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.
