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. This gradient is the cornerstone for differentiating causes of hypoxemia — distinguishing hypoventilation (normal gradient) from V/Q mismatch, shunt, and diffusion impairment (elevated gradient).
The alveolar gas equation calculates the expected alveolar partial pressure of oxygen (PAO₂) based on 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. A normal gradient increases with age (approximately 2.5 + 0.21 × age mmHg) and when breathing supplemental oxygen.
This calculator also computes the P/F ratio (PaO₂/FiO₂), a quick bedside assessment of oxygenation impairment used in ARDS criteria and ICU triage. It adjusts for altitude by calculating barometric pressure from elevation and estimates intrapulmonary shunt fraction. Use presets to explore common scenarios including normal room air, COPD, PE, and ARDS presentations.
The A-a gradient is one of the most important tools in pulmonary medicine for localizing the cause of hypoxemia. This calculator saves time, reduces arithmetic errors, and provides age-adjusted interpretation with a built-in differential diagnosis framework. Keep these notes focused on your operational context. Tie the context to the calculator’s intended domain. Use this clarification to avoid ambiguous interpretation.
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 = 109.3 mmHg, A-a Gradient = 39.3 mmHg (elevated), P/F ratio = 333
Expected gradient for age 50 is ~13 mmHg. A gradient of 39 is significantly elevated, suggesting V/Q mismatch, shunt, or diffusion impairment. P/F ratio >300 indicates mild 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.
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.