The Alveolar-arterial gradient (A-a gradient), is used to compare the causes of hypoxemia.

A-a gradient Equation

A - a gradient = PA_O2 - Pa_O2

Where:
PA_O2 = alveolar PO₂ (calculated from the alveolar gas equation)
Pa_O2 = arterial PO₂ (measured in arterial blood A-a gradient

The Alveolar Gas equation:

PA_O2 = PI_O2 - Pa_CO2/R

Where:
PI_O2 = FI_O2 x (760 mmHg - 47mmHg) = inspired O₂
       - FI_O2 = 21% at sea level atmospheric pressure = 0.21
       - 760 mmHg = atmospheric pressure at sea level
       - 47 mmHg = H₂O pressure
Pa_CO2 = arterial PCO₂ measured in plasma
R = respiratory exchange ratio or respiratory quotient = 0.8 under normal conditions

Values and Meaning:

The normal A-a gradient is < 10 mmHg, but can range from 5-20 mmHg in a normal individual. The determination of a normal A-a gradient also increases with age: For every decade a person has lived, the cutoff for a normal A-a gradient increases by 1mmHg. Therefore, while an A-a gradient in a 20 year old is likely pathological, the same A-a gradient in an 80 year old patient isn't necessarily pathological. An increased A-a gradient suggests a diffusion defect, V/Q (ventilation/perfusion) defect, or right-to-left shunt.¹

¹Costanzo, Linda (2006). Brs Physiology. Hagerstwon: Lippincott Williams & Wilkins. ISBN 0781773113.