Calculates the expected PaCO2 in metabolic acidosis, and checks whether the measured value shows a second respiratory disorder.
Result
Enter the bicarbonate.
Sources
3 studies
3
studies
200
citations
16
PubMed papers
Evidence
Known limitations
The original study: in patients with metabolic acidosis, the PaCO2 fell in a straight line with the bicarbonate, giving PaCO2 = 1.54 × HCO3 + 8.36 ± 1.1 mm Hg, the basis of Winter’s formula.
Ann Intern Med: Journal Metrics Score 4.6, Q1 · cited 200 times
In adults with rapidly developing and rapidly corrected acidosis from cholera, ventilatory compensation took hours to reach the predicted level and persisted after the bicarbonate had been corrected.
Ann Intern Med: Journal Metrics Score 4.6, Q1 · cited 59 times
A review of the physiological approach to acid-base disorders that uses Winter’s formula and the other expected compensation rules to detect mixed disorders.
N Engl J Med: Journal Metrics Score 29.8, Q1 · cited 314 times
The original paper has been cited 200 times, and 16 PubMed articles mention Winter’s formula or the expected PaCO2 in their title or abstract. Citation counts from OpenAlex and article counts from PubMed, retrieved November 11, 2026. Journal Metrics Scores and quartiles are from this site’s current release; follow the journal name for details.
After the result
PaCO2 above the range · PaCO2 below the range · Any result
Look for failing ventilation. Look for a cause of hyperventilation. Work out the cause of the acidosis.
Next steps
Avoid common errors
5 common errors to avoid
and 3 more
When the formula misleads
1Metabolic acidosis only
The formula does not apply to metabolic alkalosis or to a primary respiratory disorder. Check the pH and the bicarbonate first.
2Timing
Full compensation takes 12 to 24 hours. A PaCO2 above the range soon after the acidosis began, or a low PaCO2 during recovery, may reflect timing rather than a second disorder.
3Very low bicarbonate
Below a bicarbonate of about 5 mmol/L the lungs reach their limit and the PaCO2 rarely falls much below 10 to 15 mm Hg. That floor explains only a small excess; a PaCO2 well above 15 mm Hg still means ventilation is failing.
4Venous samples
The formula uses arterial PaCO2. Venous PCO2 runs a few mm Hg higher and can wrongly suggest a respiratory acidosis.
5Mismatched samples
Use the bicarbonate from the same blood gas, or a chemistry sample taken at the same time.
Formula
Expected PaCO2 = 1.5 × HCO3 + 8 ± 2 mm Hg; a measured PaCO2 outside the range suggests a second respiratory disorder.
1.5 × HCO3 + 8 ± 2
Expected PaCO2 = 1.5 × HCO3 + 8 ± 2 mm Hg; a measured PaCO2 outside the range suggests a second respiratory disorder.
Formula and interpretation
| Disorder | Expected PaCO2 |
|---|---|
| Metabolic acidosis (Winter’s formula) | 1.5 × HCO3 + 8 ± 2 mm Hg |
| Metabolic acidosis, rule of thumb | PaCO2 falls about 1.2 mm Hg for each 1 mmol/L fall in HCO3 below 24 |
| Metabolic alkalosis, for comparison | PaCO2 rises about 0.7 mm Hg for each 1 mmol/L rise in HCO3 above 24 |
| Result | Measured PaCO2 | Meaning |
|---|---|---|
| PaCO2 lower than expected: added respiratory alkalosis | below expected − 2 | The measured PaCO2 is below the expected range: breathing is driven beyond compensation, suggesting a respiratory alkalosis as well (sepsis, salicylate toxicity, pneumonia, pulmonary embolism, liver disease, pain or anxiety). |
| Appropriate respiratory compensation | expected ± 2 | The measured PaCO2 is within the expected range: the lungs are compensating as expected for this metabolic acidosis, with no sign of a second respiratory disorder. |
| PaCO2 higher than expected: added respiratory acidosis | above expected + 2 | The measured PaCO2 is above the expected range: ventilation is not keeping up, suggesting a respiratory acidosis on top of the metabolic acidosis (tiring, sedation, lung disease or a neuromuscular cause). Compensation may also still be developing in the first hours. |
Albert, Dell and Winters 1967
Rounding
Pierce 1970
Test cases
3 published cases, each also a test case
3 published cases; the calculator reproduces every result.
Worked examples
A 29-year-old woman with fructose-1,6-bisphosphatase deficiency presented confused, with hypoglycemia and lactic acidosis: bicarbonate 6.3 mmol/L, lactate 6.49 mmol/L and a measured PaCO2 of 16.6 mm Hg. The authors calculated an expected PaCO2 of 17.5 ± 2 mm Hg.
