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.

What is the Winter's Formula — Expected pCO2 in Metabolic Acidosis?

Computes the expected pCO2 compensation for a metabolic acidosis using Winter's formula, pCO2 equals 1.5 times HCO3 plus 8 give or take 2, and flags deviations that suggest a concurrent respiratory acid-base disorder. For acute medicine. It runs free in your browser on Gera Tools, with nothing uploaded.

Winter's Formula — Expected pCO2 in Metabolic Acidosis

Name: Winter's Formula — Expected pCO2 in Metabolic Acidosis
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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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 × 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 metabolic acidosis)
measured above range   → superimposed respiratory acidosis (under-breathing)
measured below range   → superimposed 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.

Worked example

A 58-year-old with diabetic ketoacidosis has an arterial blood gas showing pH 7.22, HCO3 10 mmol/L, pCO2 28 mmHg.

Apply Winter’s formula: expected pCO2 = (1.5 × 10) + 8 = 23 mmHg, range 21–25 mmHg.
The measured pCO2 of 28 mmHg is above the predicted range.
Interpretation: the lungs are not compensating as much as they should — there is a superimposed respiratory acidosis, suggesting additional respiratory impairment that needs to be sought clinically.

By contrast, if the measured pCO2 were 18 mmHg, that would be lower than the 21–25 range, implying the patient is over-breathing — a concurrent respiratory alkalosis — which might point to salicylate toxicity, sepsis, or anxiety driving ventilation beyond the metabolic compensation.

When and why to use it

Winter’s formula is most useful in the emergency department and ICU when a blood gas does not quite fit the clinical picture. A straightforward DKA should show appropriate compensation; if it does not, something else is going on — aspiration, pulmonary oedema, or a central cause of hypoventilation. The two-minute calculation prevents the diagnostic anchoring error of attributing a high pCO2 solely to the acidosis when there is a treatable second cause.

Tips and notes

Confirm a primary metabolic acidosis from the pH and HCO3 before applying the formula — it is not valid for a primary respiratory disorder.
Use mmHg throughout; convert kPa by multiplying by 7.5 (e.g. 3.7 kPa × 7.5 = 27.8 mmHg).
Winter’s formula does not detect a coexisting metabolic alkalosis (for example from vomiting on top of renal failure). Always check the anion gap and the delta-delta ratio.
The ±2 mmHg window is intentionally narrow: the lungs are tightly regulated. A deviation of even 5 mmHg is clinically significant and warrants explanation.
Interpret every result alongside the clinical picture — formula outputs do not substitute for examination.