Common respiratory care equations, with units and worked examples.
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Oxygen pressure, gas exchange, and arterial oxygen content.
Relates arterial oxygen pressure to the oxygen being delivered.
Use FiO₂ as a fraction. The ratio alone does not establish an ARDS diagnosis.
PaO₂ 80 mmHg on FiO₂ 0.40: 80 / 0.40 = 200 mmHg.
Estimates alveolar oxygen pressure using the abbreviated equation.
This is an approximation. Use the appropriate barometric pressure at altitude; assumed R and high FiO₂ can affect accuracy.
At sea level on room air, with PaCO₂ 40 and R 0.8: 0.21 × (760 − 47) − 40 / 0.8 ≈ 100 mmHg.
Compares calculated alveolar oxygen with measured arterial oxygen.
Expected values depend on age and inspired oxygen. Keep PAO₂ and PaO₂ distinct.
PAO₂ 100 mmHg and PaO₂ 70 mmHg: 100 − 70 = 30 mmHg.
Adds oxygen bound to hemoglobin and oxygen dissolved in blood.
1.34 is a common teaching coefficient; some references use another value. Abnormal hemoglobins require co-oximetry and more careful interpretation.
Hb 12, SaO₂ 0.95, PaO₂ 80: (1.34 × 12 × 0.95) + (0.003 × 80) ≈ 15.52 mL O₂/dL.
Minute volume, alveolar ventilation, and dead space.
Total volume moved per minute.
Convert mL to L when reporting L/min. Minute ventilation includes dead-space ventilation.
VT 0.45 L and f 16/min: 0.45 × 16 = 7.2 L/min.
Volume per minute available for gas exchange.
Use the same volume units for VT and VD. Dead-space volume is not fixed across patients.
VT 0.45 L, VD 0.15 L, f 16/min: (0.45 − 0.15) × 16 = 4.8 L/min.
Uses arterial and mixed-expired CO₂ to estimate wasted ventilation.
PĒCO₂ is not end-tidal CO₂. Enghoff also reflects shunt and V/Q abnormalities; it is not a pure measurement of dead space.
PaCO₂ 40 and mixed-expired PCO₂ 28 mmHg: (40 − 28) / 40 = 0.30, or 30%.
Relates breathing frequency to spontaneous tidal volume.
Use liters. AARC 2024 suggests RSBI is not needed to determine adult SBT readiness; it is not a stand-alone extubation rule.
f 24/min and VT 0.30 L: 24 / 0.30 = 80 breaths/min/L.
Pressure, resistance, compliance, and predicted body weight.
Volume change per unit of elastic driving pressure.
Requires passive conditions and valid holds without a significant leak. This describes lungs plus chest wall, not lung compliance alone.
VT 450 mL, Pplat 25, total PEEP 10: 450 / (25 − 10) = 30 mL/cm H₂O.
A bedside volume-to-pressure estimate during airflow.
Uses total PEEP as the baseline here. Flow resistance affects this estimate; it does not replace static compliance.
VT 450 mL, PIP 35, total PEEP 10: 450 / (35 − 10) = 18 mL/cm H₂O.
Uses the resistive pressure drop during constant-flow ventilation.
Requires passive ventilation, constant flow, and a valid plateau. Do not substitute peak flow from a decelerating waveform. Includes artificial-airway resistance.
PIP 35, Pplat 25, flow 0.50 L/s: (35 − 25) / 0.50 = 20 cm H₂O·s/L.
Pressure needed to deliver a tidal volume above the end-expiratory baseline.
Use a valid plateau measurement, not PIP. Respiratory-system driving pressure differs from transpulmonary driving pressure.
Pplat 25 and total PEEP 10: 25 − 10 = 15 cm H₂O.
Describes the speed of volume change in a single-compartment model.
About 63% of the volume change occurs in one time constant and 95% in three. Inspiratory measurements can underestimate expiratory emptying time when expiratory resistance is higher.
R 10 cm H₂O·s/L and C 0.05 L/cm H₂O: 10 × 0.05 = 0.50 seconds.
