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The A-a gradient is the difference between the partial pressure of oxygen in the alveolus (PAO2) and the partial pressure of oxygen in the arterial blood (PaO2). PAO2 is the ‘ideal’ alveolar PO2. The A-a gradient is helpful in diagnosing the cause of hypoxia. See Hypoxia/hypoxaemia.

PAO2 is calculated from the alveolar gas equation:

PAO2 = (PB – PH2O) × FiO2 – (PaCO2)/R


  • PB = barometric pressure (760 mmHg at sea level).

  • PH2O = partial pressure of H2O (47 mmHg). Gas in the lungs is fully saturated with water vapour.

  • FiO2 = fraction of inspired O2.

  • PaCO2 = partial pressure of CO2 in arterial blood (NR 35–45 mmHg).

  • R = gas exchange ratio, also called the ‘respiratory quotient’ (0.8).

Therefore, for a normal person breathing air at 1 atmosphere and assuming a PaCO2 of 40 mmHg:

PAO2 = (760 − 47 mmHg) × 0.21 − 40/0.8 = 99.73 mmHg

The simplified version of the equation is: PAO2 = FiO2 × 713 – PaCO2/0.8

Points to note

  1. PAO2 is normally about 105 mmHg.

  2. PaO2 is normally about 100 mmHg.

  3. Normal A-a gradient is 5–15 mmHg. It is 5–10 mmHg for a normal young adult.

  4. If the A-a gradient is normal and the patient is hypoxic, the problem is extrinsic to the lungs.

  5. If the A-a gradient is abnormal and the patient is hypoxic, the problem is in the lungs.

  6. A-a gradient increases with age. It should be ≤ 0.3 × age.

Hypoxaemia with a normal A-a gradient

Can be due to:

  1. decreased partial pressure of inspired O2 e.g. at altitude

  2. hypoventilation

  3. haemoglobin defects or anaemia.

Hypoxaemia with a widened A-a gradient

Can be due to:

  1. ventilation/perfusion mismatch

  2. alveolar hypoventilation—pulmonary fibrosis, interstitial lung disease.


A rapid assessment tool for a non-arrested patient. The letters relate to:

  • A – Airway—patency; is the patient talking?

  • B – Breathing-rate; pulse oximetry; is air entry equal; is trachea midline?

  • C – Circulation—pulse rate and quality; blood pressure; capillary return; skin colour.

  • D – Disability—assess conscious state using GCS or AVPU. See Glasgow coma score and AVPU.

  • E – Exposure—examine patient's entire body for any concealed evidence of injury, haemorrhage etc.


An extension of the ABCDE tool above. The letters relate to:

  • A – Airway—patency.

  • B – Breathing—respiratory rate; ...

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