A-a Gradient Calculator

Helps diagnose hypoxemia and its cause based on the difference between alveolar and arterial oxygen concentration.

In the text below the form there is more information on the formula used and on the respiratory implications of the A-a gradient.

The A-a gradient calculator determines the difference between the alveolar and arterial oxygen concentration in atmospheric pressure and at a set fraction of inspired oxygen.

The gradient obtained helps diagnose hypoxemia, retrieve its cause and indicate other respiratory and cardiac conditions the patient may be at risk of.

A-a gradient = [FiO2 (Patm – PH20) – PaCO2 /0.8] – PaO2

All variables are input by user, except for PH20 which is taken as 47 mm Hg at 37 degrees Celsius. 0.8 comes from the respiratory quotient: VCO2 / VO2.

Age of the patient:*
Partial pressure of O2 in the artery (PaO2):*
PaCO2 (value from the ABG):*
Atmospheric pressure:*
Fraction of inspired oxygen (FiO2):*
  Embed  Print  Share 

Send Us Your Feedback

Steps on how to print your input & results:

1. Fill in the calculator/tool with your values and/or your answer choices and press Calculate.

2. Then you can click on the Print button to open a PDF in a separate window with the inputs and results. You can further save the PDF or print it.

Please note that once you have closed the PDF you need to click on the Calculate button before you try opening it again, otherwise the input and/or results may not appear in the pdf.


Variables and formula

The A-a gradient represents the difference between the alveolar concentration of oxygen and the arterial concentration of oxygen. The variables used are described in the following table:

Variable Symbol Normal values Description
O2 Partial arterial pressure PaO2 75 – 100 mmHg This is the partial arterial pressure of the oxygen in the arteries. Abnormally low levels indicate hypoxia. Patients with PaO2 <60 mmHg require additional oxygen. Levels <30 mmHg are life threatening.
CO2 arterial pressure PaCO2 35 – 45 mmHg This is the partial arterial pressure of carbon dioxide in the arteries, and is main indicator of CO2 production and elimination.
Low values indicate hypocapnia or overventilation whilst high values indicate ventilation is impaired.
Atmospheric pressure Patm 760 mmHg Atmospheric pressure above sea level.
Fraction of Inspired Oxygen FiO2 0.21 This is the fraction of oxygen considered in natural air as 21%.
Patient age This is used to determine a conservative estimate of a normal A-a gradient based on the following formula: (Age + 4) / 4

The alveolar – arterial gradient formula is:

A-a gradient = [FiO2 (Patm – PH20) – PaCO2 /0.8] – PaO2

All variables are input by user, except for PH20 which is taken as 47 mm Hg at 37 degrees Celsius. 0.8 comes from the respiratory quotient: VCO2 / VO2.


Respiratory implications

The A-a is used to determine whether hypoxemia is caused by intra or extra pulmonary causes. Normal A-a values are between 5 and 20 mmHg and may be slightly increased in elderly patients (increase of 1 mmHg for every decade after middle age).

A normal gradient accompanied by a low PaO2 (hypoxemia) indicates hypoventilation by decreased respiratory drive or neuromuscular impairment. In some cases it might also indicate a low fraction of inspired oxygen.

Higher than normal A-a gradients indicate that alveolar function is impaired and ventilation issues (such as pulmonary embolism or right to left shunt) are highly likely.

An elevated gradient accompanied by hypoxemia indicates an imbalance in ventilation perfusion (V/Q mismatch), often met in pulmonary diseases such as COPD or asthma.

The following table summarizes the main causes of hypoxemia and their effect on the A-a gradient:

Hypoxemia cause Effect on A-a gradient
V/Q Mismatch (e.g. PNA, CHF, ARDS, atelectasis, etc) Elevation
Shunt (e.g. PFO, ASD, PE, pulmonary AVMs)
Alveolar Hypoventilation (e.g. interstitial lung dz, environmental lung dz, PCP PNA)
Hypoventilation (e.g. COPD, CNS d/o, neuromuscular dz, etc) Depression
Low FiO2 (e.g. high altitude)

Other respiratory tests

Here are some examples of tests performed to assess the functionality of the respiratory system:

■ Total lung capacity (TLC);

■ Expiratory reserve volume (ERV);

■ Peak expiratory flow (PEF);

■ Forced expiratory volume (FEV);

■ Forced expiratory flow 25% to 75%;

■ Forced vital capacity (FVC);

■ Maximum voluntary ventilation (MVV);

■ Residual volume (RV).


Original source

Helmholz HF Jr. The abbreviated alveolar air equation. Chest. 1979; 75(6):748.


McFarlane MJ, Imperiale TF. Use of the alveolar-arterial oxygen gradient in the diagnosis of pulmonary embolism. Am J Med. 1994; 96(1):57-62.

Specialty: Pulmonology

System: Respiratory

Objective: Diagnosis

Type: Calculator

No. Of Variables: 5

Year Of Study: 1979

Abbreviation: A-a

Article By: Denise Nedea

Published On: June 4, 2017 · 07:06 AM

Last Checked: June 4, 2017

Next Review: June 4, 2023