PaCO₂ within range
Consistent with the expected respiratory response to a primary metabolic acidosis.
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Winter's Formula Calculator
Calculate the expected PaCO₂ in metabolic acidosis, then compare it with the measured PaCO₂ to evaluate respiratory compensation and screen for a mixed respiratory disorder.
Winter's formula
Expected PaCO₂ = (1.5 × HCO₃⁻) + 8 ± 2 mmHg
For primary metabolic acidosisUpdated July 16, 2026
Step 1
Calculate expected PaCO₂
Measured PaCO₂ is optional, but entering it provides an immediate compensation interpretation.
Interpretation
How to interpret Winter's formula
Winter's formula predicts the PaCO₂ expected from respiratory compensation during primary metabolic acidosis. Compare the measured arterial PaCO₂ with the calculated range; the formula does not determine the cause of the metabolic acidosis.
PaCO₂ above range
Suggests an additional primary respiratory acidosis or inadequate ventilatory response.
PaCO₂ below range
Suggests an additional primary respiratory alkalosis beyond expected compensation.
Worked Winter's formula examples
These examples show why the measured PaCO₂ matters—not just the calculated number.
Appropriate compensation
HCO₃⁻ 18 mEq/L; measured PaCO₂ 35 mmHg
(1.5 × 18) + 8 = 35 ± 2
Expected range: 33–37 mmHg
The measured PaCO₂ is within range, consistent with expected compensation.
Concurrent respiratory acidosis
HCO₃⁻ 12 mEq/L; measured PaCO₂ 35 mmHg
(1.5 × 12) + 8 = 26 ± 2
Expected range: 24–28 mmHg
The measured PaCO₂ is above range, suggesting an additional respiratory acidosis.
Concurrent respiratory alkalosis
HCO₃⁻ 16 mEq/L; measured PaCO₂ 25 mmHg
(1.5 × 16) + 8 = 32 ± 2
Expected range: 30–34 mmHg
The measured PaCO₂ is below range, suggesting an additional respiratory alkalosis.
When to use Winter's formula
- After establishing a primary metabolic acidosis.
- To compare expected compensation with measured arterial PaCO₂.
- To screen for an accompanying respiratory acidosis or alkalosis.
When not to use it
- Do not use it as the compensation rule for metabolic alkalosis.
- Do not diagnose metabolic acidosis from bicarbonate alone.
- Do not substitute end-tidal CO₂ for arterial PaCO₂ without accounting for the clinical context and gradient.
Common calculation mistakes
Using the wrong disorder
Winter’s formula is for primary metabolic acidosis, not every low bicarbonate value.
Ignoring the ±2 range
Compare measured PaCO₂ with the full expected range rather than only the center estimate.
Stopping after one diagnosis
An out-of-range PaCO₂ suggests another primary respiratory process that requires clinical evaluation.
Skipping the anion and delta gaps
Winter’s formula evaluates respiratory compensation; it does not replace evaluation for mixed metabolic disorders.
Continue the acid-base assessment
Compensation is only one part of ABG interpretation. Connect the result with pH, the anion gap, albumin, the delta gap, clinical timing, medications, ventilation, renal function, and the suspected cause of metabolic acidosis.
Winter's formula FAQ
What is Winter's formula?
Winter's formula estimates the PaCO₂ expected from respiratory compensation during primary metabolic acidosis. The calculated range is compared with the measured arterial PaCO₂ to evaluate whether compensation is appropriate.
What is the formula for expected PaCO₂ in metabolic acidosis?
Expected PaCO₂ = (1.5 × HCO₃⁻) + 8 ± 2 mmHg. Enter bicarbonate in mEq/L or mmol/L and compare the resulting range with measured arterial PaCO₂.
What does a PaCO₂ above the expected range mean?
In a patient with primary metabolic acidosis, a measured PaCO₂ above the expected range suggests a concurrent primary respiratory acidosis or an inadequate ventilatory response.
What does a PaCO₂ below the expected range mean?
In a patient with primary metabolic acidosis, a measured PaCO₂ below the expected range suggests a concurrent primary respiratory alkalosis beyond the expected compensatory response.
Can Winter's formula be used for metabolic alkalosis?
No. Winter's formula is the expected respiratory-compensation rule for primary metabolic acidosis. Metabolic alkalosis and primary respiratory disorders use different compensation relationships.
Should I use arterial or venous PCO₂ with Winter's formula?
The formula predicts arterial PaCO₂. Venous blood gases can support acid-base assessment in appropriate settings, but venous PCO₂ is not identical to arterial PaCO₂. Use measured arterial PaCO₂ when a precise comparison with the expected range is clinically important.