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Aa Gradient Calculator

Created by Dominika Śmiałek, MD, PhD candidate
Reviewed by Dominik Czernia, PhD and Jack Bowater
Last updated: Oct 05, 2023

This Aa gradient calculator estimates the difference between the alveolar concentration of oxygen and the arterial concentration of oxygen.

Once you have the individual levels of each arterial blood gas, take a moment and use this tool to learn more about A a gradient, V Q mismatch, and the causes of oxygenation shifts (check out the oxygenation index calculator). In the article below, you can also find the hypoxemia definition and hypoxia vs. hypoxemia explanations.

We try our best to make our Omni Calculators as precise and reliable as possible. However, this tool can never replace a professional doctor's assessment. All information on this website is for informational purposes only and is not intended to serve as a substitute for medical consultation. Always consult your results with a health care provider.

Aa gradient use

Aa gradient, short for alveolar-arterial gradient, serves as a method of differentiation between the causes of hypoxemia in a patient. The hypoxemia definition is quite straightforward: it's low levels of oxygen in the blood. Technically, what we calculate is a difference between the alveolar concentration of oxygen and the arterial concentration of oxygen (check also blood pH calculator).

The origin of hypoxemia might be either:

  • Extrapulmonary:
    • Hypoventilation; and
    • Low FiO2 (fraction of inspired oxygen, estimated with PF ratio calculator).
  • Intrapulmonary:
    • Ventilation-perfusion imbalance (V Q mismatch), present in patients with pneumonia, asthma, or COPD (chronic obstructive pulmonary disease); and
    • Intrapulmonary or cardiac shunt.

Among the extrapulmonary causes of hypoxemia, there is hypoventilation. It may be present due to, e.g., depression of the central nervous system, neuromuscular diseases, scoliosis, or other chest deformities. It means the oxygen concentration in both the alveoli and the blood is low. As a result, the Aa gradient tends to remain below the ranges estimated for age.

Let's move on to intrapulmonary causes of hypoxemia: cardiac/intrapulmonary shunt and V Q mismatch. The most common example is a patient with pneumonia. The pathophysiology involves an obstruction in the alveoli, which leads to a decrease in the amount of oxygen diffused into the blood. Yet, it doesn't influence the patient's ability to breathe and ventilate. As a result, these patients have a normal oxygen concentration in their alveoli but a decreased concentration in their arterial blood, and the Aa gradient tends to be higher than the estimated for age.

Hypoxia vs hypoxemia differences

Hypoxia and hypoxemia definitions might be confusing. They represent different states and conditions of the human body.

  • Hypoxemia is a state where the partial pressure of oxygen in the blood is decreased. We can measure its levels indirectly, by pulse oximetry, and directly, by drawing blood from either an artery or a vein. The most reliable source of a person's oxygen levels is arterial blood, e.g., from the radial artery.

  • Hypoxia is defined as a diminished level of tissue oxygenation.

These two terms aren't synonyms, and they do not always happen at the same time. If a patient can still compensate with increased hemoglobin (check hemoconcentration with our hematocrit hemoglobin ratio calculator) or cardiac output, they might have hypoxemia but not hypoxia.

Hypoxia without hypoxemia is a less common occurrence and is sometimes seen in people who have been poisoned with cyanide. In this case, cyanide blocks the tissue's ability to use oxygen while the oxygen levels in the blood remain normal, causing hypoxia without hypoxemia.

How to calculate the Aa gradient?

Now that you know the difference between hypoxia vs hypoxemia, the possible causes of hypoxemia, and what Aa gradient is used for, let's move on to its formula:

AA gradient = PAO2 - PaO2


  • PaO2 is the arterial partial pressure of oxygen, measured from an artery; and

  • PAO2 is the partial pressure of alveolar oxygen, which we can also calculate as:

PAO2 = [FiO2 * (Patm - PH20) - PaCO2 / 8]


  • PH2O is the partial pressure of water;
  • FiO2 is the fraction of inspired oxygen;
  • Patm is the atmospheric pressure; and
  • PaCO2 is the partial pressure of carbon dioxide in the alveoli.

At standard pressure, one can suppose that the fraction of inspired oxygen is FiO2 = 0.21, or 21%, the atmospheric pressure at sea level is Patmis atmospheric pressure = 760 mmHg, and, if we assume 100% humidity in the alveoli, PH2O = 47 mmHg.

In this Aa gradient calculator, we also provide you with an expected AA gradient that depends on the patient's age. The formula is simple:

Aa gradient for age = age/4 + 4

Aa gradient calculator in practice

Let's take a moment to work on an example. Laura is a medical doctor working at a hospital. One day a patient with a history of shunting comes to the ER (Emergency Room), and she quickly needs to assess his hypoxemia with an Aa gradient calculator.

He's 57, breathes regular air, and from his arterial blood gases it seems that his PaCO2 = 45 mmHg while PaO2 = 70 mmHg. Both values are slightly out of the healthy range.

AA gradient = [0.21 * (760 mmHg - 45 mmHg) - 45 mmHg / 8] - 70 mmHg

AA gradient = 23.8 mmHg

The expected AA gradient for age differs from the calculated one:

AA gradient for age = 57/4 + 4

AA gradient for age = 18.3 mmHg

Dominika Śmiałek, MD, PhD candidate
Atmospheric pressure
AA gradient
Expected AA gradient for age
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