The Alveolar Gas Equation Calculator computes PAO2 and the A-a oxygen gradient from FiO2, PaCO2, atmospheric pressure, and respiratory quotient. A foundational clinical tool for diagnosing causes of hypoxemia, assessing pulmonary gas exchange, and interpreting arterial blood gas results.
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The calculator for the alveolar gas equation computes the partial pressure of oxygen in the alveoli (PAO₂) and the alveolar-arterial (A-a) oxygen gradient — the most important clinical tool for distinguishing the mechanism of hypoxemia at the bedside. The A-a gradient immediately separates hypoxemia caused by hypoventilation or low inspired oxygen (normal gradient) from intrinsic pulmonary pathology (elevated gradient).
Alveolar oxygen partial pressure is calculated from:
PAO₂ = FiO₂ × (P_atm − P_H₂O) − PaCO₂ / RQ
Where FiO₂ = fraction of inspired oxygen (0.21 on room air), P_atm = atmospheric pressure (760 mmHg at sea level), P_H₂O = water vapor pressure at 37°C = 47 mmHg, PaCO₂ = arterial CO₂ from ABG (normal 35–45 mmHg), and RQ = respiratory quotient (typically 0.8 for mixed diet). At sea level on room air: PAO₂ = 0.21 × (760−47) − 40/0.8 = 99.7 mmHg. The A-a gradient calculator uses this PAO₂ alongside measured PaO₂ to compute the gradient.
The A-a gradient = PAO₂ − PaO₂. Normal values increase with age and FiO₂:
Elevated A-a gradient indicates a pulmonary cause: V/Q mismatch (pneumonia, PE, atelectasis), diffusion impairment (fibrosis), or intrapulmonary shunt. Normal A-a gradient with hypoxemia points to hypoventilation (elevated PaCO₂) or low FiO₂ (altitude). Use this online calculator with measured arterial blood gas values for complete hypoxemia analysis.
At altitude, reduced atmospheric pressure lowers PAO₂ even with normal FiO₂. On the summit of Everest (P_atm ≈ 253 mmHg): PAO₂ = 0.21 × (253−47) − 40/0.8 = −6.7 mmHg — mathematically impossible, which is why summit attempts require extreme hyperventilation (reducing PaCO₂ to 7–10 mmHg) to maintain any alveolar oxygen. Supplemental oxygen raises FiO₂, directly increasing PAO₂ according to the alveolar gas equation.
The respiratory quotient (RQ = VCO₂/VO₂) varies with substrate metabolism: pure carbohydrate oxidation gives RQ = 1.0; fat oxidation gives RQ = 0.71; mixed diet approximately 0.8. In practice, changing RQ from 0.7 to 1.0 with normal PaCO₂ changes PAO₂ by only 7 mmHg — clinically minor. RQ becomes relevant in critically ill patients receiving high-glucose parenteral nutrition (RQ approaching 1.2 from lipogenesis), which may contribute to weaning failure in patients with marginal respiratory reserve. The oxygen consumption calculator and ventilation calculators provide complementary respiratory physiology tools.
The calculator uses the alveolar gas equation: PAO2 = FiO2 x (Patm - PH2O) - PaCO2/RQ. First, it calculates the inspired O2 pressure (PiO2) by multiplying FiO2 by the humidified atmospheric pressure (Patm minus PH2O). Then it subtracts the CO2 correction term (PaCO2 divided by the respiratory quotient) to yield the alveolar O2 pressure. The A-a gradient is computed as PAO2 minus PaO2 (the measured arterial value).
A normal A-a gradient is 5-15 mmHg in young adults breathing room air, increasing with age (expected = 2.5 + 0.21 x age). An elevated A-a gradient indicates intrinsic pulmonary gas exchange impairment (V/Q mismatch, shunt, or diffusion limitation). A normal gradient with hypoxemia suggests hypoventilation or low FiO2 as the cause. The PAO2 value represents ideal alveolar oxygen — any significant deviation of PaO2 below this value indicates impaired gas exchange.
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Normal findings: PAO2 of 99.7 mmHg with A-a gradient of 4.7 mmHg is within the expected range, indicating normal gas exchange.
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Markedly elevated A-a gradient of 169.5 mmHg indicates severe gas exchange impairment despite supplemental O2, consistent with significant V/Q mismatch from pneumonia.
The alveolar gas equation calculates the partial pressure of oxygen in the alveoli: PAO2 = FiO2 x (Patm - PH2O) - PaCO2/RQ. It accounts for inspired oxygen concentration, atmospheric pressure, humidification, CO2 dilution, and metabolic substrate (RQ). It provides the theoretical maximum PO2 achievable in the alveoli.
The A-a (alveolar-arterial) gradient is the difference between calculated alveolar O2 (PAO2) and measured arterial O2 (PaO2). It quantifies the efficiency of oxygen transfer across the alveolar-capillary membrane. Normal is 5-15 mmHg in young adults, increasing approximately 1 mmHg per decade of age.
An elevated A-a gradient indicates intrinsic lung or cardiac pathology affecting gas exchange. Common causes include V/Q mismatch (pneumonia, COPD, PE), intrapulmonary shunt (ARDS, atelectasis), diffusion impairment (interstitial lung disease), and intracardiac right-to-left shunt (ASD, VSD, PFO).
The respiratory quotient (RQ) is the ratio of CO2 produced to O2 consumed (VCO2/VO2). It varies with metabolic substrate: carbohydrate RQ = 1.0, protein = 0.8, fat = 0.7. A mixed diet gives RQ of approximately 0.8, which is the standard assumption used in clinical calculations unless indirect calorimetry is available.
At altitude, atmospheric pressure decreases while PH2O remains constant at 47 mmHg. This reduces the available PiO2. For example, at 5,000 feet (Patm about 632 mmHg), room air PiO2 drops to about 123 mmHg compared to 150 mmHg at sea level. This physiologically reduces PAO2 and PaO2, causing altitude hypoxemia.
At high FiO2, the A-a gradient becomes very large even with moderate gas exchange impairment, making interpretation difficult. The PaO2/FiO2 (P/F) ratio is preferred for assessing oxygenation on supplemental oxygen because it normalizes for the amount of oxygen delivered and is used in ARDS severity classification.
Normal PaO2 on room air at sea level is 80-100 mmHg in young adults. Expected PaO2 decreases with age: approximately PaO2 = 104 - (0.27 x age). Mild hypoxemia is 60-79 mmHg, moderate is 40-59 mmHg, and severe is below 40 mmHg. On supplemental oxygen, expected PaO2 should be roughly 5 times the FiO2 percentage.
A slightly negative A-a gradient can occur due to measurement variability or if the assumed RQ differs from the actual RQ. A significantly negative gradient suggests measurement error in PaCO2 or PaO2, or an incorrect FiO2 value. True physiological A-a gradient is always zero or positive.
Pure hypoventilation (e.g., opioid overdose, neuromuscular disease) causes hypoxemia with a normal A-a gradient because the lungs are intrinsically normal — there is simply insufficient fresh gas reaching the alveoli. The elevated PaCO2 directly reduces PAO2 through the alveolar gas equation, lowering PaO2 proportionally.
The P/F ratio is PaO2 divided by FiO2 (as a decimal). Normal is greater than 400. It is used in the Berlin ARDS criteria: mild ARDS = 200-300, moderate = 100-200, severe = less than 100 (with PEEP of at least 5 cmH2O). It is preferred over the A-a gradient for patients on supplemental oxygen.
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