# A-a Gradient Calculator

URL: https://speedycalculator.com/calculators/health/aa-gradient/
Last updated: 2026-10-25

> The A-a gradient calculator estimates the difference between oxygen in the alveoli and in arterial blood, using the alveolar gas equation. It helps find the cause of low blood oxygen.

## Inputs

- FiO₂ (%)
- PaCO₂ (mmHg)
- PaO₂ (mmHg)
- Atmospheric pressure (mmHg)
- Age (years)

## Results

- Alveolar oxygen (PAO₂)
- A-a gradient
- Expected for age

## Formula

```
PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ ÷ 0.8
A-a gradient = PAO₂ − PaO₂
Expected ≈ age ÷ 4 + 4
```

## Explanation

A normal gradient with low oxygen suggests hypoventilation or altitude; a raised gradient points to lung problems such as V/Q mismatch.

### How to use the A-a Gradient Calculator

- **FiO₂**
- **PaCO₂**
- **PaO₂**
- **Atmospheric pressure**
- **Age**

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Alveolar oxygen is calculated from inspired oxygen, pressure and carbon dioxide, then arterial oxygen is subtracted.

### Inputs explained

FieldWhat to enterFiO₂In %PaCO₂In mmHgPaO₂In mmHgAtmospheric pressureIn mmHgAgeIn years

### What each result means

- **Alveolar oxygen (PAO₂)** = [FiO₂]÷100 × ([Atmospheric pressure] - 47) - [PaCO₂]÷0.8
- **A-a gradient** = [Alveolar oxygen (PAO₂)] - [PaO₂]
- **Expected for age** = [Age]÷4 + 4

### Example values

How the main result changes when **FiO₂** changes and everything else stays at the example values above:

FiO₂ (%)A-a gradient (mmHg)219.726.2547.231.584.642159.5
*Health note: this calculator is for education and screening only and is not a diagnosis or treatment advice. Discuss your results with a qualified clinician.*

## Worked example

Inputs — FiO₂: 21 %; PaCO₂: 40 mmHg; PaO₂: 90 mmHg; Atmospheric pressure: 760 mmHg; Age: 40 years.

Results — Alveolar oxygen (PAO₂) = 99.7 mmHg; **A-a gradient = 9.7 mmHg**; Expected for age = 14 mmHg.

## FAQ

**Why 47 mmHg?**
It is the water vapour pressure at body temperature.

**Does the formula change with oxygen therapy?**
The gradient rises with higher FiO₂, so interpret with care.

**What formula does the A-a Gradient Calculator use?**
PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ ÷ 0.8.