Winter’s Formula Calculator (Expected pCO₂ in Metabolic Acidosis)

What is Winter’s formula?

Winter’s formula is an empiric rule that predicts the expected arterial carbon dioxide tension (pCO₂) in a patient with primary metabolic acidosis. It describes the degree of respiratory compensation (hyperventilation) that should occur if the respiratory system is responding appropriately.

How to interpret Winter’s formula

After calculating the expected pCO₂ range, compare it with the measured arterial pCO₂ from the ABG:

• Measured pCO₂ within expected range → appropriate respiratory compensation for metabolic acidosis.
• Measured pCO₂ > upper limit → concomitant respiratory acidosis (inadequate ventilation).
• Measured pCO₂ < lower limit → concomitant respiratory alkalosis (excessive ventilation).

Step-by-step: using this Winter’s formula calculator

1. Confirm metabolic acidosis. Check that the patient has a low pH and low HCO₃⁻.
2. Enter serum HCO₃⁻. Use the bicarbonate value (mEq/L) from the chemistry panel or ABG.
3. Optionally enter measured pCO₂. This allows the calculator to classify compensation.
4. Click “Calculate”. The tool will compute:
   • Expected pCO₂ (central estimate).
   • Expected pCO₂ range (lower and upper bounds).
   • Interpretation of respiratory compensation if measured pCO₂ is provided.

Clinical examples

Example 1 – Pure metabolic acidosis with appropriate compensation

A patient with diabetic ketoacidosis has:

• HCO₃⁻ = 10 mEq/L
• Measured pCO₂ = 24 mmHg

Using Winter’s formula:

The measured pCO₂ (24 mmHg) is within the expected range (21–25 mmHg), indicating appropriate respiratory compensation and no additional respiratory disorder.

Example 2 – Metabolic acidosis with concomitant respiratory acidosis

A patient with sepsis and COPD has:

• HCO₃⁻ = 12 mEq/L
• Measured pCO₂ = 40 mmHg

The measured pCO₂ (40 mmHg) is above the expected range, suggesting a superimposed respiratory acidosis (hypoventilation) on top of metabolic acidosis.

When not to use Winter’s formula

Winter’s formula is only valid in primary metabolic acidosis. Do not apply it in:

• Primary metabolic alkalosis.
• Primary respiratory acidosis or alkalosis.
• Situations where compensation has not yet equilibrated (very acute changes).

In other acid–base disorders, different compensation rules apply (e.g., expected HCO₃⁻ in chronic respiratory acidosis).

Formula derivation and rationale (brief)

Winter’s formula is based on observational data from patients with metabolic acidosis, showing that the respiratory system typically reduces pCO₂ in proportion to the fall in bicarbonate. The slope (~1.5) and intercept (~8) reflect the average relationship between HCO₃⁻ and pCO₂ in these patients, with ±2 mmHg capturing physiologic variability.

Limitations and clinical caveats

• It is an approximation, not an exact prediction.
• Assumes the patient has had time to reach a new steady state of compensation.
• Does not account for extremes of age, chronic lung disease, or mechanical ventilation settings.
• Should be interpreted alongside the full clinical picture, not in isolation.

Frequently asked questions

Is Winter’s formula the same as the Winter–Blythe formula?

Yes. The term “Winter–Blythe formula” is sometimes used in the literature, but in clinical practice it is almost always referred to simply as Winter’s formula.

What units should I use?

This calculator assumes:

• HCO₃⁻ in mEq/L (or mmol/L, numerically equivalent in this context).
• pCO₂ in mmHg.

Can I use Winter’s formula in chronic metabolic acidosis?

Yes, Winter’s formula is generally applied to both acute and chronic metabolic acidosis, but the degree of compensation may vary depending on chronicity and underlying lung function. Always interpret results cautiously in patients with chronic respiratory disease.

What if the HCO₃⁻ is very low (e.g., < 5 mEq/L)?

At extreme values, any compensation rule becomes less reliable. Very low bicarbonate levels often indicate severe illness, and the patient may not follow “textbook” compensation patterns. Use the formula as a rough guide only.