Winters’ Formula Calculator (expected PaCO₂ in metabolic acidosis)

Understanding the Winters' formula calculator — concept and principle

Winters' formula predicts the arterial PaCO₂ expected when the lungs are compensating normally for a metabolic acidosis. Comparing it with the measured PaCO₂ shows whether there is also a respiratory problem. It is a core step in interpreting blood gases.

Expected CO₂ from bicarbonate: with the default inputs the result is 26 (24–28) (added respiratory acidosis).

How it is calculated

Expected PaCO₂ (mmHg) = 1.5 × HCO₃⁻ (mmol/L) + 8, range ± 2

Measured PaCO₂ above the range: added respiratory acidosis.
Below the range: added respiratory alkalosis.
Within the range: appropriate compensation.

Enter PaCO₂ 0 to see only the expected value.

The principle

In metabolic acidosis, the bicarbonate buffer falls and blood becomes acidic. The brainstem senses this and increases breathing, which blows off CO₂ and pulls pH back towards normal. Winters and colleagues measured this response in patients and found a straight-line relation between bicarbonate and the PaCO₂ achieved. If the measured PaCO₂ is higher than predicted, breathing is not keeping up.

Worked example

Default inputs: HCO₃⁻ 12 mmol/L, measured PaCO₂ 30 mmHg.

Expected PaCO₂ = 1.5 × 12 + 8 = 26 mmHg; range 24–28.
Measured 30 is Above range → Added respiratory acidosis.
Bicarbonate 12 → Low (below 22 mmol/L).

Each point is the calculator re-run with only “HCO₃⁻ bicarbonate (mmol/L)” changed; the gold point is the default example. Change the inputs above and this chart follows your numbers.

HCO₃⁻ bicarbonate (mmol/L)	Expected PaCO₂ (mmHg)
3	12.5
6	17
9	21.5
12	26
15	30.5
18	35
24	44

How to read the result

An added respiratory acidosis in a patient with metabolic acidosis can signal tiring breathing muscles, sedation or lung disease and may need urgent support. Full compensation takes about 12–24 hours, and PaCO₂ cannot fall much below about 10 mmHg. The rule applies only when bicarbonate is low from a metabolic acidosis.

Common mistakes

Using the formula for metabolic alkalosis, which has a different rule.
Using venous PCO₂ instead of arterial.
Ignoring the time needed for compensation.

Keep in mind: This is a decision aid for clinicians, not a diagnosis. Acid–base disorders need full clinical assessment.

Frequently asked questions

What does a PaCO₂ lower than expected mean?

An additional respiratory alkalosis, for example from pain, anxiety or sepsis.

Is there a quick check?

In metabolic acidosis, PaCO₂ often roughly equals the last two digits of the pH.

Does Winters' formula apply to chronic kidney disease?

Yes, if the low bicarbonate is due to metabolic acidosis.

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

Checked 9 Nov 2026. Albert MS, Dell RB, Winters RW, “Quantitative displacement of acid-base equilibrium in metabolic acidosis”, Ann Intern Med 1967;66(2):312–322 (as cited by WikEM “Winters’ formula calculator”); Brandis K, Acid-base Physiology, section 9.3 “Bedside Rules for Assessment of Compensation”, rule 5 (range ± 2, 12–24 h to full compensation, limit about 10 mmHg) (Medicine LibreTexts); MSD Manual Professional Edition table “Primary Changes and Compensations in Simple Acid-Base Disorders”.

Your numbers