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Winters’ formula (expected pCO₂)

Expected respiratory compensation in metabolic acidosis, in mmHg

Sources last checked: 2026-10-13

Winters’ formula (expected pCO₂)

Expected respiratory compensation in metabolic acidosis, in mmHg

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Valid only for a primary metabolic acidosis in steady state (compensation takes 12–24 h). Measured pCO₂ above the range suggests an additional respiratory acidosis, below it an additional respiratory alkalosis.

Source: Albert MS, Dell RB, Winters RW. Quantitative displacement of acid-base equilibrium in metabolic acidosis. Ann Intern Med 1967;66(2):312-322.Open

What is the Winters’ formula (expected pCO₂)?

Winters’ formula predicts the arterial pCO₂ that the lungs should reach when they compensate for a primary metabolic acidosis. It was derived by Albert, Dell and Winters in 1967 from blood gases of patients with metabolic acidosis of varying severity. Comparing the predicted with the measured pCO₂ shows whether a respiratory disorder is hiding behind the metabolic one.

When to use it

  • Low HCO₃⁻ with acidaemia on a blood gas, once a primary metabolic acidosis is suspected
  • Diabetic ketoacidosis, lactic acidosis, toxic alcohol or salicylate poisoning — to check whether ventilation keeps up
  • Deciding whether a ‘normal’ pCO₂ in a tiring patient is in fact too high

When not to use it

  • Primary respiratory disorders or metabolic alkalosis — they have their own compensation rules
  • Within the first hours of an acute acidosis, before respiratory compensation is complete

How it is calculated

Expected pCO₂ (mmHg) = 1.5 × HCO₃⁻ (mmol/L) + 8 ± 2

Clinical pearls and limitations

  • Valid only for a primary metabolic acidosis in steady state (compensation takes 12–24 h). Measured pCO₂ above the range suggests an additional respiratory acidosis, below it an additional respiratory alkalosis.
  • Measured pCO₂ above the predicted range means the lungs are not compensating enough — a concomitant respiratory acidosis, often a warning sign of exhaustion.
  • Measured pCO₂ below the range points to an added respiratory alkalosis, classically in salicylate poisoning or sepsis.
  • Compensation has a floor: pCO₂ rarely falls much below about 10–15 mmHg even in severe acidosis.

Frequently asked questions

What is Winters’ formula?

Expected pCO₂ (mmHg) = 1.5 × HCO₃⁻ + 8, with a tolerance of ± 2 mmHg. It applies to primary metabolic acidosis.

How do I use Winters’ formula with kPa?

Multiply the result in mmHg by 0.1333, or use the kPa version of this calculator. ± 2 mmHg corresponds to about ± 0.27 kPa.

What does it mean if pCO₂ is higher than predicted?

Ventilation is inadequate for the degree of acidosis — there is an additional respiratory acidosis, for example from fatigue, sedation or lung disease.

Evidence and guidelines

  1. Primary source: Albert MS, Dell RB, Winters RW. Quantitative displacement of acid-base equilibrium in metabolic acidosis. Ann Intern Med 1967;66(2):312-322.
  2. Duška F et al. A pragmatic approach to complex acid base disturbances of critical illness: the “Stewart light”. Intensive Care Med 2026 — states Winters’ formula as expected PCO₂ (mmHg) = 1.5 × HCO₃⁻ + 8 ± 2.

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