A-a Gradient Calculator

A-a Gradient Calculator for Pulmonology. The number is the estimated alveolar-minus-arterial oxygen difference, not a universal normality classification. A negative gradient prompts review of sampling, FiO2, pressure and respiratory-quotient assumptions; age and oxygen setting affect clinical interpretation.

For shared guidance on choosing a tool and documenting results, read the clinical calculator workflow.

How this calculator works

Approximate alveolar PO2 = FiO2 fraction x (barometric pressure - 47) - PaCO2/respiratory quotient. Subtract arterial PaO2 for the A-a difference. The entered oxygen percentage is divided by 100 exactly once.

When to use this calculator

Use as a physiological calculation with a reliable arterial sample, known oxygen concentration, and an appropriate barometric pressure. The assumed respiratory quotient and simplified equation need context.

Inputs used

  • Arterial PaO2 (mmHg)
  • Arterial PaCO2 (mmHg)
  • Inspired oxygen (%)
  • Local barometric pressure (mmHg)
  • Assumed respiratory quotient

Clinical interpretation

The number is the estimated alveolar-minus-arterial oxygen difference, not a universal normality classification. A negative gradient prompts review of sampling, FiO2, pressure and respiratory-quotient assumptions; age and oxygen setting affect clinical interpretation.

Worked example

Fictional teaching case. Arterial PaO2 (mmHg): 62; Arterial PaCO2 (mmHg): 55; Inspired oxygen (%): 21; Local barometric pressure (mmHg): 760; Assumed respiratory quotient: 0.8. Result: 18.98 mmHg. Calculated alveolar-arterial oxygen difference. Estimated alveolar PO2 = 80.98 mmHg. No universal normal/abnormal cutoff is assigned.

Limitations and safety notes

The 47 mmHg water-vapor assumption corresponds to 37 C. This simplified equation is less accurate at high inspired oxygen; age, altitude, actual FiO2 and metabolic state affect interpretation. A negative number is not reassuring evidence.

Frequently asked questions

Does a normal-looking gradient exclude lung disease?

No. The calculation describes one aspect of gas exchange and cannot by itself establish or exclude the cause of respiratory illness.

What can change the meaning of this result?

The 47 mmHg water-vapor assumption corresponds to 37 C. This simplified equation is less accurate at high inspired oxygen; age, altitude, actual FiO2 and metabolic state affect interpretation. A negative number is not reassuring evidence.

References

  • Fenn, Rahn and Otis original alveolar gas paper identity; abstract unavailable. https://pubmed.ncbi.nlm.nih.gov/20996488/
  • Primary mathematical model explicitly gives the simplified alveolar gas equation and pressure terms. https://journals.physiology.org/doi/full/10.1152/ajpheart.00074.2020

Editorial review and citation methodology

Maintained by the Quick Medical Calculator Editorial Team. Content record date: September 9, 2026. A content date is not evidence of independent clinical review. Individual clinical sign-off is not recorded on this page.

  • Prefer original validation studies for scoring systems and prediction tools.
  • Use current specialty society guidance, transplant allocation policy, public health guidance, or regulator resources when they govern clinical use.
  • Include limitations and safety notes when a calculator is population-specific, context-dependent, or unsuitable as a standalone decision tool.

Related reviewed calculators