Winters' formula calculator
Enter the bicarbonate and the measured PaCO2 from a blood gas to get the expected PaCO2 by Winters' formula and whether the breathing compensation matches it. Information for clinicians and students, not a diagnosis.
Runs in your browser: nothing you enter is sent anywhere.
How to use it
- Check that the blood gas shows a metabolic acidosis: low pH and low bicarbonate.
- Enter the bicarbonate in mmol/L and the measured PaCO2 in mmHg.
- Read the expected PaCO2 with its range and the comparison.
How it works
Expected PaCO2 = 1.5 × HCO3⁻ + 8, with a range of ± 2 mmHg.
- Measured PaCO2 inside the range: the respiratory compensation is as expected.
- Above the range: an added respiratory acidosis.
- Below the range: an added respiratory alkalosis.
Worked example
A patient in diabetic ketoacidosis has HCO3⁻ 12 mmol/L. Expected PaCO2 = 1.5 × 12 + 8 = 26 mmHg (24–28). A measured PaCO2 of 26 mmHg is appropriate compensation.
With HCO3⁻ 15 and PaCO2 40: expected 30.5 (28.5–32.5), so 40 is above the range, an added respiratory acidosis.
Tips
- Compensation takes about 12 to 24 hours to develop fully, so very early gases may not fit.
- There is a limit to how far breathing can lower PaCO2, so the formula is less reliable in extreme acidosis.
- Pair it with the anion gap to work out the type of metabolic acidosis.
- The result is information and does not replace clinical judgment.
Frequently asked questions
What is Winters' formula?
Expected PaCO2 = 1.5 × HCO3⁻ + 8, plus or minus 2 mmHg. It predicts how far the lungs should lower carbon dioxide to compensate for a metabolic acidosis.
What does a PaCO2 outside the range mean?
Higher than expected means the patient is not breathing off enough CO2, a respiratory acidosis on top of the metabolic one, for example from exhaustion or sedation. Lower than expected means an added respiratory alkalosis, as in early salicylate poisoning or sepsis.
When should the formula be used?
Only in metabolic acidosis, when the bicarbonate is low and the pH is acidic. It does not apply to metabolic alkalosis or to primary respiratory disorders.
Can I use kPa?
The formula is written in mmHg. To convert, multiply kPa by 7.5 for mmHg, or divide the result by 7.5 for kPa.