What is Winter's formula?

Winter's formula predicts the pCO2 the lungs should reach when compensating for a metabolic acidosis. It is expected pCO2 equals 1.5 times the bicarbonate plus 8, with an allowance of plus or minus 2 mmHg. It tells you what normal respiratory compensation looks like.

How do I interpret the result?

If the measured pCO2 falls inside the predicted range, compensation is appropriate and the picture is a simple metabolic acidosis. If it is higher than predicted there is a superimposed respiratory acidosis, and if it is lower there is a superimposed respiratory alkalosis.

Why does a deviation mean a second disorder?

The lungs cannot over- or under-compensate beyond a predictable amount, so the expected range is tight. A measured value outside it means a separate respiratory process is also acting on the pCO2, which is the definition of a mixed acid-base disorder.

What units should I use?

Winter's formula is written for pCO2 in millimetres of mercury. If your blood gas analyser reports in kilopascals, multiply the kPa value by 7.5 to convert before comparing it against the calculated range.

Does a normal Winter's result rule out everything?

No. It only assesses respiratory compensation for a metabolic acidosis. You still need to check the pH, the anion gap, the delta ratio and the clinical context, since a normal pCO2 does not exclude a coexisting metabolic alkalosis or a high anion gap process.

Winter's Formula — Expected pCO2 in Metabolic Acidosis

When a patient has a metabolic acidosis, the lungs respond by blowing off carbon dioxide to limit the fall in pH. Winter’s formula tells you exactly how much they should respond, which lets you spot when a second acid-base disorder is hiding in the same blood gas.

How it works

The expected respiratory compensation is a simple linear function of the bicarbonate:

expected pCO2 = 1.5 x HCO3 + 8   (+/- 2 mmHg)

Compute the expected value and its narrow range, then compare it against the measured pCO2:

measured within range  -> appropriate compensation (simple acidosis)
measured above range   -> added respiratory acidosis (under-breathing)
measured below range   -> added respiratory alkalosis (over-breathing)

For example, a bicarbonate of 12 gives an expected pCO2 of 26 mmHg, range 24 to 28. A measured pCO2 of 34 would be too high, revealing a superimposed respiratory acidosis on top of the metabolic acidosis.

Tips and notes

Winter’s formula assumes a primary metabolic acidosis is already established, so confirm the acidosis from the pH and bicarbonate first. Use mmHg throughout; convert a kPa reading by multiplying by 7.5. The formula only judges respiratory compensation and says nothing about whether a coexisting metabolic alkalosis is present, so always finish the assessment with the anion gap and, where relevant, the delta-delta ratio. Interpret every result against the clinical picture rather than in isolation.