Calculate the alveolar-arterial oxygen gradient from ABG values. Includes P/F ratio, expected gradient by age, altitude adjustment, and differential diagnosis table.
The A-a Gradient Calculator computes the alveolar-arterial oxygen difference from arterial blood gas (ABG) values using the alveolar gas equation. It is a standard way to sort out hypoxemia by separating low ventilation from gas-exchange problems such as V/Q mismatch, shunt, and diffusion impairment.
The alveolar gas equation estimates alveolar oxygen pressure (PAO₂) from inspired oxygen fraction (FiO₂), barometric pressure, water vapor pressure, arterial CO₂, and the respiratory quotient. Subtracting the measured arterial PaO₂ gives the A-a gradient, which normally rises with age and with supplemental oxygen.
The calculator also reports the P/F ratio for a quick bedside oxygenation check, adjusts for altitude, and shows a simplified intrapulmonary shunt estimate. Presets cover common scenarios such as room air, COPD, pulmonary embolism, and ARDS.
The A-a gradient is most useful when the equation, age adjustment, and P/F ratio can be reviewed together instead of as separate mental steps. This page keeps those values in one place so it is easier to see whether hypoxemia looks more like low ventilation or a gas-exchange problem.
PAO₂ = FiO₂ × (PAtm − PH₂O) − (PaCO₂ / RQ) A-a Gradient = PAO₂ − PaO₂ Expected A-a Gradient = 2.5 + 0.21 × Age P/F Ratio = PaO₂ / FiO₂ PAtm at altitude = 760 × (1 − 2.26 × 10⁻⁵ × alt_ft)^5.256
Result: PAO₂ = 112.2 mmHg, A-a Gradient = 42.2 mmHg (elevated), P/F ratio = 333
At sea level with FiO₂ 21% and RQ 0.8, PAO₂ = 0.21 × (760 − 47) − (30 / 0.8) = 112.2 mmHg. Subtracting PaO₂ 70 gives an A-a gradient of 42.2 mmHg. Expected gradient for age 50 is about 13 mmHg, so this widened gradient fits a gas-exchange problem such as V/Q mismatch, shunt, or diffusion impairment.
The first step in evaluating hypoxemia is calculating the A-a gradient. If normal, consider hypoventilation (elevated PaCO₂) or low FiO₂ (high altitude). If elevated, the differential includes V/Q mismatch (most common, responds to supplemental O₂), intrapulmonary shunt (does not respond to O₂), and diffusion impairment (reflects impaired gas transfer across the alveolar-capillary membrane).
True shunt (blood bypassing ventilated alveoli) does not improve with supplemental oxygen because the shunted blood never contacts alveolar gas. V/Q mismatch (partially ventilated regions) does improve because increasing FiO₂ raises PAO₂ in poorly ventilated units. A "shunt study" with 100% FiO₂ can distinguish the two — persistent hypoxemia on 100% O₂ confirms shunt.
At 5,000 feet, barometric pressure drops to ~632 mmHg, reducing PAO₂ by about 17 mmHg compared to sea level. This alone can lower PaO₂ into the 70s while maintaining a normal A-a gradient. Always adjust for altitude when interpreting ABGs obtained in mountain communities or during air transport.
Last updated:
This page applies the alveolar gas equation to estimate alveolar oxygen pressure from the entered FiO₂, barometric pressure, water-vapor pressure, arterial carbon dioxide, and respiratory quotient, then subtracts the measured PaO₂ to report the A-a gradient. It also shows the P/F ratio, an age-expected gradient reference, and a simplified shunt estimate to help place the oxygenation problem in context.
The page is meant to support bedside interpretation of hypoxemia, not to replace full blood-gas review or ventilator assessment. The displayed shunt fraction is only a simplified estimate, and diagnosis still depends on the patient’s oxygen setting, ventilation status, and the broader respiratory picture.
Approximately 2.5 + 0.21 × age mmHg on room air. For a 20-year-old it is about 7 mmHg; for a 70-year-old, about 17 mmHg. Add ~5-10 mmHg as the upper limit of normal.
Aging reduces ventilation-perfusion matching due to loss of elastic recoil, airway closure at higher lung volumes, and decreased diffusing capacity. These changes mildly widen the gradient.
In pure hypoventilation (e.g., opiate overdose, neuromuscular weakness) and at high altitude. Both cause low PaO₂ but the gradient remains normal because gas exchange itself is intact.
The P/F ratio (PaO₂/FiO₂) is used in the Berlin ARDS definition: mild ≤300, moderate ≤200, severe ≤100. It provides a FiO₂-normalized assessment of oxygenation.
The alveolar gas equation requires FiO₂ to calculate PAO₂. On supplemental oxygen, the normal A-a gradient widens, so interpretation differs from room air values.
RQ is the ratio of CO₂ produced to O₂ consumed. It is 0.8 for a mixed diet, 1.0 for pure carbohydrates, and 0.7 for pure fat. It affects the alveolar gas equation denominator.