GET https://api.magentlab.com/api/calc/winters
- Price: $0.005/call
- Payment: x402
- Status: unknown
- Last checked: 2026-09-15
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/winters-formula-pco2-calculator-metabolic-acidosis-compensation-61dfa85e
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_U-67PZP4gLTmQ8YiuE3Pk

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability winters-formula-pco2-calculator-metabolic-acidosis-compensation-61dfa85e
```

Example prompt: My patient has a metabolic acidosis with a bicarbonate of 14 mmol/L and a measured PaCO2 of 30 mm Hg — run Winters' formula and tell me if the respiratory compensation is appropriate.

## When to prefer this

Use this endpoint when you need a fast, citeable, deterministic Winters' formula calculation for metabolic acidosis respiratory compensation assessment. Prefer it over general clinical calculators when you specifically need the Albert–Winters 1967 formulation with the ±2 mm Hg band and optional measured PaCO2 comparison. Not appropriate for metabolic alkalosis (Winter's formula only applies to acidosis), and not a treatment target.

## Known failure modes

- Bicarbonate value outside valid range (2–24 mmol/L) returns validation error
- PaCO2 value outside valid range (8–80 mm Hg) returns validation error
- Missing required bicarbonate_mmol_l parameter returns 400 error
- Formula is only valid for metabolic acidosis; results are meaningless for normal or alkalotic bicarbonate values

## How this service works

Winters' formula for expected PCO2 in metabolic acidosis: 1.5 × bicarbonate + 8 mm Hg, with a published ±2 mm Hg range. Optional comparison of measured PaCO2 to that band. Deterministic Albert–Winters 1967 arithmetic with citation; not a treatment target or a metabolic alkalosis formula.

## Output

Returns the Winters' formula expected PaCO2 (1.5 × bicarbonate + 8 mm Hg) with the ±2 mm Hg band (lower and upper bounds). If a measured PaCO2 is provided, also returns whether the measured value falls within, below, or above the expected compensation band, indicating adequate, excessive (possible concomitant respiratory alkalosis), or insufficient (possible concomitant respiratory acidosis) compensation.

## Request schema (JSON Schema)

```json
{
 "type": "object",
 "$schema": "https://json-schema.org/draft/2020-12/schema",
 "required": [
  "input"
 ],
 "properties": {
  "input": {
   "type": "object",
   "required": [
    "type",
    "method"
   ],
   "properties": {
    "type": {
     "type": "string",
     "const": "http"
    },
    "method": {
     "enum": [
      "GET",
      "HEAD",
      "DELETE"
     ],
     "type": "string"
    },
    "headers": {
     "type": "object",
     "additionalProperties": {
      "type": "string"
     }
    },
    "queryParams": {
     "type": "object",
     "required": [
      "bicarbonate_mmol_l"
     ],
     "properties": {
      "paco2_mm_hg": {
       "type": "number",
       "description": "Measured arterial PCO2 in mm Hg (8-80). When supplied, compensation is returned versus the Winters ±2 band."
      },
      "bicarbonate_mmol_l": {
       "type": "number",
       "description": "Plasma bicarbonate in mmol/L (2-24). Metabolic acidosis range."
      }
     }
    }
   },
   "additionalProperties": false
  },
  "output": {
   "type": "object",
   "required": [
    "type"
   ],
   "properties": {
    "type": {
     "type": "string"
    },
    "example": {
     "type": "object"
    }
   }
  }
 }
}
```

## Response schema (JSON Schema)

```json
{
 "type": "json",
 "example": {
  "path": "/api/calc/winters",
  "count": 2,
  "items": [
   {
    "formula": "winters",
    "citation": {
     "id": "albert-winters-1967",
     "doi": "10.7326/0003-4819-66-2-312",
     "title": "Quantitative displacement of acid-base equilibrium in metabolic acidosis",
     "source": "Ann Intern Med. 1967;66(2):312-322",
     "authors": "Albert MS, Dell RB, Winters RW"
    },
    "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.",
    "bicarbonate_mmol_l": 12,
    "formula_expression": "expected_pco2_mm_hg = 1.5 * bicarbonate_mmol_l + 8",
    "expected_pco2_mm_hg": 26,
    "expected_pco2_low_mm_hg": 24,
    "expected_pco2_high_mm_hg": 28
   },
   {
    "formula": "winters",
    "citation": {
     "id": "albert-winters-1967",
     "doi": "10.7326/0003-4819-66-2-312",
     "title": "Quantitative displacement of acid-base equilibrium in metabolic acidosis",
     "source": "Ann Intern Med. 1967;66(2):312-322",
     "authors": "Albert MS, Dell RB, Winters RW"
    },
    "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.",
    "bicarbonate_mmol_l": 12,
    "formula_expression": "expected_pco2_mm_hg = 1.5 * bicarbonate_mmol_l + 8",
    "expected_pco2_mm_hg": 26,
    "expected_pco2_low_mm_hg": 24,
    "expected_pco2_high_mm_hg": 28
   }
  ]
 }
}
```

## More

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