Alveolar-Arterial (A-a) Oxygen Gradient & PaO₂/FiO₂ Ratio Calculator

Compute alveolar gas equation PAO₂ = FiO₂(Patm − PH₂O) − PaCO₂/0.8 and A-a gradient.

Alveolar-Arterial (A-a) O₂ Gradient
17.73 mmHg
Alveolar Oxygen Tension (P_AO₂) 99.73 mmHg
Age-Adjusted Normal Upper Limit 16 mmHg
PaO₂ / FiO₂ (Horovitz Ratio) 390.48 mmHg
Inputs
%
Fraction of inspired oxygen (FiO₂ %, 21% on room air).
mmHg
Measured ABG arterial oxygen partial pressure (PaO₂) in mmHg.
mmHg
Measured ABG arterial carbon dioxide (PaCO₂) in mmHg.
years
Patient age in years for age-expected A-a cutoff.
mmHg
Ambient barometric pressure (760 mmHg at sea level).
Results & Graph
Alveolar-Arterial (A-a) O₂ Gradient
17.73 mmHg
Alveolar Oxygen Tension (P_AO₂)
99.73 mmHg
Age-Adjusted Normal Upper Limit
16 mmHg
PaO₂ / FiO₂ (Horovitz Ratio)
390.48 mmHg

Alveolar-Arterial (A-a) O₂ Gradient

Graph 1 • Fio2 Pct Sensitivity Recalculates the domain equation across 50% to 150% of the primary input while holding other parameters constant.
-57.1 mmHg 21.4 mmHg 100.0 mmHg 50%: -57.14 mmHg -57.1 50% 75%: -19.7 mmHg -19.7 75% 100%: 17.73 mmHg 17.7 100% 125%: 55.16 mmHg 55.2 125% 150%: 92.6 mmHg 92.6 150%
Graph 2 • Primary & Supporting Metric Comparison Compares the primary output alongside supporting domain benchmarks.
Alveolar-Arterial (A-a) O₂ Gradient 17.73 mmHg Alveolar Oxygen Tension (P_AO₂) 99.73 mmHg Age-Adjusted Normal Upper Limit 16 mmHg PaO₂ / FiO₂ (Horovitz Ratio) 390.48 mmHg
Graph 3 • Exact Output Table & Units Displays each calculated output in its exact domain unit.
Alveolar-Arterial (A-a) O₂ Gradient17.73 mmHgAlveolar Oxygen Tension (P_AO₂)99.73 mmHgAge-Adjusted Normal Upper Limit16 mmHgPaO₂ / FiO₂ (Horovitz Ratio)390.48 mmHg
Summary: Alveolar PAO₂ is 99.7 mmHg, giving an A-a gradient of 17.7 mmHg (age-adjusted upper normal ≤16 mmHg) and PaO₂/FiO₂ ratio of 390.
Summary: Alveolar PAO₂ is 99.7 mmHg, giving an A-a gradient of 17.7 mmHg (age-adjusted upper normal ≤16 mmHg) and PaO₂/FiO₂ ratio of 390.
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Formula & Mathematical Methodology: A-a O₂ Gradient & P/F Ratio Reference Equation

PAO₂ = FiO₂ × (Patm − 47) − (PaCO₂ / 0.8)
A-a Gradient = PAO₂ − PaO₂
ExpectedMax = Age/4 + 4
P_AO₂ = FiO₂ × (P_atm − 47) − (PaCO₂ / 0.8); A-a Gradient = P_AO₂ − PaO₂; ExpectedMax = Age/4 + 4
  • fio2Pct: Fio2 Pct (%)
  • arterialPao2Mmhg: Arterial Pao2 Mmhg (mmHg)
  • arterialPaco2Mmhg: Arterial Paco2 Mmhg (mmHg)
  • patientAgeYears: Patient Age Years (years)
  • barometricPressureMmhg: Barometric Pressure Mmhg (mmHg)

Rounding: Laboratory and clinical equations retain full floating-point precision and round displayed results to 2 decimal places.

Worked Example: Reference Calculation: A-a O₂ Gradient & P/F Ratio

Compute alveolar gas equation PAO₂ = FiO₂(Patm − PH₂O) − PaCO₂/0.8 and A-a gradient.

  1. Enter the reagent concentrations, assay readings, or clinical laboratory parameters.
  2. Compute the standard formula: P_AO₂ = FiO₂ × (P_atm − 47) − (PaCO₂ / 0.8); A-a Gradient = P_AO₂ − PaO₂; ExpectedMax = Age/4 + 4.
  3. Review the primary result, supporting reference intervals, and 3 SVG visualizations.
Result: Evaluates A-a O₂ Gradient & P/F Ratio via P_AO₂ = FiO₂ × (P_atm − 47) − (PaCO₂ / 0.8); A-a Gradient = P_AO₂ − PaO₂; ExpectedMax = Age/4 + 4.

Frequently Asked Questions

What formula is used by the Alveolar-Arterial (A-a) Oxygen Gradient & PaO₂/FiO₂ Ratio Calculator?

It computes P_AO₂ = FiO₂ × (P_atm − 47) − (PaCO₂ / 0.8); A-a Gradient = P_AO₂ − PaO₂; ExpectedMax = Age/4 + 4 and plots three custom SVG graphs showing parameter sensitivity and component breakdowns.

Can I compare different reagent dilutions or lab scenarios side by side?

Yes. Use the "Compare (0/3)" button to pin up to 3 scenarios side by side.

Are entered values stored on any server?

No. Every calculation runs 100% locally in your browser.

Health & Fitness · Clinical Diagnostics & Scoring

Alveolar-Arterial (A-a) Oxygen Gradient & PaO₂/FiO₂ Ratio Calculator: inputs, method, and how to read the result

Compute alveolar gas equation PAO₂ = FiO₂(Patm − PH₂O) − PaCO₂/0.8 and A-a gradient.

Choose inputs for the case you are checking

The defaults are illustrative. Replace them with values for your case and keep the units shown beside each field.

  • Fio2 Pct: Fraction of inspired oxygen (FiO₂ %, 21% on room air).
  • Arterial Pao2 Mmhg: Measured ABG arterial oxygen partial pressure (PaO₂) in mmHg.
  • Arterial Paco2 Mmhg: Measured ABG arterial carbon dioxide (PaCO₂) in mmHg.
  • Patient Age Years: Patient age in years for age-expected A-a cutoff.

What the calculation includes

With the default values shown, Alveolar-Arterial (A-a) O₂ Gradient is 17.73 mmHg. The calculation follows A-a O₂ Gradient & P/F Ratio Reference Equation; the formula and variable definitions above show how the inputs combine.

One-input check: With the other defaults held constant, changing Fio2 Pct from 21 % to 23.1 % changes Alveolar-Arterial (A-a) O₂ Gradient from 17.73 mmHg to 32.7 mmHg. This is a comparison inside the calculator's stated model, not a prediction.

Where to use caution

  • Uses standard IUPAC atomic weights, 25°C (298.15 K) reference thermodynamics, and published clinical literature equations.
  • Educational and laboratory reference tool only; clinical scoring calculators do not replace professional medical judgment or institutional protocols.

Scope: IUPAC / NIH Laboratory & Clinical Reference Standard Check the assumptions and limitations against your situation before relying on the estimate.

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