Alveolar Gas Equation Calculator
PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ / RQ, solved in one step.
Result
How it is calculated
The engine solves PAO2 = FiO2 × (Patm − 47) − PaCO2 ÷ RQ. FiO2 is typed in percent and divided by 100; barometric pressure (Patm) and PaCO2 are in mmHg; 47 is the fixed water vapour pressure at body temperature. RQ, the respiratory quotient, has no default, so it must be filled in (0.8 is the usual mixed-diet value). The tool prints three numbers to one decimal: alveolar PO2, the inspired PO2 (FiO2 × (Patm − 47)) and the CO2 correction (PaCO2 ÷ RQ). Inputs that make no physical sense give no result: FiO2 below 21 or above 100, pressure of 47 or less (or above 4,000), a negative PaCO2, RQ of zero or less, and any combination where the CO2 term would push alveolar PO2 below zero. It does not compute the A-a gradient, because it takes no measured PaO2.
Worked example
A person breathes room air at sea level: FiO2 21%, barometric pressure 760 mmHg, PaCO2 40 mmHg, RQ 0.8. Inspired PO2 = 0.21 × (760 − 47) = 0.21 × 713 = 149.7 mmHg. CO2 term = 40 ÷ 0.8 = 50.0 mmHg. Alveolar PO2 = 149.7 − 50.0 = 99.7 mmHg. Subtract this from a measured arterial PaO2 yourself to get the A-a gradient. With the barometric pressure set to 500 mmHg (high altitude), the same inputs give 45.1 mmHg.
Common mistakes
- Typing FiO2 as 0.21 instead of 21. The field is in percent, and a value below 21 gives no result.
- Leaving RQ empty. Unlike some other fields it has no default, so no result appears; enter 0.8 unless you know the diet or metabolic state.
- Using kPa for pressures. Barometric pressure and PaCO2 must both be in mmHg: 101.3 kPa is about 760 mmHg, and typing 101.3 as the pressure gives no result because the CO2 term exceeds the inspired oxygen.
- Assuming the 47 mmHg water vapour pressure fits any temperature. The tool fixes it for body temperature only.
- Expecting the tool to give the A-a gradient. It returns only the alveolar PO2; you still subtract the measured PaO2 yourself.
About this calculator
The alveolar gas equation, PAO₂ = FiO₂ × (Patm − PH₂O) − PaCO₂/RQ, calculates the partial pressure of oxygen inside the alveoli — the tiny air sacs where gas exchange with the blood actually happens — from the fraction of inspired oxygen (FiO₂), barometric pressure, water vapor pressure (a constant 47 mmHg at body temperature), arterial CO₂ (PaCO₂) and the respiratory quotient (RQ, typically 0.8 on a mixed diet).
Clinicians use this equation as the first step toward the A-a gradient — the difference between calculated alveolar oxygen and the patient’s measured arterial oxygen (PaO₂). This calculator does not take PaO₂ and does not return the gradient; to get it, subtract your measured PaO₂ from the alveolar PO₂ shown here. A widened gradient points to a problem with gas exchange across the lung itself (like pneumonia, pulmonary embolism or ARDS), while a normal gradient in a hypoxic patient instead points to a problem outside the lungs, like hypoventilation or high altitude. It is a routine part of interpreting arterial blood gas (ABG) results in emergency medicine, pulmonology and critical care, and the equation also underlies altitude physiology calculations for climbers and aviators exposed to lower barometric pressure.
Enter FiO₂, barometric pressure, PaCO₂ and RQ, and this calculator solves the equation in one step to give you alveolar PO₂, along with the inspired PO₂ and the CO₂ correction term.
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