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A–a gradient calculator (alveolar gas equation)
Study aid only. Not for clinical decisions. This calculator teaches textbook formulas for exam prep. It is not a medical device and does not replace clinical judgment, your facility's protocols, or a licensed clinician's assessment. Nothing you enter leaves your browser.
Formulas
PAO2 = FiO2 × (PB − 47) − PaCO2 ÷ 0.8, where 47 mm Hg is water vapor pressure at body temperature and 0.8 is the usual respiratory quotient.[1]
A–a gradient = PAO2 − PaO2. On room air, a commonly used estimate of the normal upper value is (age + 10) ÷ 4.[2] Some textbooks use age ÷ 4 + 4, which gives a slightly higher cutoff. The gradient normally rises with age and with FiO2.
Why it matters
Hypoxemia with a normal A–a gradient points to hypoventilation or low inspired O2 (for example, altitude). A widened gradient points to V/Q mismatch, shunt, or a diffusion problem.[2]
Worked example
Room air at sea level, PaCO2 40, PaO2 90, age 30: PAO2 = 0.21 × 713 − 50 ≈ 100 mm Hg, so the gradient is ≈ 10. The expected value is (30 + 10) ÷ 4 = 10, so the gradient is normal.
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