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Winters' Formula Calculator

Enter the bicarbonate to find the expected PaCO₂ for a metabolic acidosis. Add a measured PaCO₂ and the tool checks whether respiratory compensation is appropriate or a second disorder is present.

Try:
Expected PaCO₂ 26 mmHg
Range 24–28

For education and clinical decision support only. Winters' formula applies to a primary metabolic acidosis and must be interpreted with the arterial pH, the anion gap and the full clinical picture. This tool does not replace professional medical judgement.

What is Winters' formula?

Winters' formula predicts how far the PaCO₂ should fall to compensate for a metabolic acidosis. In a metabolic acidosis the body hyperventilates to blow off carbon dioxide and limit the fall in pH; Winters' formula tells you the PaCO₂ this respiratory compensation should produce.

Winters' formula equation

Expected PaCO₂ = (1.5 × HCO₃⁻) + 8 ± 2 mmHg

The ± 2 defines an acceptable range. If the patient's actual PaCO₂ falls inside that range, the respiratory compensation is appropriate and there is a single, pure metabolic acidosis. If it falls outside, a second, respiratory acid–base disorder is present as well.

How to interpret the result

  • Measured PaCO₂ within the range — appropriate respiratory compensation for the metabolic acidosis.
  • Measured PaCO₂ above the range — the lungs are not blowing off enough CO₂: a concurrent respiratory acidosis.
  • Measured PaCO₂ below the range — the lungs are blowing off too much CO₂: a concurrent respiratory alkalosis.

Winters' formula rule of thumb

A handy bedside check is that the expected PaCO₂ should roughly equal the last two digits of the arterial pH — for a pH of 7.28, expect a PaCO₂ near 28 mmHg. Winters' formula turns that approximation into a precise expected value with a ± 2 range.

Worked example

For a bicarbonate of 12 mEq/L: Expected PaCO₂ = 1.5 × 12 + 8 = 26 mmHg, with an acceptable range of 24–28 mmHg. A measured PaCO₂ of 26 confirms appropriate compensation; a value of 38 would indicate a concurrent respiratory acidosis.

Frequently asked questions

What is Winters' formula?

Winters' formula estimates the expected PaCO₂ during a metabolic acidosis: Expected PaCO₂ = 1.5 × HCO₃⁻ + 8 ± 2 (mmHg). It tells you how much the lungs should be blowing off carbon dioxide to compensate.

What is Winters' formula used for?

It checks whether respiratory compensation for a metabolic acidosis is appropriate. If the measured PaCO₂ matches the predicted value, compensation is adequate. If it is higher, a concurrent respiratory acidosis is present; if lower, a concurrent respiratory alkalosis.

Does Winters' formula apply to metabolic alkalosis?

No. Winters' formula is validated for metabolic acidosis only. Metabolic alkalosis uses a different compensation rule (expected PaCO₂ ≈ 0.7 × HCO₃⁻ + 20).

What is Winters' rule of thumb?

A quick approximation is that the expected PaCO₂ should be close to the last two digits of the arterial pH (for a pH of 7.25, PaCO₂ ≈ 25 mmHg). Winters' formula gives the more precise expected value and a ±2 range.

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