What is the A-a gradient and why does it matter?

The A-a gradient is the difference between the oxygen pressure in the alveoli and in arterial blood. A normal gradient with low oxygen points to hypoventilation or low inspired oxygen, while a widened gradient signals a problem at the gas-exchange membrane such as V/Q mismatch, shunt, or a diffusion defect.

What is a normal A-a gradient?

On room air the expected gradient rises with age. A common bedside estimate is age divided by 4, plus 4, in mmHg. So a healthy 20-year-old sits near 9 mmHg while a 70-year-old may normally reach about 21 mmHg.

Which formula does this use?

It uses the alveolar gas equation: PAO2 = FiO2 times (atmospheric pressure minus 47) minus PaCO2 divided by 0.8. The 47 is water vapour pressure at body temperature and 0.8 is the respiratory quotient. The A-a gradient is then PAO2 minus the measured PaO2.

Does the age-expected range apply on supplemental oxygen?

Strictly, no. The age formula was derived on room air. On supplemental oxygen the gradient naturally widens, so the tool falls back to a rough 15 mmHg upper limit and you should interpret values in clinical context rather than against the age rule.

Is this a diagnostic tool?

No. It is an educational calculator that reproduces a standard equation. Clinical interpretation of any blood gas requires the full picture: the patient, the ventilator settings, and the trend over time. Always confirm management with a clinician.

What is the Alveolar-Arterial (A-a) Gradient Calculator?

Calculate the alveolar-arterial oxygen gradient from PaO2, PaCO2, FiO2, and atmospheric pressure using the alveolar gas equation. Detect V/Q mismatch, shunt, and diffusion defects, with an age-adjusted normal range. Runs in your browser. It runs free in your browser on Gera Tools, with nothing uploaded.

Alveolar-Arterial (A-a) Gradient Calculator

Name: Alveolar-Arterial (A-a) Gradient Calculator
Creator: Gera Tools
License: https://creativecommons.org/licenses/by/4.0/

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The alveolar-arterial oxygen gradient measures how efficiently the lungs move oxygen from inhaled air into the bloodstream. It is one of the most useful single numbers in arterial blood gas interpretation because it separates causes of low blood oxygen that lie inside the lung from those that do not.

How it works

The gradient is the difference between the calculated oxygen pressure in the alveoli and the measured oxygen pressure in arterial blood:

PAO2     = FiO2 x (Patm - PH2O) - (PaCO2 / R)
A-a gap  = PAO2 - PaO2

Here PH2O is the water vapour pressure at body temperature, fixed at 47 mmHg, and R is the respiratory quotient, conventionally 0.8. The atmospheric pressure defaults to 760 mmHg at sea level and should be lowered at altitude.

The expected normal gradient widens with age. A widely used estimate is:

expected = (age / 4) + 4

Worked example

A 50-year-old patient on room air (FiO2 = 0.21, Patm = 760 mmHg) has a PaO2 of 70 mmHg and PaCO2 of 40 mmHg. Working through the equation:

PAO2    = 0.21 × (760 − 47) − (40 / 0.8)
        = 0.21 × 713 − 50
        = 149.7 − 50
        ≈ 99.7 mmHg

A-a gap = 99.7 − 70 = 29.7 mmHg

Expected (age 50) = 50/4 + 4 = 16.5 mmHg

A measured gradient of 29.7 mmHg against an expected of 16.5 mmHg is widened, pointing toward a gas-exchange problem rather than pure hypoventilation.

What the gradient tells you — and what it does not

The A-a gradient is a triage tool. A low PaO2 with a normal gradient means the lungs are transferring oxygen efficiently; the hypoxaemia is upstream — hypoventilation or low inspired oxygen. A low PaO2 with a widened gradient means the problem is at the gas-exchange surface itself.

The three causes of a widened gradient are:

V/Q mismatch — the most common cause, seen in pulmonary embolism, asthma, COPD exacerbation, and pneumonia. Blood perfuses areas the lung is not fully ventilating.
Right-to-left shunt — blood bypasses ventilated alveoli entirely, as in intracardiac shunts or consolidated lung. The gradient does not narrow on 100% FiO2, which helps distinguish shunt from V/Q mismatch.
Diffusion impairment — thickened alveolar membranes, as in interstitial fibrosis or severe oedema, slow oxygen transfer. This is relatively rare compared to the two causes above.

Altitude and supplemental oxygen adjustments

At altitude, Patm falls, so lower it from the default 760 mmHg. A rough guide: Patm is approximately 760 × e^(−altitude in metres / 8500). At 3,000 m this gives roughly 530 mmHg — a meaningful reduction that narrows alveolar oxygen and raises the gradient even in a healthy lung.

On supplemental oxygen the age-based expected range no longer strictly applies. The gradient widens with increasing FiO2 in health, so interpret it in clinical context rather than against the room-air age formula.

Interpretation and notes

The age-expected range applies on room air only. This calculator is educational — always confirm management with a clinician who can assess the full clinical context.