Calculate the alveolar–arterial oxygen gradient from the alveolar gas equation, compare against age-based normal limits, see the PaO2/FiO2 ratio + Berlin category, or back-calculate the FiO2 needed for a target PAO2.
⚠️ Educational tool, not a medical device. This calculator helps you understand respiratory physiology calculations from arterial blood gas (ABG) data. Results are not a diagnosis, not oxygen therapy advice, and not a substitute for clinical assessment by a doctor or healthcare professional.
Pressure units:Conversion: 1 mmHg = 0.133322 kPa
Enter as a fraction: 0.21 = room air, 1.00 = 100% oxygen.
Arterial blood partial pressure of O2, measured from blood gas analysis.
Arterial blood partial pressure of CO2.
Usually 0.8. Varies with metabolic status (0.7–1.0).
Decreases at altitude — PAO2 drops too.
47 mmHg at body temperature 37°C (100% water-saturated alveolus).
For estimating the age-based normal gradient limit.
Calculation Results
PAO2 (alveolar)–
A-a gradient (AaDO2)–
Normal limit for age (age/4 + 4)–
Alternative formula (2.5 + 0.21 × age)–
Educational interpretation–
Rasio PaO2/FiO2 (P/F)–
Berlin oxygenation category (educational)–
Rasio a/A (PaO2/PAO2)–
Calculation steps
Remember: the interpretation above is educational. A high gradient alone does not determine a diagnosis — correlate with clinical findings, imaging, and other ABG parameters together with a healthcare professional.
Educational mode: from the reversed alveolar gas equation — FiO2 = (target PAO2 + PaCO2/R) / (Patm − PH2O). Not an oxygen therapy prescription.
Desired alveolar PAO2.
Inverse Mode Results
FiO2 required–
Notes–
Remember: this is a physiology arithmetic exercise, not oxygen administration advice. Oxygen therapy is determined by a doctor based on the patient's clinical condition.
🔗 Complementary: this calculator computes the AaDO2 value from ABG data.
The APACHE II calculator instead asks you to type in the AaDO2 value as its oxygenation score input —
use the result from this page as input there.
Verified example: FiO2 0.21 · PaCO2 40 mmHg · R 0.8 · Patm 760 mmHg · PH2O 47 mmHg → PAO2 = 99.73 mmHg. With PaO2 = 95 mmHg, the A-a gradient = 4.73 mmHg. For age 40, the normal limit (age/4 + 4) ≈ 14 mmHg — the 4.73 mmHg result is within the normal limit for age.
Berlin criteria oxygenation categories (educational)
P/F ratio (mmHg)
Berlin category
200 – 300
Mild
100 – 200
Moderate
≤ 100
Severe
> 300
Does not meet Berlin oxygenation criteria
The full Berlin criteria require PEEP ≥ 5 cmH2O plus onset, chest imaging, and edema origin criteria — the table above covers only the oxygenation component and is educational.
Frequently asked questions (FAQ)
What is the A-a gradient (AaDO2)?
The A-a gradient (alveolar–arterial oxygen gradient, abbreviated AaDO2) is the difference between the partial pressure of oxygen in the alveolus (PAO2, calculated from the alveolar gas equation) and in arterial blood (PaO2, measured from arterial blood gas/ABG). It describes how efficiently oxygen moves from lung to blood: a small gradient means efficient gas exchange, a large gradient means impaired pulmonary gas exchange.
How is the A-a gradient calculated?
First compute PAO2 with the alveolar gas equation: PAO2 = FiO2 × (Patm − PH2O) − PaCO2 / R, where FiO2 is the inspired oxygen fraction, Patm is atmospheric pressure (760 mmHg at sea level), PH2O is water vapor pressure (47 mmHg at 37°C), PaCO2 comes from ABG, and R is the respiratory quotient (usually 0.8). Then A-a gradient = PAO2 − PaO2. Example: FiO2 0.21, PaCO2 40 mmHg, R 0.8, Patm 760 mmHg gives PAO2 = 99.73 mmHg; with PaO2 = 95 mmHg the A-a gradient = 4.73 mmHg.
What is the normal A-a gradient value?
The normal A-a gradient rises with age. Two rule-of-thumb formulas commonly used in the clinical literature are age/4 + 4 and 2.5 + 0.21 × age (in mmHg). For example, at age 40 the normal limit is about 14 mmHg by the first formula and about 10.9 mmHg by the second. Both are educational estimates, not diagnostic thresholds.
What does a high A-a gradient mean?
A high A-a gradient indicates oxygen is not moving efficiently from alveolus to blood, which can accompany conditions such as ventilation–perfusion mismatch (e.g., pneumonia or pulmonary embolism), right-to-left shunt, or diffusion impairment (e.g., pulmonary fibrosis). But a high gradient alone never determines a diagnosis — it must always be correlated with clinical findings, imaging, and other ABG parameters by a healthcare professional.
What are the PaO2/FiO2 ratio and the Berlin criteria?
The PaO2/FiO2 ratio (P/F ratio) is PaO2 divided by FiO2 and is used in the Berlin criteria to categorize oxygenation impairment in ARDS: 200–300 mild, 100–200 moderate, and ≤100 severe (in mmHg). The full Berlin criteria also require a minimum PEEP of 5 cmH2O plus timing, imaging, and edema origin criteria — so the categories in this calculator are educational only.
Can this calculator's results be used for diagnosis?
No. This calculator is an educational aid for understanding respiratory physiology calculations, not a substitute for clinical assessment. Its results must not be used to establish a diagnosis, determine oxygen therapy, or make medical decisions. Always discuss blood gas interpretation with a competent doctor or healthcare professional.
How does this calculator differ from the APACHE II calculator?
This calculator COMPUTES the AaDO2 value from blood gas data (FiO2, PaCO2, PaO2, and physiological constants). In contrast, the APACHE II calculator at nrtechstudio asks you to TYPE IN an already-known AaDO2 value as one of its oxygenation score inputs. The two are complementary: use the AaDO2 result from this calculator as input to the APACHE II score.
Why is my gradient result negative?
A negative A-a gradient is not physiologically possible because PAO2 is always higher than PaO2. A negative result almost always means an input error: usually the entered PaO2 is larger than the computed PAO2. Recheck FiO2 (is it a fraction, e.g., 0.21 not 21), PaCO2, atmospheric pressure, and make sure the PaO2 from ABG is correct.
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