Winters' Formula Calculator
Use Winters' formula to work out the PaCO₂ you would expect if the lungs are compensating normally for a metabolic acidosis. Comparing this expected value with the measured PaCO₂ shows whether respiratory compensation is appropriate, or whether a second, respiratory acid-base disorder is also present. Enter the bicarbonate, and optionally the measured PaCO₂, to see the expected range and the interpretation.
About Winters' formula
Winters' formula predicts the respiratory compensation for a metabolic acidosis, making it easy to spot an added respiratory disorder. Source: Albert MS, Dell RB, Winters RW, Annals of Internal Medicine 1967.
Frequently asked questions
What is Winters' formula?
Winters’ formula is expected PaCO₂ = 1.5 × HCO₃ + 8 ± 2 (mmHg), where HCO₃ is the serum bicarbonate in mEq/L. It predicts the PaCO₂ that appropriate respiratory compensation should produce in a pure metabolic acidosis, and the ± 2 gives the acceptable range around that value. For a bicarbonate of 12 mEq/L the expected PaCO₂ is 1.5 × 12 + 8 = 26 mmHg, giving an acceptable range of 24 to 28 mmHg. A measured PaCO₂ of 34 mmHg in that patient would sit well above the range and point to an additional respiratory acidosis. The formula assumes compensation has had time to develop, so it is least reliable in the first hours of an acute acidosis.
How do I use the result?
Compare the measured PaCO₂ with the expected range from Winters’ formula. If it falls inside the range, respiratory compensation is appropriate. If the measured PaCO₂ is higher than expected, there is a concurrent respiratory acidosis (the lungs are not blowing off enough CO₂). If it is lower than expected, there is a concurrent respiratory alkalosis. Either finding means a mixed acid-base disorder.
When does Winters’ formula apply?
Winters’ formula applies to a metabolic acidosis — a low bicarbonate with an acidic pH. It is not used for metabolic alkalosis or primary respiratory disorders, which have their own compensation rules. Always start from the blood gas and the clinical picture: identify the primary disorder first, then check whether compensation is adequate.
What does a mixed disorder mean here?
A mixed disorder means more than one acid-base process is happening at once — for example a metabolic acidosis from sepsis together with a respiratory acidosis from tiring respiratory muscles. Winters’ formula is one of the quickest ways to unmask the second process, because the lungs’ response to a metabolic acidosis is normally tightly predictable. The direction of the mismatch names the second process: a PaCO₂ above the expected range indicates a concurrent respiratory acidosis, while one below it indicates a concurrent respiratory alkalosis — the pattern classically seen in salicylate poisoning and in early sepsis. Spotting it matters clinically, because treating only the metabolic acidosis leaves the second disorder unaddressed.
What are the units?
For Winters’ formula, bicarbonate is entered in mEq/L (the same as mmol/L) and PaCO₂ in mmHg, as reported on most arterial blood gases. If your PaCO₂ is in kilopascals, multiply by 7.5 to convert to mmHg. This calculator is an educational reference, not medical advice.
This is a reference tool, not a diagnosis or medical advice. Results depend on the laboratory, assay and clinical context, and reference intervals vary between labs and by age and sex — always read your result against the range printed on your own report and discuss it with a qualified healthcare professional.
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