Explore 33 gas laws and principles. Move a slider, watch the result, and see what stays fixed—then connect the idea to a Fleckulator calculator.
Start with Boyle’s law or choose a topic below. Green shows your current result; the muted bar is the original example. Both bars share the same zero and scale. These are learning examples, not patient observations or operating instructions.
Core gas laws
Boyle’s law
Open interactive lesson
Squeeze a gas into less space and its pressure rises.
What stays fixed: Same gas amount and temperature. Initial state: 1 L at 1 atm absolute.
Final gas volume
1 L
Pressure × volume
1 L·atm
Gas-space sketch: width is proportional to volume; dots are schematic.
Matches the baseline.
The relationship: P₁V₁ = P₂V₂; V₂ = P₁V₁ / P₂.
Keep in mind: Applies to a flexible gas space in equilibrium. A rigid cylinder does not change its internal volume.
Higher gas partial pressure increases its equilibrium dissolved concentration.
What stays fixed: Same gas, solvent and temperature. An arbitrary concentration of 1 unit is defined at 1 atm gas partial pressure.
Relative dissolved concentration
1 × reference
Matches the baseline.
The relationship: C = kH × Pgas. At fixed kH, C₂/C₁ = P₂/P₁.
Keep in mind: Shows relative equilibrium solubility only. It does not model tissue compartments, uptake time, bubbles or decompression. Henry constants have several conventions.
More area or a larger gradient increases transfer; a thicker barrier slows it.
What stays fixed: Diffusion coefficient fixed. Area, gradient and thickness are normalized to a baseline of 1.
Relative diffusion transfer rate
1 × baseline
Matches the baseline.
The relationship: Transfer rate ∝ diffusion coefficient × area × gradient / thickness.
Keep in mind: A relative demonstration, not a measured lung diffusion capacity. Fick’s diffusion law is different from the Fick cardiac-output principle.
Compression can heat gas when heat does not leave the system.
What stays fixed: Ideal reversible adiabatic process. Initial 1 L, 1 atm and 20°C; heat-capacity ratio γ = 1.4.
Final absolute pressure
1 atm
Final temperature
20 °C
Matches the baseline.
The relationship: P₂/P₁ = (V₁/V₂)^γ; T₂/T₁ = (V₁/V₂)^(γ−1).
Keep in mind: Real cylinder filling is not this ideal closed reversible process. Gamma varies by gas and temperature; heat transfer changes the result.
Water adds pressure with depth. A diver experiences surface pressure plus water pressure.
What stays fixed: Surface pressure: 101,325 Pa; g = 9.80665 m/s². Water density is editable.
Ambient absolute pressure
1.992 atm
Water pressure above surface
100.5182 kPa
Matches the baseline.
The relationship: Absolute pressure = surface pressure + ρgh.
Keep in mind: Uses physical density rather than the rounded 33/34 ft-per-atmosphere dive approximation. Weather, altitude and water density can change pressure.
Baseline device flow and leaks can increase consumption beyond patient minute volume.
What stays fixed: Hamilton C1/T1/MR1 adult/pediatric illustration: base flow 3 L/min; patient ≥8 kg.
Estimated source oxygen draw
5.9317 L/min
Matches the baseline.
The relationship: Draw = (ExpMinVol + base flow + MVleak) × (FiO₂%−20.9)/79.1.
Keep in mind: Manufacturer 2020 equation; actual draw can be higher. Verify the specific device, software, patient group and measured source consumption.
Keep in mind: Use contemporaneous samples. Dyshemoglobins need separate co-oximetry interpretation. This is not a transfusion or oxygen recommendation.
Blood flow multiplied by the oxygen-content drop gives oxygen consumption.
What stays fixed: Content difference is arterial minus true mixed venous oxygen content; CO is independently measured. Arterial content is fixed at 20 mL O₂/dL.
Oxygen consumption
250 mL O₂/min
Oxygen extraction ratio
25 %
Matches the baseline.
The relationship: VO₂ = CO × (CaO₂−CvO₂) × 10; CO = VO₂/[10 × content difference].
Keep in mind: The factor 10 converts dL to L. Assumed VO₂, central venous substitution, shunts and unstable sampling introduce error.
The relationship: VD/VT = (reference CO₂−mixed expired CO₂)/reference CO₂.
Keep in mind: Enghoff includes shunt/VQ inequality, not just dead space. Use mean mixed expired CO₂, never end-tidal. Bohr uses mean alveolar reference instead.
The pressure needed for a breath depends on tidal volume and respiratory-system compliance.
What stays fixed: Passive linear respiratory-system model. Total PEEP is measured, including intrinsic PEEP.
Illustrative driving pressure
15 cmH₂O
Illustrative plateau pressure
25 cmH₂O
Minute volume at RR 16
7.2 L/min
Matches the baseline.
The relationship: Driving pressure = VT / Cstat; plateau = total PEEP + driving pressure. Minute volume = VT × RR / 1000.
Keep in mind: Real mechanics can be nonlinear. Appropriate holds, no effort and no leak are required for measured static compliance; this is not a ventilator setting recommendation.
Duration increases with usable gas and decreases with consumption. Reserve is excluded before estimating time.
