Expected pCO₂ in Metabolic Alkalosis Calculator
Expected pCO₂ in Metabolic Alkalosis Calculator
Check whether the measured pCO₂ shows appropriate respiratory compensation for a metabolic alkalosis — the mirror of Winter’s formula, which belongs to metabolic acidosis and must not be used here.
Expected pCO₂ in metabolic alkalosis
Compensation checkHCO₃⁻ 38 mmol/L, measured pCO₂ 48 mmHg
Formula
- HCO₃⁻
- measured serum bicarbonate in mmol/L, from a primary metabolic alkalosis
- ± 5
- the accepted tolerance. It is wider than Winter's ± 2 because respiratory compensation for an alkalosis is less consistent between patients than compensation for an acidosis — hypoventilation is limited by the hypoxaemia it causes, and by whatever else the patient's lungs are doing
- the alternative form
- many texts state the same physiology as a slope: the pCO₂ rises 0.6 to 0.75 mmHg for every 1 mmol/L rise in bicarbonate. Run from 24/40, 0.7 per mmol/L gives 0.7 × HCO₃⁻ + 23.2, which is 3.2 mmHg above this formula. Both sit inside the ± 5 tolerance across the usual range, and neither is wrong
- the cap, about 55 mmHg
- compensation for a metabolic alkalosis is limited. Hypoventilation raises the pCO₂ but lowers the alveolar pO₂, and the resulting hypoxaemia drives ventilation back up. Published guidance is that the pCO₂ should not rise above about 55 mmHg (7.3 kPa) in compensation, so above a bicarbonate of roughly 50 this formula predicts a value the body will not reach
- applies to
- a primary metabolic alkalosis only. Do not apply it to a metabolic acidosis — that is Winter's formula — and do not read it in isolation where the raised bicarbonate is itself compensation for a chronic respiratory acidosis
- units
- published in mmHg. Divide by 7.50062 for kPa: an expected pCO₂ of 46.6 mmHg is 6.21 kPa, and the ± 5 mmHg tolerance is ± 0.67 kPa
Worked example
HCO₃⁻ 38 mmol/L, measured pCO₂ 48 mmHg
Expected pCO₂ = 0.7 × 38 + 20 = 26.6 + 20 = 46.6 mmHg (range 41.6 – 51.6)
48 − 46.6 = 1.4 mmHg from expected
Inside the ± 5 mmHg tolerance, so compensation is appropriate and this is a simple metabolic alkalosis
In kPa: expected 6.21 kPa, measured 6.40 kPa, difference 0.19 kPa — the same answer, and entering 6.4 with the unit set to kPa returns the same 1.4
A reader who reached for Winter's formula instead would predict 1.5 × 38 + 8 = 65 mmHg and call a measured 48 a marked respiratory alkalosis. It is not. That 18 mmHg error is why the two calculators are separate pages that link to each other
Change the measured pCO₂ to 56 mmHg and the answer becomes +9.4, above expected: a concurrent respiratory acidosis, and a pCO₂ beyond the usual compensatory ceiling
Change it to 38 mmHg and the answer becomes −8.6: a concurrent respiratory alkalosis
Which formula belongs to which disorder
| Primary disorder | Formula | Tolerance | Page |
|---|---|---|---|
| Metabolic acidosis | Expected pCO₂ = 1.5 × HCO₃⁻ + 8 | ± 2 mmHg | Winter's formula — a separate calculator |
| Metabolic alkalosis | Expected pCO₂ = 0.7 × HCO₃⁻ + 20 | ± 5 mmHg | This page |
Expected pCO₂ across the range, in both units
| HCO₃⁻ (mmol/L) | Expected pCO₂ (mmHg) | Range ± 5 (mmHg) | Expected pCO₂ (kPa) |
|---|---|---|---|
| 28 | 39.6 | 34.6 – 44.6 | 5.28 |
| 32 | 42.4 | 37.4 – 47.4 | 5.65 |
| 36 | 45.2 | 40.2 – 50.2 | 6.03 |
| 38 | 46.6 | 41.6 – 51.6 | 6.21 |
| 40 | 48.0 | 43.0 – 53.0 | 6.40 |
| 45 | 51.5 | 46.5 – 56.5 | 6.87 |
| 50 | 55.0 | 50.0 – 60.0 | 7.33 |
| 55 | 58.5 | 53.5 – 63.5 | 7.80 |
Reading the result
| Result versus expected | Interpretation |
|---|---|
| Below −5 mmHg | Concurrent respiratory alkalosis — a second disorder, not over-compensation |
| −5 to +5 mmHg | Appropriate respiratory compensation for the metabolic alkalosis |
| Above +5 mmHg | Concurrent respiratory acidosis — check for chronic lung disease, sedation, neuromuscular weakness |
The mirror of Winter's formula, and why it is a separate page
Respiratory compensation for a metabolic alkalosis works in the opposite direction to compensation for an acidosis: as bicarbonate rises and the pH climbs, the respiratory centre is suppressed, minute ventilation falls and carbon dioxide is retained, which pulls the pH back down. The relationship is predictable enough to be written as a formula — the expected pCO₂ is 0.7 times the bicarbonate plus 20 — and a measured pCO₂ inside about 5 mmHg of that prediction means the respiratory system is doing exactly what this degree of metabolic alkalosis calls for, with no second process to invoke.
