Make the gas math clear.

Calculate arterial and mixed venous oxygen content, systemic oxygen delivery and extraction using matched measurements.

Formula & limits: Content = 1.34 × Hb in g/dL × saturation fraction + 0.003 × oxygen pressure in mmHg. DO₂ = CO × CaO₂ × 10; OER = (CaO₂ − CvO₂) / CaO₂ × 100%. Mixed venous sampling and stable conditions matter.

References: WHO: educational modules on clinical use of blood · Open respiratory textbook: oxygen content

Solve for cardiac output from measured oxygen consumption, or oxygen consumption from independently measured cardiac output.

Formula & limits: CO (L/min) = VO₂ (mL/min) / [10 × arterial–mixed venous oxygen content difference (mL/dL)]. VO₂ = CO × 10 × content difference. An assumed VO₂ gives an indirect estimate.

References: Fick cardiac output: method and limitations · Physiological Reviews: oxygen transport and Fick principle

Use mean mixed expired CO₂ and the correct alveolar or arterial reference. End-tidal CO₂ cannot replace these measurements.

Formula & limits: VD/VT = (reference CO₂ − mean mixed expired CO₂) / reference CO₂. Bohr uses mean alveolar CO₂; Enghoff uses arterial CO₂ and incorporates shunt/VQ inequality. Inspired CO₂ is assumed negligible.

References: Primary study: Bohr and Enghoff assessment · Primary study: gas-condition correction

Estimate high-flow or Hamilton ventilation consumption, or use verified measured source oxygen draw for any device. Compare demand with usable supply after reserve.

Formula & limits: Hamilton ventilation source draw = [ExpMinVol × (2 if patient <8 kg, otherwise 1) + base flow + leak] × (FiO₂% − 20.9)/79.1. T1 high-flow draw = set flow × the same fraction. Other devices need verified measurements or their own published equation.

References: Hamilton: consumption equation and base-flow table · Hamilton T1 SW 3.0.x manual: high flow, section 7.5.4

Convert common gases or a custom molecular weight at specified temperature and absolute pressure. This does not evaluate exposure limits.

Formula & limits: mg/m³ = ppm by volume × molecular weight / ideal molar volume. Molar volume (L/mol) = 8.314462618 × kelvin / absolute kPa. At 25°C and 1 atmosphere it is approximately 24.45 L/mol.

References: CDC/NIOSH: ppm and mg/m³ conversion

Convert between body-temperature saturated gas and standard-temperature dry gas, including local barometric pressure.

Formula & limits: V STPD = V BTPS × (barometric mmHg − 47)/760 × 273.15/310.15. BTPS here is fixed at 37°C saturated; STPD is 0°C, 760 mmHg dry. Do not correct already-standardized instrument values twice.

References: Primary study: gas volume corrections in intensive care

Use the cylinder’s published free-air capacity and your measured or estimated breathing rate. The example values are editable, not a manufacturer preset.

Formula & limits: Usable free air = published capacity × max(start − reserve, 0) ÷ service pressure. Working time = usable air ÷ (surface breathing rate × ambient ATA). Cylinder minute ratings do not guarantee working duration.

Estimate gas for two divers sharing one supply during a direct ascent, including problem-solving time and an entered stop. This does not calculate decompression obligations.

Formula & limits: Stage gas = combined stressed surface RMV × average absolute pressure × time. This tool adds modeled emergency ascent gas to the entered residual pressure; it does not calculate decompression or an overhead exit.

Find the maximum oxygen fraction for your chosen PO₂ limit. Whole-number mixes round down. Use the MOD and analyzed-gas check before a dive.

Formula & limits: Maximum oxygen fraction = selected PO₂ ceiling ÷ absolute pressure, capped at 100%. Whole-number oxygen percentages round down. Analyze the gas and check MOD separately.

Compare the nitrogen partial pressure of Nitrox with air at an equivalent depth.

Formula & limits: EAD = [(1 − oxygen fraction) × (depth ÷ depth-per-ATA + 1) ÷ 0.79 − 1] × depth-per-ATA. The 79% nitrogen air model is an approximation and does not produce a decompression schedule.

Calculate alveolar oxygen and its difference from arterial oxygen using measurements from the same conditions and sample. Open ABG interpretation.

Formula & limits: Simplified PAO₂ = FiO₂ × (barometric pressure − 47) − PaCO₂ ÷ RQ. Full PAO₂ = FiO₂ × (barometric pressure − 47) − PaCO₂ × [FiO₂ + (1 − FiO₂) ÷ RQ]. A–a gradient = PAO₂ − PaO₂. FiO₂ is a fraction; pressures are mmHg; water vapor is modeled at 37°C.

