A-a Gradient Calculator
Alveolar to arterial oxygen gradient from a blood gas, in mmHg or kPa, with the expected value for age.
What it does
Alveolar air holds more oxygen than arterial blood because of shunting, uneven ventilation, and diffusion limits. The alveolar to arterial oxygen gradient measures that gap: how much oxygen leaves the alveoli versus how much reaches arterial blood.
You need three numbers from a blood gas plus the oxygen setting: FiO2, PaCO2, and PaO2, along with the patient's age. The tool computes alveolar oxygen with the standard alveolar gas equation and subtracts the measured PaO2. Results read in the same unit you entered, mmHg or kPa.
A normal gradient rises with age, roughly (age + 10) / 4 mmHg on the common version, so 9.7 at age 40 sits comfortably in range while the same gap at age 80 would be unusual. The direction matters more than a single cutoff: a gradient above the age-expected band suggests the lung is losing oxygen between the alveoli and the blood.
Clinicians use the gradient to separate hypoxemia from hypoventilation, where the gradient stays normal, from shunt, dead space, and diffusion problems, where it widens. It also feeds the shunt fraction estimate. Treat it as one input to the clinical picture, not a diagnosis on its own.
How to use
- Pick the pressure unit that matches your blood gas report.
- Enter FiO2 as a percent, room air being 21.
- Enter the PaO2 and PaCO2 values from the same arterial sample.
- Enter the patient's age for the expected gradient.
- Compare the gradient with the expected band and read the note for the full step chain.
Formula
- FiO2
- Fraction of inspired oxygen as a percent, 21 on room air.
- Patm
- Atmospheric pressure in mmHg, 760 at sea level.
- PaCO2
- Arterial carbon dioxide pressure from the blood gas.
- PAO2
- Calculated alveolar oxygen pressure.
- PaO2
- Measured arterial oxygen pressure from the same sample.
The 47 in the equation is water vapor pressure in fully humidified alveoli. A respiratory quotient of 0.8 fits a mixed diet; a pure carbohydrate diet pushes RQ toward 1 and shifts the last term slightly. At altitude, Patm falls and PAO2 falls with it, and this tool does not adjust for that. Some references give the expected value as age / 4 + 4 instead of (age + 10) / 4; the two differ by under 2 mmHg on most ages and the note shows both.
Worked example
Example: age 40 on room air
FiO2 21%, PaO2 90 mmHg, PaCO2 40 mmHg, age 40.
- Oxygen fraction: 21% x 713 mmHg = 149.73 mmHg.
- Carbon dioxide term: 40 / 0.8 = 50.00 mmHg.
- Alveolar oxygen: 149.73 - 50.00 = 99.73, shown as 99.7 mmHg.
- Gradient: 99.73 - 90 = 9.73, shown as 9.7 mmHg.
- Expected for age: (40 + 10) / 4 = 12.5 mmHg.
- 9.7 sits under 12.5, so the tool reads the result as within the expected range.
Reference table
| Age | (age + 10) / 4 | age / 4 + 4 |
|---|---|---|
| 20 | 7.5 mmHg | 9 mmHg |
| 40 | 12.5 mmHg | 14 mmHg |
| 60 | 17.5 mmHg | 19 mmHg |
| 80 | 22.5 mmHg | 24 mmHg |
Limits
- Fixed at sea level pressure of 760 mmHg; altitude lowers PAO2 and needs its own baseline.
- Assumes RQ 0.8 and water vapor 47 mmHg; ventilation settings and diet shift the result slightly.
- A venous or delayed sample misleads the gradient completely.
- It flags a problem but does not name the cause; imaging and the exam do that.
Common mistakes
- Feeding a venous or capillary sample into the PaO2 field.
- Comparing against a fixed 15 mmHg cutoff instead of the age-based expectation.
- Switching to kPa and retyping mmHg values, or the reverse.
- Using the ventilator's FiO2 setting when the sample was drawn on a different one.
- Reading a single high value as a shunt diagnosis without the full picture.
Try it yourself
Quick checks. Answers sit tucked under each question.
FiO2 21%, PaO2 70 mmHg, PaCO2 45 mmHg, age 70. What is the gradient?
PAO2 93.5 mmHg and a gradient of 23.5 mmHg against 20 mmHg expected for age 70.
On 40% oxygen in kPa mode: PaO2 9.3 kPa, PaCO2 6.0 kPa, age 60?
PAO2 30.5 kPa and a gradient of 21.2 kPa, above the 2.3 kPa expected for age 60.
PaO2 60, PaCO2 60, FiO2 21, age 40: what happens to the gradient?
PAO2 falls to 74.7 mmHg and the gradient reads 14.7 mmHg, above the 12.5 mmHg expected at age 40.
Questions
What is a normal A-a gradient?
Roughly (age + 10) / 4, so about 12.5 mmHg at 40 and 22.5 at 80. Values at or under that mark are expected for age.
Why does the gradient rise with age?
Ventilation and blood flow grow less even and lungs lose some elastic recoil, so more oxygen is lost between the alveoli and the blood.
What does a widened gradient mean?
Common causes are shunt, V/Q mismatch, and diffusion problems. Plain hypoventilation usually keeps the gradient normal.
Can I work in kPa?
Yes, switch the unit selector before entering values. The tool converts internally and shows every output in kPa.
Does the tool adjust for altitude?
No. It assumes standard sea level pressure of 760 mmHg. At altitude, PAO2 falls and the gradient should be read against that lower baseline.
Which age formula should I use?
(age + 10) / 4 is the most common. Some sources use age / 4 + 4; the note shows both so you can compare.