Adult ARDS Network height-based equations used for ventilator tidal-volume calculations.
These are the adult protocol's sex-specific equations. Use height, not actual body weight. They are not pediatric formulas.
At 70 inches: male PBW = 50 + 2.3 × 10 = 73 kg; female PBW = 68.5 kg.
Lung capacities, spirometry, and bronchodilator response.
Capacities combine the individual lung volumes.
Spirometry alone cannot measure RV, FRC, or TLC. These require an additional lung-volume measurement method.
IRV 2.5 L, VT 0.5 L, ERV 1.0 L, RV 1.5 L: IC 3.0 L, VC 4.0 L, FRC 2.5 L, TLC 5.5 L.
Fraction of the forced vital capacity exhaled in the first second.
A ratio of 0.625 and 62.5% mean the same thing. Interpret against appropriate reference limits and test quality.
FEV1 2.0 L and FVC 3.2 L: (2.0 / 3.2) × 100 = 62.5%.
Change in FEV1 or FVC as a percentage of its predicted value.
The 2022 ERS/ATS criterion is greater than 10% of predicted in FEV1 or FVC. This uses predicted, not baseline, as the denominator.
FEV1 increases from 2.0 to 2.3 L; predicted FEV1 is 3.5 L: 100 × 0.3 / 3.5 ≈ 8.6% of predicted.
pH, anion gap, and expected respiratory compensation.
Relates pH to the bicarbonate–CO₂ buffer system.
Keep the entire denominator in parentheses. This relationship does not identify the primary disorder by itself.
HCO₃⁻ 24 and PaCO₂ 40: 6.1 + log₁₀[24 / (0.03 × 40)] ≈ 7.40.
Calculates the gap between routinely measured plasma cations and anions.
Compare with the laboratory's reference interval. Some formulas include potassium; those use a different reference range.
Na⁺ 140, Cl⁻ 104, HCO₃⁻ 20: 140 − (104 + 20) = 16 mEq/L.
Adjusts the observed gap for reduced albumin, using 4.0 g/dL as the reference here.
This is an estimate. If albumin is reported in g/L, convert to g/dL by dividing by 10 before using this version.
AG 12 and albumin 2.0 g/dL: 12 + 2.5 × (4.0 − 2.0) = 17 mEq/L.
Estimates respiratory compensation for a primary metabolic acidosis.
Use only for metabolic acidosis. A measured PaCO₂ outside the expected range suggests an additional respiratory disorder.
HCO₃⁻ 16: (1.5 × 16) + 8 = 32 ± 2 mmHg, or 30–34 mmHg.
Cardiac output, blood pressure, vascular resistance, and oxygen transport.
Volume pumped by the heart each minute.
HR × SV gives mL/min when SV is in mL. Divide by 1,000 to report L/min.
HR 90 and SV 60 mL: (90 × 60) / 1,000 = 5.4 L/min.
Indexes cardiac output to body surface area.
Use L/min for CO and m² for BSA.
CO 5.4 L/min and BSA 1.8 m²: 5.4 / 1.8 = 3.0 L/min/m².
Estimates average systemic arterial pressure during the cardiac cycle.
This is an approximation, especially when heart rate or waveform shape is abnormal. MAP here is not mean airway pressure.
Blood pressure 120/60 mmHg: (120 + 2 × 60) / 3 = 80 mmHg.
Relates the systemic vascular pressure gradient to blood flow.
The factor 80 converts mmHg·min/L to dyn·s/cm⁵. CVP is used as an estimate of right atrial pressure.
MAP 80, CVP 5, CO 5 L/min: 80 × (80 − 5) / 5 = 1,200 dyn·s/cm⁵.
Amount of oxygen delivered to the systemic circulation each minute.
The factor 10 converts L of blood to dL. Delivery is not the same as oxygen consumption.
CO 5 L/min and CaO₂ 18 mL O₂/dL: 5 × 18 × 10 = 900 mL O₂/min.
Equations and conventions checked October 28, 2026. Examples use invented study values.