A-a Gradient Calculator (Alveolar-Arterial Oxygen Gradient)
Compute the A-a oxygen gradient from an arterial blood gas result to distinguish hypoventilation from V/Q mismatch, diffusion impairment, or shunt as causes of low blood oxygen.
years
%
mmHg
mmHg
mmHg
Normal for this age — hypoxia may be due to hypoventilation alone
- 1
Corrected inspired O₂ pressure
21% × (760 − 47) = 149.7 mmHg47 mmHg = water vapour pressure at body temperature (37 °C). - 2
Alveolar PO₂ (PAO₂)
149.7 − 40 ÷ 0.8 = 99.7 mmHg - 3
A-a Gradient
99.7 − 90 = 9.7Normal upper limit ≈ age/4 + 4 mmHg on room air.
How does this calculator work?
The A-a gradient = PAO₂ − PaO₂, where PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ ÷ 0.8. Enter patient age, FiO₂, PaCO₂, and PaO₂. A gradient above age/4 + 4 mmHg (on room air) indicates a gas-exchange defect such as V/Q mismatch, shunt, or diffusion impairment rather than simple hypoventilation.
Formula
How this is calculated
The A-a gradient compares how much oxygen reaches the alveoli (PAO₂) with how much actually enters the bloodstream (PaO₂). The alveolar oxygen tension is estimated with the alveolar gas equation: PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ / 0.8. The 47 mmHg term accounts for water vapour pressure at body temperature (37 °C), and 0.8 is the standard respiratory quotient (RQ) — the ratio of CO₂ excreted to O₂ consumed on a mixed diet.
The difference between calculated PAO₂ and the measured arterial PaO₂ (from a blood gas) is the A-a gradient. In healthy lungs the gradient is small; a widely used age-adjusted upper limit of normal on room air is age / 4 + 4 mmHg, rising from about 4 mmHg in young adults to roughly 25 mmHg at age 80. An elevated gradient suggests impaired gas exchange — most commonly V/Q mismatch (COPD, pulmonary embolism), intra-pulmonary shunt (atelectasis, pneumonia), or diffusion impairment (pulmonary fibrosis). A normal gradient with low PaO₂ points to pure hypoventilation (e.g. sedative overdose, neuromuscular weakness).
This tool is a clinical decision-support aid only. The RQ and normal-range formula are standard estimates that may not apply to extremes of diet, altitude, or body temperature. Results must always be interpreted by a qualified clinician in the full clinical context.
Frequently asked questions
A gradient above the age-adjusted normal (≈ age/4 + 4 mmHg on room air) suggests a gas-exchange problem: V/Q mismatch (the most common, seen in COPD, PE, asthma), shunt (blood bypasses ventilated alveoli, e.g. atelectasis, pneumonia), or diffusion impairment (pulmonary fibrosis). A normal gradient with low PaO₂ indicates pure hypoventilation.
Use 21 for room air. For patients on supplemental oxygen, enter the actual delivered FiO₂ in percent. The age/4 + 4 normal-range formula applies specifically to room air; on supplemental oxygen the expected absolute gradient is larger and clinical thresholds differ.
The RQ is the ratio of CO₂ produced to O₂ consumed, averaging about 0.8 on a mixed Western diet (0.7 for pure fat oxidation, 1.0 for pure carbohydrates). The value 0.8 is the standard clinical approximation used in the alveolar gas equation.
Also known as
TG we-Calculate Editorial Team. (2026). A-a Gradient Calculator (Alveolar-Arterial Oxygen Gradient) [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/aa-gradient-calculator
TG we-Calculate Editorial Team. "A-a Gradient Calculator (Alveolar-Arterial Oxygen Gradient)." TG we-Calculate. 2026. https://we-calculate.com/calculator/aa-gradient-calculator.
TG we-Calculate Editorial Team, "A-a Gradient Calculator (Alveolar-Arterial Oxygen Gradient)," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/aa-gradient-calculator
@misc{wecalculate_aa_gradient_calculator, title = {A-a Gradient Calculator (Alveolar-Arterial Oxygen Gradient)}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/aa-gradient-calculator}}, year = {2026}, note = {TG we-Calculate} }
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