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What is the Winter's Formula?

Published in Acid-Base Balance 2 mins read

Winter's formula is used to estimate the expected PaCO2 (partial pressure of carbon dioxide in arterial blood) in a patient with metabolic acidosis to determine if there is appropriate respiratory compensation.

The Formula:

The formula is:

Expected PaCO2 = (1.5 x serum HCO3-) + (8 ± 2)

Where:

  • PaCO2 is the partial pressure of carbon dioxide in arterial blood.
  • HCO3- is the serum bicarbonate concentration.

How it Works and What it Means:

In metabolic acidosis, the body attempts to compensate by increasing ventilation, which lowers the PaCO2. Winter's formula predicts what the PaCO2 should be if the respiratory system is appropriately compensating.

  • If the actual measured PaCO2 is close to the calculated expected PaCO2, then the respiratory compensation is appropriate for the degree of metabolic acidosis.

  • If the actual measured PaCO2 is higher than the calculated expected PaCO2, the patient likely has a concurrent respiratory acidosis (in addition to the metabolic acidosis). They are not breathing off enough CO2.

  • If the actual measured PaCO2 is lower than the calculated expected PaCO2, the patient likely has a concurrent respiratory alkalosis (in addition to the metabolic acidosis). They are breathing off too much CO2.

Example:

Let's say a patient has a serum bicarbonate (HCO3-) level of 12 mEq/L.

Expected PaCO2 = (1.5 x 12) + (8 ± 2)
Expected PaCO2 = 18 + (8 ± 2)
Expected PaCO2 = 26 ± 2
Expected PaCO2 range: 24-28 mmHg

If the patient's measured PaCO2 is between 24 and 28 mmHg, their respiratory compensation is appropriate. If it's higher than 28 mmHg, they have a superimposed respiratory acidosis. If it's lower than 24 mmHg, they have a superimposed respiratory alkalosis.

Shortcut:

As the reference indicates, a quick and dirty shortcut to estimate the expected PaCO2 is to use the last two digits of the pH +/- 2. However, it is much better to calculate using the full formula provided.

Important Note:

Winter's formula only applies in maximally compensated metabolic acidosis, which usually takes 12-24 hours to develop.

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