Winter’s Formula Calculator
Winter's Formula Calculator
Check whether the measured pCO₂ shows appropriate respiratory compensation for a metabolic acidosis, or a second acid-base disorder.
Winter's Formula
Compensation checkHCO₃⁻ 12 mmol/L, measured pCO₂ 26 mmHg
Formula
- HCO₃⁻
- measured serum bicarbonate, mmol/L
- ± 2
- the accepted tolerance around the predicted value — treat anything inside it as appropriate compensation
- applies to
- a primary metabolic acidosis only — do not apply it to a metabolic alkalosis, or read it in isolation in a known mixed disorder
Worked example
HCO₃⁻ 12 mmol/L, measured pCO₂ 26 mmHg
Expected pCO₂ = 1.5 × 12 + 8 = 26 mmHg (range 24 – 28)
26 − 26 = 0.0 mmHg from expected
The measured value sits exactly at the predicted midpoint — compensation is appropriate
Reading the result
| Result vs expected | Interpretation |
|---|---|
| Below −2 | Concurrent respiratory alkalosis |
| −2 to +2 | Appropriate respiratory compensation |
| Above +2 | Concurrent respiratory acidosis — evaluate for respiratory failure |
Why compensation has a predictable range
When metabolic acid accumulates, the respiratory centre responds within minutes by increasing minute ventilation and blowing off CO₂, which partly restores pH. Winters and colleagues showed this response is not open-ended but falls within a narrow, predictable band: expected pCO₂ equals 1.5 times the bicarbonate plus 8, give or take 2 mmHg. A measured pCO₂ inside that band means the respiratory system is doing exactly what it should for the severity of the metabolic acidosis present — no second process needs to be invoked.
A measured pCO₂ below the expected range means ventilation has gone further than compensation requires, which is only explained by a coexisting respiratory alkalosis — sepsis, salicylate toxicity, pain, anxiety or pregnancy are common drivers. A measured pCO₂ above the expected range is the more urgent finding: the lungs are under-compensating relative to what the metabolic acidosis demands, which signals a concurrent respiratory acidosis. In a patient who is tiring — reduced respiratory effort, rising pCO₂ on serial gases, altered mental status — this is a warning of impending respiratory failure and a trigger for ventilatory support.
The formula is derived specifically for metabolic acidosis and should not be extrapolated to a metabolic alkalosis, which has its own compensation formula, or read as a standalone diagnostic tool in a patient already known to have a mixed disorder from the history.
Frequently asked questions
What is Winter's formula used for?
It predicts the pCO₂ that appropriate respiratory compensation should produce for a given degree of metabolic acidosis, so a measured pCO₂ can be checked against it to detect a second, respiratory, acid-base disorder.
What does it mean if the measured pCO₂ is above the expected range?
The lungs are not compensating enough for the metabolic acidosis present, indicating a concurrent respiratory acidosis. In a patient who appears to be tiring, this is an emergency and a signal to prepare for ventilatory support.
What does it mean if the measured pCO₂ is below the expected range?
Ventilation has exceeded what compensation requires, indicating a concurrent respiratory alkalosis — consider sepsis, salicylate toxicity, pain, anxiety or pregnancy.
Does Winter's formula apply to metabolic alkalosis?
No. It was derived for, and applies only to, a primary metabolic acidosis. Metabolic alkalosis has a separate expected-compensation formula.
Related calculators
References
- Albert MS, Dell RB, Winters RW. Quantitative displacement of acid-base equilibrium in metabolic acidosis. Ann Intern Med. 1967;66(2):312–22.
- Berend K, de Vries APJ, Gans ROB. Physiological approach to assessment of acid-base disturbances. N Engl J Med. 2014;371(15):1434–45.