A-a Gradient Calculator (Alveolar-Arterial Oxygen)
Enter your arterial blood gas (ABG) values and patient age to calculate the alveolar-arterial (A-a) oxygen gradient. The calculator uses the alveolar gas equation to find PAO2, then subtracts the measured PaO2. You also get the age-adjusted normal range and a plain-English interpretation distinguishing pulmonary from non-pulmonary causes of hypoxemia. Values update as you type.
Formula
Worked example
A 40-year-old on room air (FiO2 0.21, Patm 760 mmHg): PAO2 = 0.21 x (760 - 47) - (40 / 0.8) = 0.21 x 713 - 50 = 149.7 - 50 = 99.7 mmHg. If PaO2 from ABG is 90 mmHg, then A-a gradient = 99.7 - 90 = 9.7 mmHg. Age-adjusted normal = 40/4 + 4 = 14 mmHg. The measured gradient of 9.7 mmHg is within the normal range for this patient.
What is the A-a gradient?
The alveolar-arterial (A-a) oxygen gradient quantifies the difference between the partial pressure of oxygen in the alveoli (PAO2, calculated from the alveolar gas equation) and the partial pressure of oxygen measured directly in arterial blood (PaO2, from an arterial blood gas). In a healthy lung, gas exchange is nearly perfect and the two values are close; when the lung is diseased or blood is bypassing ventilated alveoli, the gap widens. The A-a gradient is therefore one of the most useful single numbers for deciding whether hypoxemia is caused by a lung problem or by something outside the lung entirely, such as hypoventilation due to a sedative or a neuromuscular disease.
How to interpret your result
The normal A-a gradient increases with age because ageing stiffens small airways, leading to mild ventilation-perfusion mismatch even in healthy lungs. The commonly used formula for the age-adjusted normal is: (age in years / 4) + 4 mmHg. A gradient at or below this value in a hypoxemic patient points toward a non-pulmonary cause, most often hypoventilation (check if PaCO2 is raised). A gradient above the normal range means oxygen is not crossing the alveolar membrane normally, which suggests V/Q mismatch (most common: pneumonia, atelectasis), diffusion impairment (interstitial lung disease), or shunting of blood past ventilated alveoli (cardiac shunt, severe consolidation). Pulmonary embolism is important to consider because it is present in roughly 85 percent of PE cases but can occasionally be normal. An A-a gradient greater than 65 mmHg on room air, or greater than 150 mmHg on 100 percent oxygen, is associated with serious illness requiring urgent evaluation.
The alveolar gas equation explained
The formula that drives this calculator is the standard clinical version of the alveolar gas equation: PAO2 = FiO2 x (Patm - PH2O) - (PaCO2 / RQ). Each term has a clear physical meaning. FiO2 is the fraction of inspired oxygen, from 0.21 on room air to 1.0 on a 100 percent non-rebreather mask. Patm is the ambient barometric pressure, which equals 760 mmHg at sea level but falls at altitude, which is why patients with lung disease may decompensate when flying or travelling to high elevations. PH2O is the partial pressure of water vapour in the warm, fully humidified respiratory tract, effectively a constant of 47 mmHg at body temperature. The term PaCO2 / RQ corrects for the fact that CO2 produced by metabolism replaces some of the oxygen consumed; RQ (the respiratory quotient) is typically 0.8 on a mixed diet.
Clinical uses and limitations
Clinicians use the A-a gradient alongside the PaO2/FiO2 (P/F) ratio and oxygen saturation to stratify severity in conditions such as ARDS, pneumonia, and suspected pulmonary embolism. It is most informative on room air; at very high FiO2 values the gradient widens even in healthy lungs due to absorption atelectasis, so the cut-offs shift. The age-adjusted formula is an approximation and the gradient varies with body position, metabolic state, and cardiac output. The gradient does not replace imaging, cultures, D-dimer, or CT pulmonary angiography for definitive diagnosis; it is a triage and reasoning tool to prioritize the differential diagnosis.
