What is Winters' formula used for?

Winters' formula calculates the expected PaCO2 in a primary metabolic acidosis. Comparing the patient's measured PaCO2 to this expected value shows whether respiratory compensation is appropriate or whether a second, concomitant respiratory disorder is present.

What does it mean if the measured PaCO2 is higher than expected?

A measured PaCO2 above the expected range indicates a concomitant respiratory acidosis (inadequate ventilation) superimposed on the metabolic disorder. This may signal respiratory fatigue or a CNS or airway problem and can be a medical emergency.

What does it mean if the measured PaCO2 is lower than expected?

A measured PaCO2 below the expected range indicates a concomitant respiratory alkalosis superimposed on the metabolic disorder. Common causes include salicylate toxicity, sepsis, and liver failure.

Can Winters' formula be used for metabolic alkalosis?

No. Winters' formula (1.5 x HCO3 + 8) applies to metabolic acidosis. Metabolic alkalosis uses a different expectation, approximately 0.7 x HCO3 + 21 (plus or minus 2). This calculator provides a mode selector so the correct constants are applied.

Why is there a plus or minus 2 range?

The plus or minus 2 mmHg accounts for normal individual variation in the degree of respiratory compensation. A measured PaCO2 anywhere within that range is considered appropriate compensation rather than a separate respiratory disorder.

Does appropriate compensation return the pH to normal?

No. Respiratory compensation is a normal physiologic response but does not fully normalize the pH. A normal pH combined with an abnormal HCO3 and PaCO2 suggests a mixed acid-base disorder rather than a single fully compensated one.

Winters' Formula Calculator — Expected PaCO2

Primary metabolic disorder (mode)

Bicarbonate, HCO₃⁻ (mEq/L)

Measured PaCO₂ (mmHg) — optional

Expected PaCO₂ (Winters’ formula)

— mmHg

Show calculation steps

Recent Updates

June 2026 — Medical review. Compensation expectations were aligned with the current physiologic approach to acid-base assessment: the acidosis mode uses Winters’ formula (1.5 × HCO₃⁻ + 8, ± 2) and the alkalosis mode uses 0.7 × HCO₃⁻ + 21 (± 2) (Berend 2014) rather than older fixed rules. A measured PaCO₂ outside the ± 2 mmHg band flags a concomitant respiratory disorder.

Source: Berend K, de Vries APJ, Gans ROB. Physiological approach to assessment of acid-base disturbances. N Engl J Med 2014;371(15):1434-1445. PMID: 25295502.

Key Knowledge Points

Winters’ formula applies to a primary metabolic acidosis. If the measured PaCO₂ falls outside the expected range, a second (concomitant) respiratory disorder is present.
Respiratory compensation is a normal physiologic response, not a separate disorder. It does not fully normalize the pH — a normal pH alongside an abnormal HCO₃⁻ and PaCO₂ points to a mixed disorder.
Quick bedside check: the expected PaCO₂ in mmHg roughly equals the last two digits of the pH (pH 7.25 → PaCO₂ ≈ 25 mmHg).
Compensation for a metabolic alkalosis is limited by the hypoxic ventilatory drive, so the rise in PaCO₂ is modest; a PaCO₂ above roughly 55 mmHg suggests a true superimposed respiratory acidosis.
Interpret alongside the anion gap and delta ratio — for example, salicylate toxicity classically combines a high-anion-gap metabolic acidosis with a primary respiratory alkalosis.

About This Winters’ Formula Calculator

The Winters’ Formula Calculator determines the expected arterial PaCO₂ for a patient with a primary metabolic acid-base disorder. In a primary metabolic acidosis, the lungs compensate by increasing ventilation to blow off CO₂; in a primary metabolic alkalosis, they hypoventilate to retain CO₂. Winters’ formula quantifies how much respiratory compensation should occur. By comparing the patient’s measured PaCO₂ with the expected PaCO₂, the clinician can judge whether compensation is appropriate or whether a second, concomitant respiratory disorder is masking or adding to the picture — a key step in identifying mixed acid-base disturbances.

