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Winter's Formula Calculator

Find the expected PaCO₂ with Winter's formula.

Result

26.00 mmHg
24.00 mmHg
28.00 mmHg

How it is calculated

The tool applies expected PaCO₂ = 1.5 × HCO₃⁻ + 8, where bicarbonate is the serum HCO₃⁻ in mEq/L (mmol/L) and the result is in mmHg. It then shows the usual tolerance of ±2, so you get an expected value plus a low and a high bound. The formula describes the respiratory compensation expected in a metabolic acidosis.

Only a bicarbonate above zero is accepted; zero or negative input gives no result. The calculator does not diagnose anything: it does not check pH, does not confirm that an acidosis is present, and uses PaCO₂ in mmHg only, so a value in kPa must be converted first. Compare the range with the patient's measured PaCO₂ from the same blood gas, and interpret it with the clinical picture.

Worked example

Serum bicarbonate 12 mEq/L. Multiply: 1.5 × 12 = 18. Add 8: 18 + 8 = 26.00 mmHg expected PaCO₂. With the ±2 tolerance the range runs from 24.00 mmHg to 28.00 mmHg. If the measured PaCO₂ lies inside 24 to 28, the respiratory response matches the acidosis; a value above the range points to less ventilatory compensation than expected, and below it to more.

Try this example →

Common mistakes

  • Using it for a problem that is not a metabolic acidosis. The formula is built for that case; for a metabolic alkalosis or a primary respiratory disorder it does not apply.
  • Entering the anion gap, base excess or total CO₂ instead of the serum bicarbonate (HCO₃⁻).
  • Comparing the result with a PaCO₂ given in kPa. The output is in mmHg, so convert first.
  • Forgetting the ±2 band and treating 26 as a single exact target. A measured value of 25 or 27 is still inside the expected range.
  • Using the venous or capillary CO₂ as if it were arterial PaCO₂, which can differ from the arterial value.

Sources

About this calculator

Winter's formula, expected PaCO₂ = 1.5 × [HCO₃⁻] + 8 ± 2, predicts how much a patient's lungs should be blowing off CO₂ to compensate for a metabolic acidosis. It's derived from the empirical relationship between measured bicarbonate and the respiratory compensation seen in acid-base studies, giving an expected range rather than a single number.

Emergency and critical care physicians apply it when reading an arterial blood gas alongside a low bicarbonate: if the patient's actual PaCO₂ falls within the predicted range, the respiratory system is compensating appropriately for the metabolic acidosis alone; if it's higher or lower than expected, a second, independent respiratory acidosis or alkalosis is also present — a mixed disorder that changes management.

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Comments (1)

  • Editorial team

    The tool gives three numbers: the expected PaCO2 and the two bounds at plus and minus 2 mmHg. It does not take your patient's measured PaCO2 or pH, so the comparison against the range is yours to make. Bicarbonate must be above zero, otherwise nothing is shown. Using it on a normal-pH sample answers a question the formula was not built for. Which bedside step do you find most error-prone when reading acid-base results?

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