Alveolar–Arterial Oxygen Gradient (A–a) Calculator
Calculate estimated alveolar oxygen tension and the alveolar–arterial oxygen gradient from FiO₂, arterial PaO₂ and PaCO₂, barometric pressure, and R.
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About
This educational calculator estimates inspired and alveolar oxygen tension and the alveolar–arterial (A–a) oxygen gradient from an arterial blood-gas sample and explicit oxygen assumptions. It is not a direct measurement, does not establish a diagnosis, and does not determine treatment. Use PaO₂ and PaCO₂ from the same arterial blood-gas sample; pulse-oximetry and venous values are not substitutes. [3, 4]
The full equation treats PH₂O as 47 mmHg at 37°C water-vapour saturation, uses PaCO₂ as a clinical approximation of alveolar CO₂, and assumes inspired CO₂ is negligible. Significant rebreathing or an unusual inspired-gas composition is outside this model; oxygen delivery, barometric pressure, respiratory exchange ratio, timing, and sampling assumptions can materially affect the estimate. [1, 2, 4]
Interpretation
How the calculation works
The page uses the full alveolar gas equation. PH₂O is fixed at 47 mmHg for 37°C water-vapour saturation, PaCO₂ is used as a clinical approximation of alveolar CO₂, and the standard form assumes negligible inspired CO₂. Significant rebreathing or an unusual inspired-gas composition is outside this model; PB and R are explicit assumptions rather than hidden defaults. [1, 2, 4]
Use PaO₂ and PaCO₂ from the same ABG
PaO₂ and PaCO₂ should come from the same arterial blood-gas sample. SpO₂ readings and venous blood-gas values cannot replace those inputs. [3, 4]
FiO₂ and oxygen-delivery limitations
Enter a measured or device-set FiO₂ for controlled supplemental oxygen. The calculator does not infer FiO₂ from oxygen flow, cannula settings, or a device name. [1, 4]
Barometric pressure and altitude
Sea-level standard pressure is 760 mmHg. Select custom pressure when a known local pressure is available; this page does not convert altitude to pressure. The 250–800 mmHg technical input range is not a normal range and this page does not model hyperbaric oxygen or other hyperbaric environments. [1, 2]
Respiratory exchange ratio (R)
R is an assumption in the equation. The standard reference value is 0.80, but a custom value can be entered when it is explicitly justified. [1, 2]
Historical age reference
The age / 4 + 4 mmHg expression is displayed only for this page’s room-air, sea-level, R 0.80 reference configuration. It is a limited historical reference, not a diagnostic threshold. [5]
What a wider gradient can and cannot indicate
A widened calculated gradient can be seen with ventilation–perfusion mismatch, right-to-left shunt, or diffusion limitation. A relatively preserved gradient can occur with low inspired oxygen or alveolar hypoventilation. These mechanisms are explanatory context, not a disease diagnosis or treatment rule; the calculation does not identify a cause or replace clinical assessment and objective testing. [3, 5, 6]
Negative gradients
A negative calculated gradient usually reflects measurement variability or mismatched assumptions rather than gas exchange that is “better than normal.” [4]
A normal calculated gradient has limits
A normal or narrow calculated gradient does not exclude pulmonary embolism or another disease process. [5, 6]
Different from PAO₂, P/F ratio, and oxygenation index
PAO₂ is the equation’s estimated alveolar oxygen tension. P/F ratio compares PaO₂ with FiO₂, while oxygenation index uses mean airway pressure and is a different measurement context. [4, 6]
References
- Fenn WO, Rahn H, Otis AB. A theoretical study of the composition of the alveolar air at altitude. Am J Physiol. 1946;146:637–653. PMID 20996488. DOI 10.1152/ajplegacy.1946.146.5.637.
- Curran-Everett D. A classic learning opportunity from Fenn, Rahn, and Otis (1946): the alveolar gas equation. Adv Physiol Educ. 2006;30(2):58–62. PMID 16709734. DOI 10.1152/advan.00076.2005.
- Mellemgaard K. The alveolar-arterial oxygen difference: its size and components in normal man. Acta Physiol Scand. 1966;67(1):10–20. PMID 5963295. DOI 10.1111/j.1748-1716.1966.tb03281.x.
- Davis MD, Walsh BK, Sittig SE, Restrepo RD. AARC clinical practice guideline: blood gas analysis and hemoximetry: 2013. Respir Care. 2013;58(10):1694–1703. PMID 23901131. DOI 10.4187/respcare.02786.
- Stein PD, Goldhaber SZ, Henry JW. Alveolar-arterial oxygen gradient in the assessment of acute pulmonary embolism. Chest. 1995;107(1):139–143. PMID 7632205. DOI 10.1378/chest.107.1.139.
- Sarkar M, Niranjan N, Banyal PK. Mechanisms of hypoxemia. Lung India. 2017;34(1):47-60. PMID 28144061.
FAQ
It uses the full form: PAO₂ = FiO₂ × (PB − 47) − PaCO₂ × [FiO₂ + (1 − FiO₂) / R]. The 47 mmHg term represents water-vapour pressure at 37°C; PaCO₂ is used as a clinical approximation of alveolar CO₂, and the standard form assumes negligible inspired CO₂. Significant rebreathing or unusual inspired-gas composition is outside this model. The page does not substitute the simplified room-air expression when a different FiO₂ or R is selected.
Barometric pressure changes inspired oxygen tension, including at altitude. R is an assumption in the alveolar gas equation. The calculator uses sea-level standard pressure and R 0.80 only when those contexts are selected, and it does not convert altitude to pressure. Its 250–800 mmHg pressure range is a technical input range, not a normal range, and this page does not model hyperbaric oxygen or other hyperbaric environments.
No. A widened gradient can be seen with ventilation–perfusion mismatch, right-to-left shunt, or diffusion limitation, while low inspired oxygen or alveolar hypoventilation can leave the gradient relatively preserved. These are mechanisms, not a diagnosis or treatment rule; clinical context and objective testing remain necessary.
A negative result is retained rather than relabeled. It usually indicates measurement variability or a mismatch in FiO₂, barometric pressure, R, timing, or sample assumptions; it does not mean gas exchange is better than normal.
Sources: [4]
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Oxygenation Index
Calculate conventional Oxygenation Index from matched FiO₂, ventilator mean airway pressure, and arterial PaO₂ during invasive mechanical ventilation.
Disclaimer
Educational and informational reference only. Not intended to replace professional medical advice, diagnosis, treatment, or independent verification.