The Formula Explained

For a primary metabolic acidosis, the classic Winters’ equation predicts the expected PaCO₂ from the serum bicarbonate, with an accepted variation of plus or minus 2 mmHg:

Expected PaCO₂ (mmHg) = 1.5 × HCO₃⁻ + 8 (± 2)

For a primary metabolic alkalosis, a separate expectation is used (Berend 2014); some references instead cite “+20” or “ΔPaCO₂ ≈ 0.7 × ΔHCO₃⁻ (±5)”:

Expected PaCO₂ (mmHg) = 0.7 × HCO₃⁻ + 21 (± 2)

HCO₃⁻ is entered in mEq/L (equivalent to mmol/L) and PaCO₂ is in mmHg; no unit conversion is required. This calculator applies the constants for the selected mode automatically.

Clinical Interpretation & Limitations

Once a measured PaCO₂ is entered, the result is interpreted against the expected range for the active mode:

Within the expected range: respiratory compensation is appropriate for the primary metabolic disorder. No separate respiratory disorder is identified.
Below the expected range: a concomitant respiratory alkalosis is present. Classic triggers include salicylate toxicity, sepsis, and liver failure.
Above the expected range: a concomitant respiratory acidosis is present, signalling inadequate ventilation (respiratory fatigue, or a CNS or airway problem) — often a medical emergency. In metabolic alkalosis specifically, compensatory hypoventilation is limited by the hypoxic drive, so a PaCO₂ above roughly 55 mmHg points to a true respiratory acidosis rather than expected compensation.

Example: A patient in DKA has an HCO₃⁻ of 12 mEq/L. Expected PaCO₂ = 1.5 × 12 + 8 = 26 mmHg (range 24–28). A measured PaCO₂ of 26 mmHg confirms appropriate respiratory compensation; a value of 34 mmHg would indicate a superimposed respiratory acidosis.

Limitations

Mode matters: the acidosis and alkalosis constants are different and must not be interchanged. Confirm the primary disorder before reading the result, and use the mode selector deliberately.
Primary disorder must be established first: the formula assumes you have already identified a primary metabolic acidosis or alkalosis from the pH, HCO₃⁻ and clinical context.
Steady state: compensation takes time to develop; in acute, rapidly evolving disturbances the steady-state assumption may not hold.
Physiologic ceiling on alkalosis compensation: hypoventilation is limited by hypoxic drive, so very high PaCO₂ values are unlikely to be purely compensatory.
Not a complete assessment: the formula does not evaluate oxygenation or the underlying cause. Interpret alongside the full ABG and the anion gap.

Frequently Asked Questions (FAQ)

1. What is this calculator used for?

It computes the expected PaCO₂ in a primary metabolic acidosis (and, in alkalosis mode, a metabolic alkalosis) so you can detect a second, concomitant respiratory disorder.

2. What if the measured PaCO₂ is higher than expected?

A measured PaCO₂ above the expected range indicates a concomitant respiratory acidosis — ventilation is inadequate, which can be an emergency.

3. What if the measured PaCO₂ is lower than expected?

A measured PaCO₂ below the expected range indicates a concomitant respiratory alkalosis, classically from salicylate toxicity, sepsis, or liver failure.

4. Can I use this for metabolic alkalosis?

Not with Winters’ formula itself. Metabolic alkalosis uses a separate expectation (0.7 × HCO₃⁻ + 21, ±2). Select the alkalosis mode and the calculator switches to the correct constants.

5. Why the plus or minus 2?

The ±2 mmHg reflects normal individual variation in compensation. A measured PaCO₂ anywhere within that range counts as appropriate compensation.

6. Does compensation normalize the pH?

No. Compensation does not fully correct the pH. A normal pH alongside an abnormal HCO₃⁻ and PaCO₂ suggests a mixed acid-base disorder.

📖 Sources:

⚠️ Disclaimer:

This tool is for informational and educational purposes only and is not a substitute for professional clinical judgment. All treatment decisions must be made by a qualified healthcare professional considering the individual patient’s full clinical context.

Winters’ Formula Calculator