Winters' formula predicts the expected respiratory compensation for a primary metabolic acidosis, letting clinicians check whether a patient's measured pCO2 reflects appropriate compensation or signals a second, concurrent acid-base disorder. This calculator computes the expected range and classifies a measured pCO2 against it.

How Winters' formula works

Winters' formula — Expected pCO2 = 1.5 × HCO3 + 8, ±2 mmHg — was derived by Albert MS, Dell RB, and Winters RW in a 1967 study of patients with metabolic acidosis from causes including diarrhea, diabetic ketoacidosis, and renal disease (Ann Intern Med. 1967;66(2):312-322). It quantifies the near-linear relationship the authors observed between a falling bicarbonate and the compensatory fall in pCO2 driven by increased minute ventilation.

When a patient's measured arterial pCO2 falls within the expected ±2 mmHg range, respiratory compensation is considered adequate. When it falls outside that range, a second, primary acid-base disorder is present alongside the metabolic acidosis.

Inputs and what they mean

Bicarbonate (HCO3), in mEq/L, comes from a basic metabolic panel or arterial/venous blood gas and reflects the severity of the metabolic acidosis.

Measured pCO2, in mmHg, comes from an arterial blood gas drawn at the same time as the bicarbonate. Comparing it to the expected range — entered on the Compare to Measured tab — is what actually screens for a mixed disorder; the Expected pCO2 tab alone only shows what compensation should look like.

Limits and edge cases

Winters' formula applies only to a primary metabolic acidosis. It does not describe expected compensation for metabolic alkalosis, which follows a different relationship, and it is not meant to evaluate a primary respiratory disorder on its own. The formula also assumes the patient has reached a steady state of compensation; in acute, rapidly evolving acidosis the measured pCO2 may not yet reflect the eventual compensated value. As with any acid-base screening tool, an out-of-range result flags the need for further workup rather than delivering a diagnosis on its own.