Winter's formula predicts the expected PaCO₂ in metabolic acidosis: expected PaCO₂ = 1.5 × HCO₃⁻ + 8 ± 2 mmHg. If the measured PaCO₂ falls in that range, respiratory compensation is appropriate. Above it means a concurrent respiratory acidosis; below it, a concurrent respiratory alkalosis. For HCO₃⁻ 12 mEq/L the expected range is 24–28 mmHg.
The formula comes from Albert, Dell and Winters (1967) and is the compensation check used in StatPearls' acid-base chapters. This page is written for clinicians, nurses and students working through blood gas interpretation.
How to use this calculator
- Confirm the primary disorder is a metabolic acidosis: pH below 7.35 with a low bicarbonate.
- Enter the serum bicarbonate (HCO₃⁻) in mEq/L (the same number in mmol/L).
- Read the expected PaCO₂ range and its midpoint.
- Optionally enter the measured arterial PaCO₂. The calculator tells you whether it sits inside, above or below the expected range.
- Interpret the result alongside the anion gap, the history and the rest of the blood gas.
How Winter's formula is calculated
Expected PaCO₂ (mmHg) = (1.5 × HCO₃⁻) + 8 ± 2
- HCO₃⁻ is the serum bicarbonate in mEq/L. StatPearls notes it is conventionally taken from a venous sample, which usually reads 2–4 mEq/L higher than the arterial value.
- 1.5 is the slope: each 1 mEq/L fall in bicarbonate should lower PaCO₂ by about 1.5 mmHg once compensation is established.
- + 8 is the intercept, and ± 2 the tolerance band around the prediction.
Compensation is a ventilatory response. StatPearls describes it developing within 12 to 24 hours, and notes that PaCO₂ cannot be driven much below roughly 8–12 mmHg. On examination, the deep, labored Kussmaul breathing of severe metabolic acidosis is this compensation in action.
Worked examples
Each result below comes from the same code that runs the calculator.
- Example A: HCO₃⁻ 12, measured PaCO₂ 26. 1.5 × 12 + 8 = 26 mmHg, so the expected range is 24–28 mmHg. A PaCO₂ of 26 is inside the range: appropriate compensation.
- Example B: HCO₃⁻ 8, measured PaCO₂ 30. 1.5 × 8 + 8 = 20 mmHg, so the expected range is 18–22 mmHg. A PaCO₂ of 30 is above the range: concurrent respiratory acidosis.
- Example C: HCO₃⁻ 15, measured PaCO₂ 20. 1.5 × 15 + 8 = 30.5 mmHg, so the expected range is 28.5–32.5 mmHg. A PaCO₂ of 20 is below the range: concurrent respiratory alkalosis.
Example C is the pattern StatPearls describes in early salicylate toxicity, where direct stimulation of the respiratory center adds a respiratory alkalosis to the metabolic acidosis. Example B means ventilation is not keeping up with the acid load.
Expected PaCO₂ by bicarbonate
| HCO₃⁻ (mEq/L) | Midpoint (mmHg) | Expected PaCO₂ (mmHg) |
|---|---|---|
| 4 | 14 | 12–16 |
| 6 | 17 | 15–19 |
| 8 | 20 | 18–22 |
| 10 | 23 | 21–25 |
| 12 | 26 | 24–28 |
| 14 | 29 | 27–31 |
| 15 | 30.5 | 28.5–32.5 |
| 16 | 32 | 30–34 |
| 18 | 35 | 33–37 |
| 20 | 38 | 36–40 |
| 22 | 41 | 39–43 |
Normal blood gas values for context
StatPearls' arterial blood gas chapter lists these adult reference ranges, noting that they vary between laboratories and across age groups:
| Measure | Normal range |
|---|---|
| pH | 7.35–7.45 |
| PaCO₂ | 35–45 mmHg |
| HCO₃⁻ | 22–26 mEq/L |
| PaO₂ | 75–100 mmHg |
If you only have a venous gas, remember StatPearls' figures: venous pH runs about 0.02–0.05 lower and venous PCO₂ about 4–6 mmHg higher than arterial, and the gap can widen a lot in severe hypoperfusion. Winter's formula predicts an arterial PaCO₂.
Where Winter's formula fits in blood gas interpretation
The archived StatPearls chapter on metabolic acidosis lays out a stepwise approach:
- pH: below 7.35 is acidemia, above 7.45 alkalemia.
- PaCO₂ and HCO₃⁻: decide whether the primary process is metabolic or respiratory.
- Anion gap: classify the metabolic acidosis as high gap or normal gap. Use the anion gap calculator, which also corrects for albumin and gives the delta ratio.
- Winter's formula: check whether the respiratory response is appropriate or a second respiratory disorder is present.
