Winter’s Formula Calculator (Expected PaCO₂)

How it works

Metabolic acidosis: expected PaCO₂ = 1.5 × HCO₃⁻ + 8 (± 2). Metabolic alkalosis: 0.7 × HCO₃⁻ + 21. Respiratory acidosis: HCO₃⁻ ↑ 1 (acute) / 3.5 (chronic) per 10 mmHg. Respiratory alkalosis: HCO₃⁻ ↓ 2 / 5 per 10 mmHg

When acid accumulates, the lungs compensate by blowing off carbon dioxide, and Winter’s formula predicts by how much: for every 1 mmol/L fall in bicarbonate the PaCO₂ should fall about 1.5 mmHg. If the measured PaCO₂ is higher than predicted, the patient is not ventilating enough for their acidosis — a concurrent respiratory acidosis that may herald respiratory fatigue; if it is lower, something is driving extra hyperventilation, as in salicylate poisoning or sepsis. The same logic applies in reverse to metabolic alkalosis and to the renal compensation for respiratory disorders, which is slow (days) and therefore differs between acute and chronic states. Together with the anion gap and delta ratio, these rules let a single blood gas reveal two or three coexisting disorders.

Worked example

Bicarbonate 14, PaCO₂ 24, pH 7.28: expected PaCO₂ = 1.5 × 14 + 8 = 29 (27–31); measured 24 is lower, so there is an additional respiratory alkalosis on top of the metabolic acidosis.

Frequently asked questions