What this calculator does
When the blood becomes acidotic for metabolic reasons, breathing speeds up to blow off carbon dioxide and partly compensate. Winters' formula predicts how far that compensation should go.
Comparing prediction against measurement is the point. A bicarbonate of 14 mEq/L predicts a pCO2 of 29.0 mmHg with a range of 27.0 to 31.0. A measured 25 falls below that, which indicates a second process rather than compensation alone.
The formula
Expected pCO2 is 1.5 times the bicarbonate plus 8, with a tolerance of 2 mmHg either side. A measured value outside that range indicates an additional respiratory disorder.
| Term | Meaning |
|---|---|
| Compensation | The respiratory response to a metabolic acidosis, which is expected rather than a separate problem. |
| Expected range | The prediction plus or minus 2 mmHg. |
| Mixed disorder | A measured pCO2 outside the range, indicating a concurrent respiratory problem. |
The inputs explained
| Field | What to enter |
|---|---|
| Bicarbonate (HCO3) (mEq/L) | Serum bicarbonate in mEq/L. |
| Measured pCO2 (0 if unknown) (mmHg) | Measured arterial pCO2 in mmHg, for comparison. Leave at zero to see the prediction alone. |
When to use it
Assessing a metabolic acidosis
Checking compensation is a standard step in acid-base interpretation.
Detecting a mixed disorder
Compensation outside the expected range means a second process is present.
Learning blood gas interpretation
Winters' formula is the standard compensation check in teaching.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
What pCO2 is expected at each bicarbonate?
Three bicarbonate levels and their expected compensation.
| Bicarbonate | Expected pCO2 | Expected range |
|---|---|---|
| 8 mEq/L | 20.0 mmHg | 18.0 - 22.0 mmHg |
| 14 mEq/L | 29.0 mmHg | 27.0 - 31.0 mmHg |
| 20 mEq/L | 38.0 mmHg | 36.0 - 40.0 mmHg |
Questions
What does a pCO2 below the range mean?
That the patient is breathing off more carbon dioxide than compensation alone explains, which indicates a concurrent respiratory alkalosis. Salicylate poisoning and sepsis are classic examples of that combination.
What does a pCO2 above the range mean?
That compensation is inadequate, indicating a concurrent respiratory acidosis. Respiratory muscle fatigue or a depressed respiratory drive are common reasons.
Does the formula apply to metabolic alkalosis?
No. It is specific to metabolic acidosis, and a different relationship governs the expected compensation for alkalosis. Applying it in the wrong direction gives a meaningless answer.
Is compensation ever complete?
No, and that is an important principle. Compensation reduces the pH disturbance but never fully corrects it, so a normal pH alongside abnormal bicarbonate and pCO2 indicates a mixed disorder rather than perfect compensation.
For the unmeasured ion balance, see the anion gap calculator. For the delta comparison, see the delta ratio calculator.