Gas Pressure at Depth Calculator
Calculate absolute and gauge pressure at any depth using P = ρgh + P_atm.
Returns pressure in PSI, bar, atm, and kPa for scuba and hydraulic engineering.
Boyle’s Law describes the inverse relationship between the pressure and volume of a gas at constant temperature. As pressure increases, volume decreases proportionally, and vice versa. This principle is fundamental to pneumatics, diving, and respiratory physiology.
Boyle’s Law Formula: P₁ × V₁ = P₂ × V₂
Rearranged forms:
- Find new pressure: P₂ = (P₁ × V₁) ÷ V₂
- Find new volume: V₂ = (P₁ × V₁) ÷ P₂
Ideal Gas Law (full relationship): PV = nRT
What each variable means:
- P₁, P₂: initial and final pressure (Pa, kPa, atm, or psi)
- V₁, V₂: initial and final volume (liters, m³, or cubic feet)
- n: number of moles of gas
- R: universal gas constant = 8.314 J/(mol·K)
- T: temperature in Kelvin (K = °C + 273.15)
Pressure unit conversions:
- 1 atm = 101.325 kPa = 14.696 psi = 760 mmHg = 760 torr
Worked example: A gas occupies 4.0 L at 2.0 atm. The pressure is increased to 5.0 atm. What is the new volume?
V₂ = (P₁ × V₁) ÷ P₂ = (2.0 × 4.0) ÷ 5.0 = 8.0 ÷ 5.0 = 1.6 L
Real-world applications:
- SCUBA diving: At 10 m depth (2 atm), a 6-liter breath of air from the surface would compress to 3 liters.
- Tire inflation: Increasing pressure in a fixed-volume tire forces more gas molecules in, Boyle’s Law at fixed V.
- Syringe: Pulling the plunger back increases volume, decreasing pressure and drawing fluid in.
- Breathing: Diaphragm expands lung volume → pressure drops below atmospheric → air flows in.