A-a Gradient Calculator
Calculate the alveolar-arterial (A-a) oxygen gradient to evaluate oxygenation and differentiate causes of hypoxemia.
About this calculator
The A-a gradient compares the oxygen level the lungs SHOULD be delivering to blood (calculated alveolar PO2, from the alveolar gas equation PAO2 = FiO2 x (Patm - 47) - PaCO2 / 0.8) against the oxygen level actually measured in an arterial blood gas (PaO2). Subtracting the two isolates whether hypoxemia is coming from a problem getting air into the lungs (hypoventilation, which lowers both numbers together and keeps the gradient normal) or from a problem getting oxygen from the alveoli into the bloodstream (a widened gradient, seen with pneumonia, pulmonary edema, pulmonary embolism, or any process that impairs gas exchange itself). A normal gradient rises gradually with age -- a common rule of thumb estimates it as roughly age/4 + 4 mmHg on room air -- so what counts as "elevated" isn't a single fixed number across every patient.
The 47 mmHg constant is the vapor pressure of water at body temperature, and the 0.8 divisor is the respiratory quotient, both physiologic constants rather than adjustable inputs. This calculator reports the calculated alveolar PO2, the gradient itself, the age-adjusted expected value, and whether the measured gradient exceeds that expectation.
Medical Disclaimer
This calculator is for informational and educational purposes only. It is not a substitute for professional medical advice, diagnosis, or treatment. Always consult a qualified healthcare provider before making decisions about your health. Never disregard professional medical advice or delay seeking it because of results from this tool.
Inputs
Normal PaO₂: 80–100 mmHg (room air); mild hypoxemia 60–79; moderate 40–59; severe <40 mmHg
Normal PaCO₂: 35–45 mmHg; <35 resp. alkalosis; >45 resp. acidosis; used in alveolar gas equation
Results
A-a Gradient
4.7mmHg
Elevated
0(0=No, 1=Yes)
How to Use This Calculator
- Enter FiO₂, PaO₂, PaCO₂, atmospheric pressure, and patient age.
- Review the A-a gradient — normal is < age/4 + 4 mmHg on room air.
- An elevated A-a gradient suggests a parenchymal, vascular, or diffusion lung abnormality.
How the result changes with Atmospheric Pressure
| Atmospheric Pressure | A-a Gradient | Elevated |
|---|---|---|
| 400 | -70.9mmHg | 0(0=No, 1=Yes) |
| 570 | -35.2mmHg | 0(0=No, 1=Yes) |
| 800 | 13.1mmHg | 0(0=No, 1=Yes) |
What each input means
- FiO₂
- Fraction of inspired oxygen as a percentage. Room air = 21%.
- PaO₂
- Arterial partial pressure of oxygen from arterial blood gas (ABG). Normal range: 80–100 mmHg on room air (age-adjusted: ≈104 − 0.27×age mmHg). Mild hypoxemia: 60–79 mmHg; moderate: 40–59; severe: <40 mmHg.
- PaCO₂
- Arterial partial pressure of carbon dioxide from ABG. Normal range: 35–45 mmHg. Respiratory alkalosis: <35 mmHg (hyperventilation); respiratory acidosis: >45 mmHg (hypoventilation). Used in alveolar gas equation: PAO₂ = FiO₂×(Patm−47) − PaCO₂/0.8.
- Atmospheric Pressure
- Barometric pressure. Sea level = 760 mmHg. Adjust for altitude.
- Patient Age
- Patient age for calculating expected A-a gradient.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersFiO₂ = 21, PaO₂ = 95, PaCO₂ = 40, Atmospheric Pressure = 760 = 5 input(s) provided
- Calculate A-a GradientA-a Gradient4.7 = 4.7
- Calculate ElevatedElevated0 = 0
- Calculate Expected GradientExpected Gradient14 = 14
- Calculate Alveolar PO₂Alveolar PO₂99.7 = 99.7
Engine last updated . Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
What does a normal A-a gradient but low PaO2 suggest?
When PaO2 is low but the A-a gradient stays within the expected range for the patient's age, the problem is typically hypoventilation or a low inspired oxygen fraction (such as high altitude) rather than a lung parenchymal or vascular disease -- because both the calculated alveolar oxygen and the measured arterial oxygen fall together, keeping their difference normal even though both numbers are low.
Why does the expected A-a gradient increase with age?
Small ventilation-perfusion mismatches accumulate in the lungs over a normal lifetime even without overt disease, so an A-a gradient that would be considered abnormal in a healthy 20-year-old can be an entirely normal finding in an 80-year-old. The age/4 + 4 mmHg rule of thumb this calculator uses is one commonly cited approximation for that expected upward drift, not a hard biological limit.
Does atmospheric pressure change the A-a gradient the same way FiO2 does?
Both enter the alveolar gas equation as multipliers on the same term -- PAO2 scales with FiO2 x (Patm - 47) -- so at typical room-air FiO2 a given percentage change in atmospheric pressure moves the calculated alveolar oxygen, and therefore the gradient, by a comparable amount to an equivalent percentage change in FiO2 near sea-level defaults. The two variables aren't interchangeable in general, though: across their full clinically realistic ranges, FiO2 (which can range from 21% room air to 100% on a ventilator) and PaO2 itself move the gradient more than atmospheric pressure typically does, since altitude rarely varies as widely as inspired oxygen or measured arterial oxygen do in practice.
Why is 47 mmHg subtracted from atmospheric pressure in the formula?
That's the partial pressure of water vapor in fully humidified air at normal body temperature (37°C), and inspired air is saturated with water vapor by the time it reaches the alveoli. Subtracting it before multiplying by FiO2 accounts for the fact that not all of the total atmospheric pressure is available to carry oxygen -- some of it is occupied by water vapor regardless of how much oxygen is being delivered.
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