Use measured plateau pressure and total PEEP, including intrinsic PEEP. Peak pressure and set PEEP are not interchangeable with these measurements.

Formula & limits: Driving pressure = measured plateau pressure − measured total PEEP. Static compliance = exhaled tidal volume ÷ driving pressure, in mL/cmH₂O. Measurements require appropriate holds in a passive patient without leaks.

Estimate the pressure change in a closed cylinder after its gas reaches a different temperature.

Formula & limits: Final gauge pressure = (initial gauge pressure + ambient absolute pressure) × final kelvin ÷ initial kelvin − ambient pressure. Assumes fixed volume, fixed gas quantity and temperature equilibrium; high-pressure real gases may differ.

Combine cylinders with individual pressures and reserves. Enter total oxygen consumption from the transport oxygen calculator or the device display. Cylinders are used in the order listed.

Formula & limits: Usable oxygen per cylinder = max(start − reserve, 0) × verified cylinder factor. Demand = total source oxygen flow × (trip + buffer). Cylinders are used sequentially, with each reserve excluded.

Convert volume, flow, temperature and gas concentration. Enter a value in either unit system to see its equivalents.

Formula & limits: 1 ft³ = 28.316846592 L; 1 CFM = 28.316846592 L/min; kelvin = °C + 273.15; °F = °C × 9/5 + 32; 1% = 10,000 ppm by volume. Volume and flow comparisons require matching pressure and temperature references.

Convert pressure conventions with a user-entered local ambient pressure. PSI, bar and kPa remain selectable.

Formula & limits: Absolute pressure = gauge pressure + local ambient absolute pressure. At an ambient pressure of 14.6959 PSI, 100 PSI gauge equals 114.6959 PSI absolute. This is a convention conversion, not a change in the physical pressure.

Estimate the ideal final pressure of two connected cylinders. Enter their internal water volumes, not their free-air capacities.

Formula & limits: For two rigid cylinders at the same temperature and ambient pressure, final gauge pressure = (P₁V₁ + P₂V₂) ÷ (V₁ + V₂). V is internal water volume, not rated surface gas capacity. Real transfer heating and pressure limits require equipment-specific procedures.

Compare static buoyancy with measured submerged load. kgf and lbf describe force-equivalent weight, not object mass or dry weight.

Formula & limits: Required displaced water volume = measured submerged load × entered multiplier ÷ water density, using kgf-equivalent load and density in kg/L. Surface-equivalent gas = displaced volume × ambient ATA. This is static buoyancy, not a lift or rigging plan.

See how an unconstrained trapped gas volume expands or compresses between two depths.

Formula & limits: At constant temperature and gas quantity, V₂ = V₁ × P₁ absolute ÷ P₂ absolute. An unconstrained 1 L gas space at 3 ATA expands to 3 L at 1 ATA; a rigid sealed cylinder does not.

Calculate dry-gas partial pressures from analyzed oxygen and helium percentages. Nitrogen is the remaining fraction.

Formula & limits: Each dry-gas partial pressure = analyzed gas fraction × total absolute pressure. Nitrogen is the remaining fraction after oxygen and helium. Fractions must total no more than 100%; oxygen exposure and surface suitability are separate checks.

Convert flow referenced to one pressure and temperature into flow at another. Verify the manufacturer’s definition of standard conditions.

Formula & limits: Actual flow = reference flow × reference absolute pressure ÷ actual absolute pressure × actual kelvin ÷ reference kelvin. Verify the manufacturer’s temperature, pressure and dry/wet definition for standard liters or standard cubic feet.

Compare two gauge readings while accounting for temperature. An unexplained drop is a reason to investigate, not proof of a leak.

Formula & limits: Expected final gauge pressure with no gas loss = (initial gauge + ambient pressure) × final kelvin ÷ initial kelvin − ambient pressure. Compare temperature-normalized readings; an unexplained loss is not proof of a leak.

Estimate time from published free-air delivery and the amount of gas required. Manufacturer fill-rate limits still apply.

Formula & limits: Required surface gas = rated cylinder capacity × (target − start pressure) ÷ rated pressure. Ideal time = required gas ÷ published free-air delivery. The editable delivery fraction adjusts the estimate; compressor behavior and permitted filling rates can differ.

Explore gas density and END with explicit temperature and oxygen-narcosis assumptions. This does not produce a complete dive plan.

Formula & limits: Ideal-gas density = absolute pressure × mixture molar mass ÷ (gas constant × kelvin). END compares the entered narcotic fraction with air under the selected oxygen-narcosis assumption. Density, PO₂ and END do not establish a complete technical dive plan.