Winter's formula
Winter’s formula predicts the PaCO2 a metabolic acidosis should produce: PaCO2 = 1.5 × HCO3− + 8, plus or minus 2. [Merck Manual: acid-base disorders] If the measured PaCO2 is in that band, the lungs have compensated as expected. If not, a second disorder is suspected.
Expected PaCO2 calculator
Enter an HCO3− from 1 to 90.
Winter’s formula applies when a metabolic acidosis is present. Study aid only, not for patient care.
What it tells you
When there is a metabolic acidosis, the Merck Manual applies Winter’s formula to decide whether respiratory compensation is appropriate or reflects a second acid-base disorder. Its wording: “predicted Pco2 = 1.5 [HCO3−] + 8 ± 2; if Pco2 is higher, there is also a primary respiratory acidosis—if lower, respiratory alkalosis.” [Merck Manual: acid-base disorders]
- Measured PaCO2 inside the band: appropriate compensation.
- Above the band: a respiratory acidosis is also present.
- Below the band: a respiratory alkalosis is also present.
Worked example from the Merck Manual
The Merck Manual works a case that looks normal at first glance: pH 7.40, HCO3− 22, PaCO2 41. The anion gap (25) shows a metabolic acidosis, so Winter’s formula is applied: predicted PaCO2 = 1.5 (22) + 8 ± 2 = 41 ± 2. The measured value equals the predicted one, so respiratory compensation is appropriate. [Merck Manual: acid-base disorders]
Three more, by the same arithmetic
| HCO3− | 1.5 × HCO3− + 8 | Band (± 2) |
|---|---|---|
| 12 | 26 | 24 to 28 |
| 15 | 30.5 | 28.5 to 32.5 |
| 18 | 35 | 33 to 37 |
So an HCO3− of 15 with a PaCO2 of 30 is inside the band. With a PaCO2 of 40 it is above it, which the Merck Manual reads as a primary respiratory acidosis on top. [Merck Manual: acid-base disorders]
Limits
The formula is for metabolic acidosis only. The other three simple disorders have their own expected compensation on compensation rules. The Merck Manual also says to calculate the anion gap, and, when a metabolic acidosis is present, a delta gap to look for a concomitant metabolic alkalosis. [Merck Manual: acid-base disorders] Our app runs Winter’s formula on the numbers you type in; this page does the same sum.
Sources
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