A-a gradient interpretation by severity
| Gradient vs. normal | Severity | Likely cause category |
|---|---|---|
| At or below age-normal | Normal | Hypoventilation or low FiO2 (non-pulmonary) |
| 1-10 mmHg above normal | Mildly elevated | Early V/Q mismatch, mild pneumonia |
| 11-25 mmHg above normal | Moderately elevated | Pneumonia, pulmonary embolism, ARDS |
| Greater than 25 mmHg above normal | Severely elevated | Severe shunt, massive PE, severe ARDS |
| On 100% O2, gradient > 100 | Significant shunt | Intracardiac shunt or large consolidation |
Guidance for interpreting the A-a gradient relative to the age-adjusted normal. Consult clinical context for diagnosis.
Frequently asked questions
What is a normal A-a gradient?
On room air at sea level, the normal A-a gradient for a young adult is approximately 5-15 mmHg. The upper limit of normal increases with age: the widely used formula is (age in years / 4) + 4 mmHg, so a 20-year-old has a normal up to about 9 mmHg, while a 60-year-old can have a normal up to about 19 mmHg. This calculator computes the age-adjusted normal automatically.
What causes an elevated A-a gradient?
An elevated gradient means that oxygen is not moving efficiently from the alveoli into arterial blood. The main causes are: ventilation-perfusion (V/Q) mismatch (pneumonia, atelectasis, chronic lung disease), intrapulmonary or intracardiac shunting (blood reaching the arterial side without passing ventilated alveoli), and diffusion impairment (interstitial lung disease, pulmonary edema). Pulmonary embolism is a classic cause because clots block perfusion to ventilated lung regions.
What does a normal A-a gradient with hypoxemia mean?
If a patient is hypoxemic but the A-a gradient is normal, the problem is not in the lungs. The most common cause is hypoventilation: the patient is not breathing deeply or frequently enough to clear CO2 and oxygenate the blood, often due to opiates, sedatives, CNS lesions, or neuromuscular disease. A raised PaCO2 alongside a normal gradient supports this conclusion. Breathing a hypoxic gas mixture (for example, at altitude) also produces hypoxemia with a normal gradient.
How does FiO2 affect the A-a gradient?
The FiO2 (fraction of inspired oxygen) directly sets the alveolar oxygen pressure PAO2. On room air (FiO2 0.21), PAO2 at sea level is roughly 99-100 mmHg. On 100 percent oxygen, PAO2 rises above 650 mmHg, and a healthy person should achieve an arterial PaO2 above 500 mmHg, giving a gradient below 150 mmHg. A gradient greater than 300-400 mmHg on 100 percent oxygen suggests a significant shunt fraction. The cut-offs for what is elevated are therefore different at high FiO2, so always interpret the result in context.
What is the respiratory quotient (RQ) and what value should I use?
The respiratory quotient is the ratio of carbon dioxide produced to oxygen consumed by metabolism. On a typical mixed diet it is approximately 0.8. It rises toward 1.0 on a high-carbohydrate diet (for example, in patients receiving glucose-heavy total parenteral nutrition) and can fall below 0.7 with starvation or a high-fat diet. For most clinical purposes, the default of 0.8 is appropriate. Changing RQ has a modest effect on the calculated PAO2: using 1.0 instead of 0.8 lowers PAO2 by a few mmHg at normal PaCO2.
Does altitude change the A-a gradient?
Yes. At altitude, barometric pressure (Patm) is lower, which reduces the driving pressure for oxygen and lowers PAO2 even at the same FiO2. This causes hypoxemia with a normal or minimally elevated A-a gradient in acclimatized healthy individuals. At very high altitude or during acute mountain sickness, the gradient may rise slightly due to pulmonary edema or mild V/Q mismatch. Always enter the local atmospheric pressure if the patient is not at sea level.
Is the A-a gradient useful for pulmonary embolism?
Yes, but it is not specific. About 85 percent of patients with confirmed PE have an elevated A-a gradient because the clot blocks perfusion to ventilated lung, creating a region of high V/Q or dead space. However, approximately 15 percent of PE patients have a normal gradient, so a normal A-a gradient does not rule out PE. The Wells score, D-dimer, and CT pulmonary angiography remain the definitive tests. An elevated gradient simply adds weight to clinical suspicion.