“Winter's formula predicts a partial pressure of carbon dioxide (PCO₂) of 1.5 × 6.3 + 8 = 17.5 ± 2 mmHg”
1.5 × 6.3 + 8 = 17.45, shown as 17.5. The measured 16.6 mm Hg lies inside 15.5 to 19.5, so compensation was appropriate.
Entered as: Bicarbonate (HCO3): 6.3 mmol/L (mEq/L); Measured PaCO2: 16.6 mm Hg.
Source: Farah Ahmed M et al., Cureus 2026 (PubMed · Free full text · DOI)
A 63-year-old woman with Sjögren’s syndrome and diabetes on trimethoprim-sulfamethoxazole for Pneumocystis pneumonia had a pH of 7.41 with a bicarbonate of 18.6 mEq/L and a PaCO2 of 31.9 mm Hg. Winter’s formula gave 35.9 mm Hg, so the PaCO2 was lower than expected.
“Using Winter’s formula, the expected PaCO₂ was calculated as (1.5 x 18.6) + 8 = 35.9 mmHg.”
The measured 31.9 mm Hg is below 33.9, the bottom of the range: a respiratory alkalosis from the pneumonia on top of the metabolic acidosis, which is why the pH looked normal.
Entered as: Bicarbonate (HCO3): 18.6 mmol/L (mEq/L); Measured PaCO2: 31.9 mm Hg.
Source: Gerçek ÖZ et al., Cureus 2025 (PubMed · Free full text · DOI)
A 33-year-old woman with COVID-19 and newly diagnosed type 1 diabetes had diabetic ketoacidosis with a bicarbonate of 4.8 mmol/L and an anion gap of 27.2. The expected PaCO2 by Winter’s formula was 13.2 to 17.2 mm Hg, but the measured PaCO2 was 37.7 mm Hg.
“The expected pCO2 was between 13.2 and 17.2 mmHg according to Winter's formula.”
The authors read the high PaCO2 as a combined metabolic and respiratory acidosis, and she needed invasive ventilation. The calculator agrees. Its low-bicarbonate warning also appears, but 37.7 mm Hg is far above the 10 to 15 mm Hg ventilatory floor, so that limit does not explain it.
Entered as: Bicarbonate (HCO3): 4.8 mmol/L (mEq/L); Measured PaCO2: 37.7 mm Hg.
Source: Ishii K et al., Clin Case Rep 2021 (PubMed · Free full text · DOI)
FAQ
6 questions and answers
and 4 more answers
Questions
Winter’s formula predicts the PaCO2 that the lungs should reach when they compensate for a metabolic acidosis: expected PaCO2 = 1.5 × HCO3 + 8 ± 2 mm Hg. A bicarbonate of 12 mmol/L gives 1.5 × 12 + 8 = 26, so a PaCO2 between 24 and 28 mm Hg is appropriate compensation.
Ventilation is not lowering the PaCO2 as much as it should, so there is a respiratory acidosis as well as the metabolic acidosis. Causes include tiring of the respiratory muscles, sedative drugs, lung disease and neuromuscular weakness. In severe acidosis it can be a warning that the patient needs ventilatory support. In the first hours, compensation may simply not have caught up yet.
Breathing is driving the PaCO2 lower than compensation alone explains, so there is a respiratory alkalosis as well. Typical causes are sepsis, salicylate poisoning, pneumonia, pulmonary embolism, liver disease, pain and anxiety. The two disorders can cancel out and leave a near-normal pH.
No. Winter’s formula is for metabolic acidosis only. In a metabolic alkalosis the PaCO2 rises by about 0.7 mm Hg for each 1 mmol/L rise in bicarbonate above 24, and the rise is limited because hypoventilation lowers oxygen.
Breathing starts to increase within minutes, but full compensation takes about 12 to 24 hours. During recovery the PaCO2 can stay low for a while after the bicarbonate has risen, which can look like a respiratory alkalosis.
Yes. Choose kPa for the measured PaCO2. The calculator converts it (1 kPa = 7.50 mm Hg) and shows the expected range in both units. The formula itself was written in mm Hg.
Further reading
6 references with PubMed and DOI links
6
references
3
free full text
From Albert MS et al., Ann Intern Med 1967 to the newest case reports.
References
Contributed by Dr. Meng Zhao (MD · Former Neurosurgeon · Medical AI Researcher), from the original publications listed here. Last updated November 11, 2026. LinkedIn
The calculator code is tested against every worked example on this page before each release.
This calculator supports, and does not replace, clinical judgment. It is meant for healthcare professionals and is not medical advice for patients. Report an error through the contact page.
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