Winters’ formula is used to evaluate respiratory compensation when analyzing acid-based disorders and a metabolic acidosis is present.
 

• Winters’ formula gives an expected value for the patients’ PCO₂.
• If the patient’s actual (measured) PCO₂ is the same as the expected value, then respiratory compensation is considered adequate. This may be present in a patient with chronic obstructive pulmonary disease (COPD) who has a chronically elevated CO₂ and whose kidneys have compensated so that the pH remains normal.  
• If PCO₂ is higher than the calculated value, there is also a secondary respiratory acidosis or mixed acid-base disorder. This may be present in a patient that has both poor perfusion and hypoventilation, for example, a patient with cardiac arrest.
• If the measured PCO₂ is lower than the calculated value, there is a secondary respiratory alkalosis or mixed acid base disorder. This may be present in a patient with diabetic ketoacidosis (DKA) who is hyperventilating to compensate for the metabolic acidosis associated with DKA. 

Reference:
Albert, M., Dell, R., & Winters, R. (1967). Quantitative Displacement of Acid-Base Equilibrium in Metabolic Acidosis. Annals of Internal Medicine, 66 (312-322). doi: 10.7326/0003-4819-66-2-312