How do you use Winter's formula?

Calculate expected PaCO₂ using the patient's HCO₃⁻. If measured PaCO₂ is within the expected range (± 2), compensation is appropriate (simple metabolic acidosis). If PaCO₂ is lower than expected, there is a concurrent respiratory alkalosis. If PaCO₂ is higher than expected, there is a concurrent respiratory acidosis.

When does Winter's formula apply?

Winter's formula applies ONLY to primary metabolic acidosis. It does not apply to metabolic alkalosis (use different compensation rules), respiratory disorders, or mixed acid-base disturbances. For metabolic alkalosis, expected PaCO₂ = 0.7 × HCO₃⁻ + 21 ± 2.

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Winter's Formula

Calculate the expected pCO₂ in primary metabolic acidosis to assess adequacy of respiratory compensation.

Inputs

Serum Bicarbonate (HCO₃⁻, mEq/L)

Measured pCO₂ (mmHg) (optional, for comparison)

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Enter HCO₃⁻ to calculate expected pCO₂.

pCO₂ within rangeAppropriate compensation

pCO₂ above rangeConcurrent respiratory acidosis

pCO₂ below rangeConcurrent respiratory alkalosis

Formula: Expected pCO₂ = 1.5 × [HCO₃⁻] + 8 ± 2

Quick check: Expected pCO₂ ≈ last 2 digits of pH (e.g., pH 7.25 → pCO₂ ≈ 25 mmHg)

Disclaimer: For educational purposes only. Not a substitute for clinical judgment.

When to use

Apply Winter's formula whenever an ABG shows primary metabolic acidosis (low pH, low HCO₃⁻) to determine if the respiratory compensation is appropriate or if a concurrent respiratory acid-base disorder is present.

Clinical pearls

Winter's formula applies ONLY to primary metabolic acidosis — not alkalosis or respiratory disorders.
If measured pCO₂ is higher than expected, the patient has a concurrent respiratory acidosis (e.g., COPD + DKA).
If measured pCO₂ is lower than expected, the patient has a concurrent respiratory alkalosis (e.g., sepsis + metabolic acidosis).
Respiratory compensation occurs within hours but maxes out at pCO₂ ≈ 10–12 mmHg — below this, compensation is limited.

References

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

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About This Tool

What Is Winter's Formula?

Winter's formula (named after Winters, Dell, and Albert who published it in 1967) predicts the expected pCO₂ in a patient with primary metabolic acidosis, assuming appropriate respiratory compensation. The formula is: Expected pCO₂ = 1.5 × [HCO₃⁻] + 8 ± 2. This relationship was derived from observations of patients with isolated metabolic acidosis and represents the body's normal physiological response — hyperventilation to blow off CO₂ and partially correct the pH decline caused by bicarbonate loss.

How to Use It

First, confirm that the patient has a primary metabolic acidosis (low pH with low HCO₃⁻). Then calculate the expected pCO₂ using Winter's formula. Compare the measured pCO₂ from the ABG to the expected range. If the measured pCO₂ falls within the expected range (±2), respiratory compensation is appropriate and no additional respiratory disorder is present. If the measured pCO₂ is HIGHER than expected, the patient has a concurrent respiratory acidosis superimposed on the metabolic acidosis. If LOWER, there is a concurrent respiratory alkalosis.

Clinical Significance

Identifying mixed acid-base disorders is critical because it changes both the differential diagnosis and the management plan. For example, a patient in DKA (metabolic acidosis) who also has pneumonia (respiratory acidosis) will have a measured pCO₂ higher than predicted by Winter's formula. This "inadequate compensation" is actually a second primary disorder and may require intubation sooner than expected. Conversely, a septic patient with lactic acidosis AND respiratory alkalosis from sepsis-driven hyperventilation will have a pCO₂ lower than expected — representing two separate pathological processes rather than simple overcompensation.

🔑 Clinical Pearls

Winter's formula is ONLY for metabolic ACIDOSIS — different rules apply to metabolic alkalosis (expected pCO₂ = 0.7 × HCO₃⁻ + 21 ± 2).
Quick bedside check: pCO₂ should approximately equal the last 2 digits of the pH in metabolic acidosis (pH 7.20 → pCO₂ ≈ 20).
Respiratory compensation has a physiological floor — pCO₂ rarely drops below 10–12 mmHg even in severe metabolic acidosis.
Always combine Winter's formula with the anion gap and delta-delta ratio for complete acid-base analysis.

Key References

Albert MS, Dell RB, Winters RW. Quantitative displacement of acid-base equilibrium in metabolic acidosis. Ann Intern Med. 1967;66(2):312-322.
Narins RG, Emmett M. Simple and mixed acid-base disorders: a practical approach. Medicine (Baltimore). 1980;59(3):161-187.
Berend K, de Vries APJ, Gans ROB. Physiological approach to assessment of acid-base disturbances. N Engl J Med. 2014;371(15):1434-1445.

Formula last verified: February 2026