Compute the expected pCO2 from serum bicarbonate (HCO3) in metabolic acidosis, then compare it with the actual pCO2 from arterial blood gas (ABG) analysis to assess the adequacy of respiratory compensation.
Primary source: Albert MS, Dell RB, Winters RW. Quantitative displacement of acid-base equilibrium in metabolic acidosis. Ann Intern Med 1967;66:312–322. HCO3 in mEq/L (equivalent to mmol/L).
Inverse of Winter's formula — useful for checking the consistency of an ABG value pair.
pCO2 26 mmHg → estimated HCO3 = 12.0 mEq/L. This estimate is only valid if compensation is assumed adequate.
| HCO3 (mEq/L) | Expected pCO2 (mmHg) | ±2 range (mmHg) | Equivalent (kPa) |
|---|---|---|---|
| 6 | 17 | 15–19 | 2.27 |
| 8 | 20 | 18–22 | 2.67 |
| 10 | 23 | 21–25 | 3.07 |
| 12 | 26 | 24–28 | 3.47 |
| 15 | 30.5 | 28.5–32.5 | 4.07 |
| 20 | 38 | 36–40 | 5.07 |
| 24 | 44 | 42–46 | 5.87 |
Example: HCO3 12 → 26 (range 24–28) mmHg; HCO3 20 → 38 (range 36–40) mmHg. Conversion: 26 mmHg = 3.47 kPa.
Full compensation takes 12–24 hours; pCO2 rarely falls below 10–12 mmHg (maximal hyperventilation limit).
Winter's formula 1.5 × HCO3 + 8 ± 2 remains the most precise and is the reference standard.
Winter's formula estimates the pCO2 a patient SHOULD achieve if their lungs compensate metabolic acidosis appropriately. The formula: expected pCO2 = 1.5 × HCO3 + 8 ± 2 (mmHg). It was derived by R.W. Winters et al. via linear regression on documented metabolic acidosis patients (Albert, Dell & Winters, Annals of Internal Medicine, 1967; 66:312–322). The actual ABG (arterial blood gas) value is then compared with this expected range to assess compensation adequacy.
Take serum bicarbonate (HCO3) in mEq/L, multiply by 1.5, add 8, then apply a ±2 mmHg tolerance. Example: HCO3 = 12 mEq/L → 1.5 × 12 + 8 = 26 mmHg, range 24–28 mmHg. Another example: HCO3 = 20 mEq/L → 1.5 × 20 + 8 = 38 mmHg, range 36–40 mmHg. For kPa units, multiply the mmHg result by 0.133322 (e.g. 26 mmHg = 3.47 kPa).
Only for pure metabolic acidosis (low HCO3 with pH < 7.35) that has been present long enough for full respiratory compensation — generally 12–24 hours after onset. This formula does NOT apply to metabolic alkalosis (different rule: pCO2 rises 0.5–0.7 mmHg per 1 mEq/L increase in HCO3) and is not designed for primary respiratory disorders.
There are three possibilities: (1) actual pCO2 is WITHIN the expected range → adequate respiratory compensation, simple metabolic acidosis; (2) actual pCO2 is BELOW the lower range limit → coexisting respiratory alkalosis (excessive hyperventilation); (3) actual pCO2 is ABOVE the upper range limit → coexisting respiratory acidosis (relative hypoventilation, e.g. respiratory depression). Interpretation is always confirmed with the clinical picture and anion gap.
Physiologic hyperventilation has a limit: pCO2 rarely falls below 10–12 mmHg even in severe acidosis. In practice, when Winter's formula predicts pCO2 below ~15 mmHg, be aware the body may be unable to reach that value, and an actual pCO2 higher than expected at very low HCO3 does not necessarily mean additional respiratory acidosis — it may simply be the compensation limit.
No. Winter's formula is specifically for metabolic acidosis. For metabolic alkalosis, respiratory compensation is estimated with a different rule: pCO2 rises 0.5–0.7 mmHg for each 1 mEq/L increase in HCO3 above 24. Applying Winter's formula to alkalosis gives directionally wrong numbers.
Winter's formula assesses the RESPIRATORY component of mixed disorders, while delta gap [(AG − 12) − (24 − HCO3)] and delta ratio [(AG − 12) / (24 − HCO3)] assess the mixed METABOLIC component — whether behind a high-anion-gap acidosis there is a coexisting metabolic alkalosis or non-gap acidosis. The two complement each other: Winter for the respiratory axis, delta gap/ratio for the metabolic axis. See our anion gap calculator to compute them.
Yes, but less precise: (1) pCO2 falls 1.3 mmHg per 1 mEq/L drop in HCO3 from 24 — e.g. HCO3 12 → 40 − 1.3×12 = 24.4 mmHg; (2) the HCO3 + 15 rule — e.g. HCO3 12 → 27 mmHg; (3) the last two digits of pH — e.g. pH 7.25 → pCO2 around 25 mmHg. Winter's formula 1.5 × HCO3 + 8 ± 2 remains the most precise and is the reference standard.
Physiologic compensation never fully corrects the primary disorder — that is the key principle of ABG interpretation. If pH looks normal despite low HCO3 and low pCO2, it actually indicates TWO primary disorders masking each other (e.g. metabolic acidosis + respiratory alkalosis), not perfect compensation.
No. This calculator is purely an educational tool for learning blood gas analysis interpretation. It does not establish diagnoses, does not determine therapy, and does not replace clinical assessment by health professionals. Medical decisions are always made by a physician considering the patient's entire condition, not from a single calculator number.
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