In a hyperglycemic patient, check the sodium too. The corrected sodium calculator adjusts it for glucose.
Common mistakes and when not to use it
- Using it for the wrong primary disorder. Winter's formula applies only to metabolic acidosis. For metabolic alkalosis StatPearls uses expected PaCO₂ = 0.7 × HCO₃⁻ + 20 ± 5 mmHg; respiratory disorders are judged by the kidney's bicarbonate response instead.
- Reading it too early. Full compensation takes 12–24 hours, so a very early sample can look like a respiratory acidosis when the lungs are simply still catching up.
- Expecting a normal pH. Compensation limits the fall in pH but never fully corrects it. A normal pH with a low bicarbonate points to a mixed disorder.
- Mixing sample types. Compare an arterial PaCO₂ with the prediction, and know whether your bicarbonate came from a venous chemistry panel or a blood gas.
- Treating the ± 2 as absolute. A value just outside the band is a prompt to look again at the whole picture, not a diagnosis on its own.
Why a mismatch matters
A PaCO₂ higher than predicted means ventilation is not matching the metabolic load. StatPearls' respiratory acidosis chapter lists causes of failing ventilation such as stroke, central nervous system depressants like opioids, and inability to use the muscles of respiration. A PaCO₂ lower than predicted means something else is driving ventilation; StatPearls gives salicylate toxicity as the classic example and notes anxiety-related hyperventilation as a common cause of a low PaCO₂. Either way, the formula flags that one diagnosis does not explain the whole gas.
For healthcare professionals and students only. This calculator is an educational aid, not medical advice, and must not be used on its own for diagnosis or treatment decisions. Interpret every result with the full clinical picture, your laboratory's reference ranges and local protocols. If you are a patient, discuss your results with your doctor.
Frequently asked questions
What is Winter's formula?
Expected PaCO₂ = 1.5 × HCO₃⁻ + 8 ± 2 mmHg. It predicts the arterial carbon dioxide level when the lungs are compensating appropriately for a metabolic acidosis. It comes from Albert, Dell and Winters (1967).
How do you interpret Winter's formula?
If the measured PaCO₂ is within the expected range, respiratory compensation is appropriate. If it is higher, there is a concurrent respiratory acidosis; if it is lower, a concurrent respiratory alkalosis.
What is the expected PaCO₂ for a bicarbonate of 12?
1.5 × 12 + 8 = 26 mmHg, so the expected range is 24–28 mmHg.
What is the expected PaCO₂ for a bicarbonate of 10?
1.5 × 10 + 8 = 23 mmHg, so the expected range is 21–25 mmHg.
When should Winter's formula be used?
Only for a primary metabolic acidosis, which is the setting of the original 1967 study and of StatPearls' acid-base guidance. Other primary disorders use different compensation rules.
Can I use Winter's formula for metabolic alkalosis?
No. StatPearls gives a separate rule for metabolic alkalosis: expected PaCO₂ = 0.7 × HCO₃⁻ + 20 ± 5 mmHg. For a bicarbonate of 30 that is about 41 mmHg. Applying Winter's formula to an alkalosis gives the wrong answer.
How long does respiratory compensation take?
StatPearls states that metabolic acidosis causes compensatory hyperventilation within 12 to 24 hours. A blood gas drawn very early may therefore show less compensation than the formula predicts.
Should I use venous or arterial bicarbonate?
StatPearls notes that the bicarbonate used is conventionally taken from a venous sample, which is generally 2 to 4 mEq/L higher than an arterial value. The PaCO₂ you compare against should be arterial.
Does appropriate compensation bring the pH back to normal?
No. StatPearls states that compensation never completely corrects an acidemia. A normal pH with a low bicarbonate and low PaCO₂ should make you look for a second disorder.
What does a PaCO₂ above the Winter's range mean?
The patient is not blowing off as much CO₂ as expected, so there is an additional respiratory acidosis. Causes of hypoventilation, such as central nervous system depressants, should be considered, and the finding warrants prompt clinical review.
Sources & method
- StatPearls (NCBI Bookshelf) — Anion gap and non-anion gap metabolic acidosis (Winter's formula, 12–24 h onset, venous vs arterial HCO₃⁻)
- StatPearls (NCBI Bookshelf) — Metabolic acidosis (archived; stepwise interpretation)
- StatPearls (NCBI Bookshelf) — Arterial blood gas (normal ranges)
- StatPearls (NCBI Bookshelf) — Physiology, metabolic alkalosis (expected PaCO₂ = 0.7 × HCO₃⁻ + 20 ± 5)
- Albert, Dell & Winters (1967), Ann Intern Med — quantitative displacement of acid-base equilibrium in metabolic acidosis
Results are estimates for general information. Found an error? It helps everyone — see our methodology.