Alveolar Gas Equation Calculator: Essential Tool for Respiratory Physiology:
Alveolar Gas Equation Explained:
The alveolar gas equation calculates the partial pressure of oxygen in alveoli (PAO₂), which is critical for:
- Evaluating causes of hypoxemia
- Calculating the A-a gradient
- Determining oxygen diffusion capacity
- Assessing ventilation-perfusion (V/Q) mismatch
Standard Alveolar Gas Equation Formula:
PAO₂ =
(FiO₂ × (Patm − PH₂O)) −
PaCO₂
R
Key Components:
• FiO₂: Fraction of inspired oxygen (0.21-1.0)
• Patm: Atmospheric pressure (760 mmHg at sea level)
• PH₂O: Water vapor pressure (47 mmHg at 37°C)
• PaCO₂: Arterial CO₂ partial pressure (35-45 mmHg)
• R: Respiratory quotient (0.7-1.0, typically 0.8)
• Patm: Atmospheric pressure (760 mmHg at sea level)
• PH₂O: Water vapor pressure (47 mmHg at 37°C)
• PaCO₂: Arterial CO₂ partial pressure (35-45 mmHg)
• R: Respiratory quotient (0.7-1.0, typically 0.8)
Clinical Significance:
• Alveolar gas equation estimates oxygen available for diffusion
• Determines A-a gradient (PAO₂ – PaO₂)
• Normal gradient: 5-15 mmHg (increases with age)
• Critical for assessing gas exchange efficiency
• Determines A-a gradient (PAO₂ – PaO₂)
• Normal gradient: 5-15 mmHg (increases with age)
• Critical for assessing gas exchange efficiency
Standard Calculation:
Room air at sea level:
PAO₂ = (0.21 × (760 – 47)) – (40/0.8)
= (0.21 × 713) – 50
= 149.7 – 50 = 99.7 mmHg
(Expected PaO₂: 80-100 mmHg)
PAO₂ = (0.21 × (760 – 47)) – (40/0.8)
= (0.21 × 713) – 50
= 149.7 – 50 = 99.7 mmHg
(Expected PaO₂: 80-100 mmHg)
Oxygen Therapy Example:
100% O₂ at sea level:
PAO₂ = (1.0 × (760 – 47)) – (40/0.8)
= 713 – 50 = 663 mmHg
(PaO₂ <600 mmHg suggests shunt)
PAO₂ = (1.0 × (760 – 47)) – (40/0.8)
= 713 – 50 = 663 mmHg
(PaO₂ <600 mmHg suggests shunt)
Practical Notes:
• For FiO₂ ≤0.6: PAO₂ ≈ FiO₂ × 713 – PaCO₂ × 1.25
• Age-adjusted A-a gradient ≈ (Age/4) + 4
• R varies by diet: Carbs=1.0, Fats=0.7, Protein=0.8
• At altitude: Patm decreases ~24 mmHg per 1000ft
• Always compare PAO₂ to measured PaO₂ for clinical interpretation
• For FiO₂ ≤0.6: PAO₂ ≈ FiO₂ × 713 – PaCO₂ × 1.25
• Age-adjusted A-a gradient ≈ (Age/4) + 4
• R varies by diet: Carbs=1.0, Fats=0.7, Protein=0.8
• At altitude: Patm decreases ~24 mmHg per 1000ft
• Always compare PAO₂ to measured PaO₂ for clinical interpretation
🫁 Alveolar Gas Equation Calculator
The Alveolar Gas Equation calculates the oxygen pressure in alveoli (PAO₂), helping determine the cause of hypoxemia and evaluate pulmonary gas exchange efficiency.