The tolerance is wider than Winter's ± 2, and that is not sloppiness. Hypoventilation is an intrinsically limited response: raising the pCO₂ lowers the alveolar pO₂, and the hypoxaemia that follows stimulates ventilation and works against the alkalotic suppression. Published guidance puts the ceiling at a pCO₂ of about 55 mmHg, which means that above a bicarbonate of roughly 50 the formula predicts a value the body will not reach. Compensation for a metabolic alkalosis is also more variable between patients than compensation for an acidosis, because it depends on whatever else the patient's lungs and respiratory drive are doing.
A value outside the expected range means a second disorder. It does not mean over-compensation, and the distinction is the whole reason to calculate it. A measured pCO₂ above the prediction is a concurrent respiratory acidosis, which in a patient with chronic lung disease is both common and self-reinforcing: metabolic alkalosis blunts respiratory drive, so the alkalosis worsens the hypercapnia that then needs treating. A measured pCO₂ below the prediction is a concurrent respiratory alkalosis, which points at sepsis, pain, liver failure, pregnancy, pulmonary embolism or mechanical over-ventilation.
This calculator is deliberately a separate page from Winter's formula rather than a switch on one page, because the commonest error in this area is applying one formula to the other disorder. The two diverge quickly — at a bicarbonate of 38 they differ by 18 mmHg — so a reader who uses Winter's on an alkalosis will diagnose a respiratory alkalosis that does not exist and may ventilate a patient who needs potassium and chloride. Neither formula makes a diagnosis. Once compensation is accounted for, the question that decides treatment is the urinary chloride, and after that it is the patient: this arithmetic supports a clinician's judgement rather than replacing it, and a blood gas is read alongside the person it came from.
Frequently asked questions
What is the expected pCO₂ in a metabolic alkalosis?
0.7 × bicarbonate + 20 mmHg, with a tolerance of about ± 5 mmHg. At a bicarbonate of 38 that is 46.6 mmHg, or 6.21 kPa, with a range of 41.6 to 51.6 mmHg. Many texts state the same relationship as a slope instead: the pCO₂ rises 0.6 to 0.75 mmHg for every 1 mmol/L rise in bicarbonate.
Can I use Winter's formula for a metabolic alkalosis?
No, and this is the error the two pages exist to prevent. Winter's formula was derived for and applies only to a primary metabolic acidosis. At a bicarbonate of 38 it predicts a pCO₂ of 65 mmHg where the correct formula predicts 46.6 — an 18 mmHg gap that would turn appropriate compensation into an apparent respiratory alkalosis.
Is there a limit to respiratory compensation in metabolic alkalosis?
Yes. Hypoventilation raises the pCO₂ but lowers the alveolar pO₂, and the hypoxaemia that results drives ventilation back up. Published guidance is that the compensatory pCO₂ should not rise above about 55 mmHg (7.3 kPa), so above a bicarbonate of roughly 50 the formula predicts a value the body will not produce.
What does a pCO₂ above the expected value mean?
A concurrent respiratory acidosis — a second disorder, not excessive compensation. Look for chronic lung disease, obesity hypoventilation, neuromuscular weakness, sedation or opioids. It matters because a metabolic alkalosis blunts respiratory drive, so correcting the alkalosis with chloride and potassium is part of treating the hypercapnia.
What should I do once compensation is appropriate?
Send a urinary chloride, which is the measurement that directs treatment. Below about 20 mmol/L indicates a chloride-responsive alkalosis — vomiting, nasogastric aspiration, diuretics, post-hypercapnia — which corrects with sodium chloride and potassium. Above about 20 mmol/L indicates a chloride-resistant alkalosis, and the differential turns to mineralocorticoid excess, Bartter and Gitelman syndromes and current diuretic use.
Related calculators
References
- Schwartz WB, Relman AS. A critique of the parameters used in the evaluation of acid-base disorders. N Engl J Med. 1963;268:1382–8.
- Berend K, de Vries APJ, Gans ROB. Physiological approach to assessment of acid-base disturbances. N Engl J Med. 2014;371(15):1434–45.
- Galla JH. Metabolic alkalosis. J Am Soc Nephrol. 2000;11(2):369–75.
- Merck Manual Professional Edition. Acid-Base Disorders: Primary Changes and Compensations in Simple Acid-Base Disorders. Rahway, NJ: Merck & Co.
- Emmett M. Metabolic alkalosis: a brief pathophysiologic review. Clin J Am Soc Nephrol. 2020;15(12):1848–56.
Medical Disclaimer: The tools and content provided here are for educational and reference purposes only. They are not intended to substitute for professional medical advice, diagnosis, or treatment. Clinical decisions should always be based on the comprehensive assessment of a qualified healthcare professional.