Work out the alveolar–arterial (A–a) oxygen gradient from an arterial blood gas with the alveolar gas equation, and compare it with the expected value for age. In mmHg or kPa, for healthcare professionals.
Expected upper normal for age 40: age ÷ 4 + 4 = 14 mmHg; Mellemgaard's 2.5 + 0.21 × age = 10.9 mmHg. Both were derived for people breathing room air; the gradient rises with FiO₂.
For healthcare professionals. A calculation from the alveolar gas equation, not an interpretation: verify against current guidelines and the clinical picture.
How to use it
Choose mmHg or kPa, then enter the inspired oxygen (FiO₂) and the arterial PaO₂ and PaCO₂ from the blood gas.
Add the age to see the expected gradient. At altitude, change the atmospheric pressure under Altitude and constants.
Read the A–a gradient, the alveolar oxygen pressure, the P/F ratio and the a/A ratio, with the working below.
Formula
PAO₂ = FiO₂ × (Patm − PH₂O) − PaCO₂ ÷ R and A–a gradient = PAO₂ − PaO₂, with Patm = 760 mmHg at sea level, PH₂O = 47 mmHg at 37 °C and R = 0.8. Expected upper normal on room air: age ÷ 4 + 4 or 2.5 + 0.21 × age (mmHg).
Worked example
On room air (FiO₂ 21%) with PaO₂ 90 mmHg and PaCO₂ 40 mmHg: PAO₂ = 0.21 × (760 − 47) − 40 ÷ 0.8 = 149.73 − 50 = 99.7 mmHg, so the A–a gradient is 99.7 − 90 = 9.7 mmHg. For a 40-year-old the expected upper value is 40 ÷ 4 + 4 = 14 mmHg (or 10.9 mmHg by Mellemgaard), the P/F ratio is 90 ÷ 0.21 = 429 and the a/A ratio 0.90.
References
Hantzidiamantis PJ, Amaro E. Physiology, Alveolar to Arterial Oxygen Gradient. StatPearls (PMID 31424737).
McFarlane MJ, Imperiale TF. Use of the alveolar-arterial oxygen gradient in the diagnosis of pulmonary embolism. Am J Med 1994;96:57–62 (PMID 8304364): normal gradient defined as no more than age ÷ 4 + 4.
Mellemgaard K. The alveolar-arterial oxygen difference: its size and components in normal man. Acta Physiol Scand 1966;67:10–20 (PMID 5963295).
Formulas checked on 7 October 2026. For professionals: interpret with the clinical picture and current guidelines; this is not medical advice.
Frequently asked questions
What is a normal A–a gradient?
It rises with age. Two published estimates of the upper normal limit for adults breathing room air are age ÷ 4 + 4 mmHg (used by McFarlane and Imperiale, 1994) and 2.5 + 0.21 × age mmHg (Mellemgaard, 1966). At 40 they give 14 and 10.9 mmHg. The calculator shows both when you enter an age.
Why does FiO₂ change the result?
The gradient grows as the inspired oxygen goes up, even in healthy lungs, so the age-based normal values only apply on room air (21%). On supplemental oxygen, many clinicians look at the P/F ratio (PaO₂ ÷ FiO₂) as well, which the calculator also shows.
What are the respiratory quotient and water vapour pressure?
The respiratory quotient (R) is the ratio of CO₂ produced to O₂ used; 0.8 is the usual assumption on a mixed diet. Air in the lungs is saturated with water vapour, which at body temperature (37 °C) exerts 47 mmHg (6.27 kPa), so it's taken off the atmospheric pressure.
How do I allow for altitude?
Open Altitude and constants and enter the local barometric pressure instead of 760 mmHg (101.3 kPa). Lower atmospheric pressure lowers the alveolar oxygen pressure, so PaO₂ is lower even with a normal gradient.
Can I use kPa?
Yes. Switch to kPa and the values you've typed are converted (1 kPa = 7.50062 mmHg). The age-based normal values were published in mmHg and are converted too; the P/F ratio stays in mmHg, as it's usually reported.