What stays fixed: One E cylinder model: factor 0.28 L/PSI. Reserve 200 PSI. Planned use including buffer: 50 min.
Estimated duration above reserve
44.8 min
Usable oxygen
448 L
Supply minus 50-minute demand
-52 L
Matches the baseline.
The relationship: Usable L = max(start−reserve,0) × factor. Duration = usable L / source draw.
Keep in mind: Cylinder factors are linear approximations and must be verified. SCBA uses its actual rated capacity and breathing demand; minute ratings are not guaranteed duration.
Usable gas adds across independently accessible cylinders; each cylinder keeps its own reserve.
What stays fixed: Two E cylinder models, each factor 0.28 L/PSI and reserve 200 PSI. Cylinder A starts at 1,800 PSI. Used sequentially.
Combined duration above reserves
89.6 min
Combined usable oxygen
896 L
Matches the baseline.
The relationship: Total usable volume = Σ max(startᵢ−reserveᵢ,0) × cylinder factorᵢ. Time = total usable / source draw.
Keep in mind: Requires independently accessible, compatible supplies. Switching delays, manifold equalization and leaks are excluded; include operational buffer separately.
Pressure drop per minute depends on cylinder size; a surface-equivalent volume rate makes comparisons useful.
What stays fixed: Test depth 66 ft seawater = 3 atm absolute; cylinder rated 2,265.3477 surface L at 3,000 PSI. One cylinder supplies the diver.
Surface-equivalent RMV
12.5853 L/min
Pressure SAC
16.6667 PSI/min
Matches the baseline.
The relationship: Pressure SAC = pressure used / time / ATA. RMV = pressure SAC × rated surface volume / rated pressure.
Keep in mind: A single test does not predict stressed breathing. Gauge errors, pressure/temperature changes and cylinder specifications affect the estimate.
More missing gas takes longer to replace; higher free-air delivery reduces ideal fill time.
What stays fixed: Rated free-air capacity 2,265.3477 L at 3,000 PSI. Target 3,000 PSI. Delivery fraction fixed at 80%.
Time at entered 80% delivery fraction
23.5974 min
Required free air
1887.7898 L
Matches the baseline.
The relationship: Required free air = capacity × (target−start)/rated pressure; time = required air / free-air delivery.
Keep in mind: Compressor free-air delivery is not piston displacement or compressed-line volume flow. Cooling, duty cycles, filters and permitted fill rates are not modeled.
The relationship: Surface-equivalent use = surface RMV × absolute pressure × time. Stage demands add.
Keep in mind: Direct open-water ascent only; no decompression, overhead or gas switches. The entered RMV is an illustration, not a sufficient emergency breathing allowance.
Gas fractions and depth determine partial pressures; different gases change nitrogen exposure and narcotic comparisons.
What stays fixed: Nitrox: oxygen plus nitrogen balance, no helium; seawater 33 ft/atm. MOD ceiling 1.4 atm; END treats O₂ + N₂ as narcotic.
Oxygen partial pressure
1.2897 atm
Theoretical MOD at 1.4 atm
111.375 ft
Maximum oxygen fraction at this depth
34.7368 %
Nitrogen-equivalent air depth
81.481 ft
END if both O₂ and N₂ are narcotic
100 ft
Matches the baseline.
The relationship: PO₂ = FO₂ × ATA. MOD = (1.4/FO₂−1)×33. EAD = [(1−FO₂)×ATA/0.79−1]×33.
Keep in mind: These are separate comparisons, not a complete dive plan. EAD is not a decompression schedule. Negative EAD is mathematical, not a usable table depth. END depends on the chosen narcosis assumption.
At the same pressure and temperature, a lower mixture molar mass gives lower ideal gas density.
What stays fixed: Oxygen fixed 18%; helium variable; nitrogen balance. Temperature 20°C; seawater 33 ft/atm. END assumes O₂ + N₂ narcotic, He nonnarcotic.
Ideal gas density at depth
3.4057 g/L
Equivalent narcotic depth
53.45 ft
Oxygen partial pressure
0.7255 atm
Matches the baseline.
The relationship: ρ = Pabsolute × mixture molar mass/(R × Tkelvin). END compares narcotic fractions with air.
Keep in mind: Lower density alone does not establish a suitable breathing gas. Oxygen exposure, surface suitability and decompression need separate checks.
Not a Clinical or HIPAA Secure Interface. Always double-check your work, the system for leaks and clinically correlate. These idealized demonstrations do not provide clinical treatment, filling, rigging or decompression instructions.
Formulas, examples & assumptions
Content updated October 10, 2026 · Created by Bryan Fleck. Independently verify measurements and scoring assumptions.
Absolute pressure and kelvin
Gas equations use absolute pressure and temperature in kelvin. Kelvin = Celsius + 273.15; absolute pressure = gauge pressure + local ambient pressure.
Boyle’s law holds gas amount and temperature fixed; Charles’s law holds gas amount and pressure fixed. Each lesson states its assumptions.
Laws versus applications
Henry’s law describes equilibrium solubility; Graham’s law describes molecular effusion. Fick’s diffusion law and the Fick cardiac-output principle are different relationships.
A model that explains a trend does not supply an equipment procedure, clinical decision or decompression schedule.
