# A-a Gradient (Alveolar-Arterial O₂) Calculate the alveolar-arterial O₂ gradient to distinguish hypoxemia causes. PAO₂ = FiO₂×(P_atm−47) − PaCO₂/0.8; A-a = PAO₂ − PaO₂. Normal ≈ (Age+10)/4. Elevated → V/Q mismatch, shunt, diffusion impairment. Derived from StatPearls, LITFL, Cornell PICU, and Martin 1999. Not medical advice. > Canonical page: https://elysiatools.com/en/tools/a-a-gradient-calculator - **Category:** Health - **Keywords:** a-a gradient, alveolar arterial gradient, alveolar gas equation, pao2, hypoxemia, oxygenation, v q mismatch, shunt, pulmonary embolism, blood gas, critical care, pulmonology ## Overview The A-a Gradient calculator estimates the alveolar-arterial oxygen gradient from PaO₂, PaCO₂, FiO₂, age, and atmospheric pressure. It calculates PAO₂ with the alveolar gas equation, then compares the result with an age-adjusted expected normal value to help assess hypoxemia patterns. It is not medical advice. ## Inputs - **PaO₂ (mmHg)** (number): Arterial partial pressure of oxygen (mmHg) from ABG. - **PaCO₂ (mmHg)** (number): Arterial partial pressure of CO₂ (mmHg) from ABG. - **FiO₂ (inspired oxygen fraction)** (select) - **Age (years)** (number): Patient age (years), used for age-adjusted normal A-a gradient. - **Atmospheric Pressure (mmHg)** (number): Atmospheric pressure (mmHg). Default 760 at sea level. Lower at altitude (e.g. Denver ~630). - **Decimal Places** (number) ## When to use - Assess whether hypoxemia is associated with a normal or elevated A-a gradient. - Review arterial blood gas results using a selected FiO₂ and atmospheric pressure. - Support clinical reasoning about hypoventilation versus conditions associated with V/Q mismatch, shunt, or diffusion impairment. ## How it works - Enter PaO₂ and PaCO₂ values from an arterial blood gas. - Select the inspired oxygen fraction, or FiO₂, used when the sample was collected. - Enter the patient’s age; optionally adjust atmospheric pressure for altitude instead of using the default sea-level value of 760 mmHg. - The calculator computes PAO₂, subtracts PaO₂ to find the A-a gradient, and reports the expected normal value, ratio, and category. ## Use cases - Interpret arterial blood gas results in respiratory and critical-care education. - Compare oxygenation calculations at sea level and at altitude. - Estimate whether a low PaO₂ occurs with an approximately normal or significantly elevated A-a gradient. ## Frequently asked questions ### What does the A-a gradient measure? It is the difference between estimated alveolar oxygen pressure, PAO₂, and arterial oxygen pressure, PaO₂. ### What formula does the calculator use? PAO₂ = FiO₂ × (P_atm − 47) − PaCO₂ / 0.8, and A-a = PAO₂ − PaO₂. ### What does a normal A-a gradient suggest? A normal value can be consistent with hypoventilation or other causes of low oxygen that do not substantially widen the alveolar-arterial difference. ### What does an elevated A-a gradient suggest? An elevated value may occur with V/Q mismatch, shunt, or diffusion impairment, but it must be interpreted with the clinical context. ### Why can atmospheric pressure be changed? Atmospheric pressure is lower at altitude, so adjusting it can make the PAO₂ estimate more representative of the measurement conditions. ## Related tools - [Alveolar Gas Equation (PAO₂ Calculator)](https://elysiatools.com/en/tools/alveolar-gas-equation): Calculate PAO₂ = FiO₂ × (P_atm − 47) − PaCO₂ / RQ. Defaults: P_atm 760 mmHg (sea level), RQ 0.8. Gives a directional hint vs expected ~100 mmHg. For full A-a gradient interpretation use a-a-gradient-calculator. Derived from StatPearls, LITFL, Cornell PICU, and West. Not medical advice. - [Alveolar Ventilation Calculator (VA)](https://elysiatools.com/en/tools/alveolar-ventilation-calculator): Calculate VA = (VT − VD) × RR in L/min. VD may be supplied or estimated as ~2 mL/kg body weight. Normal resting ~4–6 L/min; low → hypercapnia, high → hypocapnia. Derived from West, LITFL, StatPearls, and Radford 1955. Not medical advice. - [Apgar Score (Newborn 1 & 5 min)](https://elysiatools.com/en/tools/apgar-score): Calculate the Apgar score to assess newborn condition at 1 minute and 5 minutes after birth. Five signs are each scored 0–2 at both time points: Appearance (skin color), Pulse (heart rate), Grimace (reflex irritability), Activity (muscle tone), and Respiration. Each time point totals 0–10. Interpretation: 7–10 reassuring; 4–6 moderately abnormal (may need assistance); 0–3 critically low (immediate resuscitation). The tool reports both the 1-min and 5-min scores, the change (delta), and per-time-point interpretation. A 5-min score, and especially the change from 1 to 5 min, indicates response to resuscitation; persistent low 5-min scores warrant continued resuscitation and reassessment at 10 min. Derived from Apgar 1953, reaffirmed by ACOG/AAP. The Apgar is a physiologic snapshot at a moment in time and is not, by itself, a marker of asphyxia or long-term neurologic outcome. Not medical advice. - [Henderson-Hasselbalch Equation (pH / HCO₃⁻ / PCO₂)](https://elysiatools.com/en/tools/bicarbonate-ph-conversion): Solve any one of pH/HCO₃⁻/PaCO₂ from the other two via pH = 6.1 + log10(HCO₃⁻/(0.03×PaCO₂)). Reports linear Henderson \[H⁺\] cross-check. Derived from Henderson 1908, Hasselbalch 1916, Siggaard-Andersen 1974, LITFL, StatPearls, Berend 2016. Not medical advice. - [Child-Pugh Score (Cirrhosis Severity)](https://elysiatools.com/en/tools/child-pugh-score): Calculate the Child-Pugh score to grade chronic liver disease / cirrhosis severity and estimate perioperative mortality. Five parameters scored 1–3 each (total 5–15): Total bilirubin (<2 mg/dL =1, 2–3 =2, >3 =3) — supports mg/dL or µmol/L input (auto ÷17.1); Serum albumin (>3.5 g/dL =1, 2.8–3.5 =2, <2.8 =3); INR (<1.7 =1, 1.7–2.3 =2, >2.3 =3); Ascites (absent =1, slight/controlled =2, moderate–severe =3); Hepatic encephalopathy (none =1, grade I–II =2, grade III–IV =3). Classes: A (5–6) well-compensated (1-y ~100%, 2-y ~85%); B (7–9) significant compromise (1-y ~80%, 2-y ~60%); C (10–15) decompensated (1-y ~45%, 2-y ~35%). Derived from Pugh et al. 1973 (Br J Surg) and the original Child-Turcotte classification. Not medical advice. - [CURB-65 Score (Pneumonia Severity)](https://elysiatools.com/en/tools/curb-65-score): Calculate the CURB-65 score to assess community-acquired pneumonia (CAP) severity and guide the site of care. Each component scores 1 point: Confusion (new-onset disorientation), Urea > 7 mmol/L (BUN > 20 mg/dL), Respiratory rate ≥ 30/min, Blood pressure (systolic < 90 OR diastolic ≤ 60 mmHg), and Age ≥ 65. Range 0–5. Interpretation: 0–1 low risk (likely outpatient; 30-day mortality ~1.5–2.4%), 2 moderate (consider admission or supervised discharge, ~9.2%), 3–5 high risk (hospital admission; consider ICU for 4–5; mortality rises to ~57% at score 5). Endorsed by the British Thoracic Society. Derived from Lim et al. 2003 (Thorax). Not medical advice. - [Dead Space Fraction (VD/VT, Bohr & Enghoff)](https://elysiatools.com/en/tools/dead-space-fraction): Calculate VD/VT using both the Bohr equation (PACO₂-based) and the Enghoff modification (PaCO₂-based). Normal ~0.20–0.40; >0.60 signals severe dead space in ARDS/PE. Derived from Bohr 1891, Enghoff 1938, Tusman 2012, LITFL, StatPearls. Not medical advice. - [Dose by Body Surface Area Calculator (BSA = √(H·W/3600))](https://elysiatools.com/en/tools/dose-by-body-surface-area): Calculate an individualized drug dose from body surface area using the Mosteller formula: BSA (m²) = √(Height(cm) · Weight(kg) / 3600), then Dose = Drug_dose_per_m² × BSA. BSA is the recommended normalization for many cytotoxic and pediatric regimens because drug clearance scales more linearly with BSA than with body weight across patients of different sizes. Also reports the standard adult dose at the reference adult BSA of 1.73 m² for comparison. Valid only for linear drug clearance — BSA dosing does not apply to saturable (Michaelis-Menten) pathways. 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