For healthcare professionals
Winters Formula Calculator
In metabolic acidosis the bicarbonate falls and breathing changes to lower the PaCO2. The Winters formula gives the PaCO2 expected from that respiratory response. Comparing the measured PaCO2 with the expected range helps judge whether the response is appropriate. This tool is written for clinicians and is not a diagnosis.
Blood gas values
For a metabolic acidosis as the primary disorder. Use values from the same sample. Nothing you enter leaves this page.
What you will see
The expected PaCO2 range and, if you enter it, whether the measured PaCO2 is within, above or below it.
Educational only, not medical advice. Not a diagnosis. Decisions belong to the treating team.
Source
The Winters formula and its plus or minus 2 range as printed by Ayala-De la Cruz S and colleagues, Journal of Clinical Medicine 2025, and Korus J and colleagues, Diagnostics 2025, both open access (CC BY). The tests check the formula, that a PaCO2 exactly on a bound counts as within the range, and that a bound is never displayed so that it looks equal to, or on the wrong side of, the measured value.
Validated in
Ayala-De la Cruz 2025 used the formula to interpret 200 arterial blood gas results at a single center. Korus 2025 is a review of metabolic acidosis in chronic kidney disease.
Limits
The formula applies only when metabolic acidosis is the primary disorder; first decide that from the pH and the bicarbonate. A plus or minus 2 tolerance is the value consistently reported in the literature cited by Ayala-De la Cruz 2025. A result outside the range suggests, but does not prove, an additional disorder.
The formula
Expected PaCO2 (mm Hg) = (1.5 x HCO3) + 8, plus or minus 2 (Ayala-De la Cruz 2025) (Korus 2025).
A measured PaCO2 within 2 mm Hg of the expected value is taken as an appropriate compensatory response (Ayala-De la Cruz 2025). A PaCO2 higher than the formula gives goes with an impaired respiratory response, and comparing the two helps identify a mixed metabolic and respiratory acidosis (Korus 2025). More generally, deviations in the size or direction of the expected change may indicate additional disorders (Ayala-De la Cruz 2025).
Worked example: a bicarbonate of 12 mmol/L gives 1.5 x 12 + 8 = 26 mm Hg, so the expected range is 24 to 28 mm Hg. The tool counts a PaCO2 of exactly 24 or 28 as within the range.
For reference, Korus 2025 gives a normal PaCO2 of 35 to 45 mm Hg (Korus 2025).
Where it fits
The usual stepwise reading of a blood gas is: decide acidosis or alkalosis from the pH, identify the primary disorder from the bicarbonate and PaCO2, check the compensation, and in metabolic acidosis calculate the anion gap (Ayala-De la Cruz 2025). The Winters formula is the compensation step for metabolic acidosis.
Related tools
For the next step in metabolic acidosis, see the anion gap calculator. For oxygenation on the same blood gas, see the A-a gradient calculator. Other bedside scores are listed under For healthcare professionals. The delta ratio calculator compares the rise in the anion gap with the fall in bicarbonate.
Sources
- Ayala-De la Cruz S, Arenas-Hernández PE, Fernández-Herrera MF, et al. Human-in-the-loop performance of LLM-assisted arterial blood gas interpretation: a single-center retrospective study. J Clin Med. 2025;14(18):6676. doi:10.3390/jcm14186676. PMID 41010880. Open access (CC BY). Introduction (stepwise evaluation) and Methods: Equation 1 (Winters formula, plus or minus 2 tolerance), Equations 7 and 8 (anion gap, delta ratio), the 12 mmol/L anion gap cut-off and the delta ratio reading; Discussion (the ratio as a supportive tool). pmc.ncbi.nlm.nih.gov/articles/PMC12470526/
- Korus J, Szymczak M, Gołębiowski M, et al. Metabolic acidosis in patients with chronic kidney disease: diagnosis, pathogenesis, and treatment. A narrative review. Diagnostics (Basel). 2025;15(16):2052. doi:10.3390/diagnostics15162052. PMID 40870903. Open access (CC BY). Section 4 (Winters formula; impaired respiratory response; normal pCO2 35 to 45 mm Hg). pmc.ncbi.nlm.nih.gov/articles/PMC12385983/
Written and maintained by the uncovermyrisk.com editorial team. We do not have a medical reviewer; every claim links to its primary source above. Last reviewed: 2026-11-02. Spotted an error? See About.