Formula:
PAO₂ = FiO₂ × (Patm − PH₂O) − (PaCO₂ ÷ R)
PH₂O = 47 mmHg | Default Patm = 760 mmHg | R = 0.8
PAO₂ = FiO₂ × (Patm − PH₂O) − (PaCO₂ ÷ R)
PH₂O = 47 mmHg | Default Patm = 760 mmHg | R = 0.8
Example:
PAO₂ = 0.21 × (760 − 47) − (40 ÷ 0.8) = 149.73 − 50 = 99.73 mmHg
PAO₂ = 0.21 × (760 − 47) − (40 ÷ 0.8) = 149.73 − 50 = 99.73 mmHg
🖊️ Enter Values:
Step-by-Step Calculation Example
Patient Data:
- FiO₂ = 0.4 (40% oxygen)
- Pₐₜₘ = 760 mmHg (sea level)
- Pₕ₂ₒ = 47 mmHg
- PaCO₂ = 35 mmHg
- R (RQ) = 0.8
1. Calculate PAO₂:
PAO2 =
(0.4 × (760 – 47)) –
35
0.8
PAO2 =
(0.4 × 713) – 43.75
PAO2 =
285.2 – 43.75 = 241.45 mmHg
2. Compare with Measured PaO₂ (from ABG)
- If PaO₂ = 180 mmHg, then:
- A-a Gradient = PAO₂ – PaO₂ = 241.45 – 180 = 61.45 mmHg
(Elevated gradient suggests V/Q mismatch or diffusion impairment)
Clinical Interpretation of PAO₂ & A-a Gradient
| PAO₂ (mmHg) | A-a Gradient (mmHg) | Interpretation | Possible Causes |
|---|---|---|---|
| Normal (~100 on RA) | Normal (≤15 in young adults) | Normal gas exchange | Healthy lungs |
| Low (<80 on RA) | Normal | Hypoventilation | Sedation, obesity, neuromuscular disease |
| Low (<80 on RA) | High (>20) | V/Q mismatch or diffusion defect | COPD, PE, pulmonary fibrosis |
| Very Low (<60 on RA) | Very High (>40) | Shunt physiology | ARDS, atelectasis, pneumonia |
Key Clinical Applications
- Hypoxemia Workup
Differentiates hypoventilation (normal A-a gradient) from pulmonary disease (elevated A-a gradient). - Oxygen Therapy Monitoring
Predicts expected PaO₂ for a given FiO₂. - Pulmonary Embolism (PE) Screening
Unexplained ↑A-a gradient suggests PE. - ARDS Diagnosis
PAO₂/PaO₂ ratio <200 mmHg (on FiO₂ ≥0.6) supports ARDS.
Adjustments for Special Conditions
| Factor | Adjustment |
|---|---|
| High Altitude | Pₐₜₘ decreases (~24 mmHg per 1000 ft elevation) |
| Fever/Hypothermia | Adjust Pₕ₂ₒ (if not 37°C) |
| Carboxyhemoglobin (COHb) | PAO₂ overestimates true oxygenation |
| Non-Standard RQ | RQ changes with ketosis (↓) or overfeeding (↑) |
Limitations & Best Practices
⚠️ Avoid When:
- Severe anemia (Hb <7 g/dL)
- CO poisoning (use co-oximetry instead)
- Major air leaks (pneumothorax, bronchopleural fistula)
✅ Best Practices:
- Use measured PaCO₂ (not end-tidal CO₂)
- Account for altitude if not at sea level
- Consider P/F ratio (PaO₂/FiO₂) in ARDS
Specialty Uses:
- Pulmonology (ILD, COPD assessment)
- Critical Care (ARDS, ventilator management)
- Anesthesiology (perioperative oxygenation)
- High-Altitude Medicine (aviation, mountaineering)
Access Calculator:
Enter FiO₂, PaCO₂, Pₐₜₘ → Get PAO₂ + A-a gradient
✅ Key Features:
- Altitude compensation
- Adjustable RQ (0.7-1.0)
- Real-time A-a gradient calculation
- Normal reference ranges by age
Disclaimer:
- Always correlate with clinical findings and imaging.
- Not valid in severe hemoglobinopathies.
⚠️ Disclaimer:
The content on LabTestsGuide.com is for informational and educational purposes only. We do not guarantee the accuracy, completeness, or timeliness of the information provided. Always consult qualified healthcare professionals for medical advice, diagnosis, or treatment. LabTestsGuide.com is not liable for any decisions made based on the information on this site.
