Gas Pressure at Depth Calculator

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.