Acid–Base Calculator (ABG pattern and expected compensation)

Understanding the acid–base calculator — concept and principle

This calculator interprets an arterial blood gas in three steps: it classifies the pH, identifies the main acid–base pattern from PaCO₂ and bicarbonate, and checks whether the compensation is as expected or suggests a second disorder. Medical students, nurses and clinicians use it to practise and double-check blood gas interpretation.

pH → main problem → compensation — with the default inputs: 30 = as expected.

How it is calculated

pH below 7.35: acidaemia; above 7.45: alkalaemia
Low HCO₃⁻ (below 22 mmol/L) → metabolic acidosis; high PaCO₂ (above 45 mmHg) → respiratory acidosis; high HCO₃⁻ (above 26) → metabolic alkalosis; low PaCO₂ (below 35) → respiratory alkalosis; both pushing the same way → mixed
Expected compensation: metabolic acidosis PaCO₂ = 1.5 × HCO₃⁻ + 8 ± 2 (Winters); metabolic alkalosis PaCO₂ = 0.7 × HCO₃⁻ + 20 ± 5
Respiratory acidosis: HCO₃⁻ rises 1–2 (acute) or 3–4 (chronic) mmol/L per 10 mmHg PaCO₂ above 40; respiratory alkalosis: falls 1–2 (acute) or 4–5 (chronic) per 10 mmHg below 40, from 24 mmol/L

The principle

Blood pH depends on the ratio of bicarbonate, controlled by the kidneys, to carbon dioxide, controlled by the lungs. When one changes, the other system responds to limit the change in pH: this is compensation. Bedside rules predict how large that response should be. If the measured value falls outside the expected range, a second process is probably present. Winters' formula, published by Albert, Dell and Winters in 1967, predicts the respiratory response to metabolic acidosis.

Worked example

Defaults: pH 7.28, PaCO₂ 30 mmHg, HCO₃⁻ 14 mmol/L.

pH below 7.35: Acidaemia.
HCO₃⁻ is low and PaCO₂ is not high: Metabolic acidosis.
Expected PaCO₂ = 1.5 × 14 + 8 = 29 ± 2: from 27 to 31 mmHg; value checked: PaCO₂ (mmHg).
Measured 30 is within the range: As expected; possible second disorder: None suggested.

How to read the result

"As expected" means the lungs are compensating appropriately for the metabolic acidosis. A PaCO₂ above the range would suggest an additional respiratory acidosis, below it an additional respiratory alkalosis. The next step in metabolic acidosis is usually the anion gap, which helps identify the cause.

Common mistakes

Using venous values with arterial rules without adjustment.
Calling a compensated disorder "normal" because pH is in range.
Forgetting to choose acute or chronic for respiratory problems.
Skipping the anion gap.

Keep in mind: These are rules of thumb for learning and checking, not a diagnosis. Blood gases must be interpreted by clinicians with the history and examination.

Frequently asked questions

What is Winters' formula?

Expected PaCO₂ = 1.5 × HCO₃⁻ + 8 ± 2, used to check respiratory compensation in metabolic acidosis.

What does full compensation mean?

Compensation rarely returns pH completely to normal; a normal pH with abnormal gases may indicate a mixed disorder.

What are normal blood gas values?

Commonly cited ranges are pH 7.35–7.45, PaCO₂ 35–45 mmHg and HCO₃⁻ 22–26 mmol/L.

Sources: Brandis K, Acid-base Physiology, section 9.3 "Bedside Rules for Assessment of Compensation" (Medicine LibreTexts) · Albert MS, Dell RB, Winters RW, Ann Intern Med 1967;66(2):312–322 · MSD Manual Professional Edition, "Primary Changes and Compensations in Simple Acid-Base Disorders"

Checked 9 Nov 2026. Bedside compensation rules: Brandis K, Acid-base Physiology, section 9.3 “Bedside Rules for Assessment of Compensation” (Medicine LibreTexts); compensation ranges and pH limits: MSD Manual Professional Edition, table “Primary Changes and Compensations in Simple Acid-Base Disorders” (Lewis JL III, reviewed 2025); Winters’ rule: Albert MS, Dell RB, Winters RW, Ann Intern Med 1967;66(2):312–322; normal PaCO₂ 35–45 mmHg and HCO₃⁻ 22–26 mmol/L as listed by Life in the Fast Lane (LITFL), “Blood Gas Interpretation”.

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