Formula:

A-a Oxygen Gradient = [(pAtm-pH2O)xFiO2]-pCO2/RespQ

pAtm = Atmospheric pressure [mmHg] (760mmHg at sea level)

pH2O = Partial Pressure of Water [mmHg] (47mmHg at 37 deg C)

FiO2 = % of Oxygen inspired (21% with room air)

RespQ = Respiratory Quotient (approx 0.8, depends on food intake)

pCO2 = Arterial CO2 measured [mmHg]

References:

Mellemgaard, K. The alveolar-arterial oxygen difference. Size and components in normal man. Acta Physiol Scand 1966; 67:10.

Kanber, GL et al. The alveolar-arterial oxygen gradient in young and elderly men during air and oxygen breathing. Am Rev Respir Dis 1968; 97:376.