Boyle's Law Calculator

Calculate pressure or volume of a gas at constant temperature using P₁V₁ = P₂V₂. Enter any three values to solve for the fourth.

Initial State
Final State

How to use

  • Choose what to solve for
    Select P₁, V₁, P₂, or V₂ from the dropdown. That field will be disabled — enter the other three.
  • Enter three known values
    Each value has its own unit selector. Mix and match pressure and volume units freely.
  • Use quick examples
    Load preset scenarios like scuba diving or a syringe to see Boyle's Law in action.
  • Constant temperature
    Boyle's Law assumes temperature is held constant (isothermal process). For temperature changes, use the Combined Gas Law.

Boyle's Law Formula

P₁V₁ = P₂V₂
At constant temperature and amount of gas
P₂ = P₁V₁ ÷ V₂
Find Final Pressure
V₂ = P₁V₁ ÷ P₂
Find Final Volume
P₁ = P₂V₂ ÷ V₁
Find Initial Pressure
V₁ = P₂V₂ ÷ P₁
Find Initial Volume

Pressure Unit Reference

UnitEqual to 1 atm
Pascal (Pa)101,325 Pa
Kilopascal (kPa)101.325 kPa
Bar1.01325 bar
Millibar (mbar)1,013.25 mbar
psi14.6959 psi
mmHg (Torr)760 mmHg
Atmosphere (atm)1 atm

What Is Boyle's Law?

Boyle's Law states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional — when one increases, the other decreases proportionally. The relationship is expressed as P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume. This law was formulated by Anglo-Irish chemist Robert Boyle in 1662 and was one of the first quantitative gas laws.

Real-World Applications

Boyle's Law applies in many everyday situations. Scuba diving tanks store compressed air at high pressure in small volumes — as a diver breathes, the regulator reduces pressure and gas expands to fill the lungs. Bicycle pumps compress air into a smaller volume, increasing pressure to inflate tyres. Syringes use the inverse relationship: pulling the plunger back increases volume and decreases pressure, drawing fluid in. Weather balloons expand as they rise into lower-pressure upper atmosphere. Internal combustion engines compress fuel-air mixtures before ignition.

Frequently Asked Questions

What are the limitations of Boyle's Law?

Boyle's Law applies strictly to ideal gases at constant temperature. Real gases deviate from ideal behavior at very high pressures or very low temperatures, where intermolecular forces and the finite volume of gas molecules become significant. At extreme conditions, equations like the Van der Waals equation provide more accurate results.

What is the difference between Boyle's Law and Charles's Law?

Boyle's Law relates pressure and volume at constant temperature (P₁V₁ = P₂V₂). Charles's Law relates volume and temperature at constant pressure (V₁/T₁ = V₂/T₂). Together with Gay-Lussac's Law (pressure and temperature at constant volume), they combine into the Combined Gas Law and the Ideal Gas Law (PV = nRT).

Why are pressure and volume inversely proportional?

Gas molecules exert pressure by colliding with container walls. If you reduce the volume of a container, the same number of molecules occupy a smaller space and collide with the walls more frequently — increasing pressure. If you increase the volume, molecules have more space, collide less frequently, and pressure drops. Temperature determines the speed of the molecules, so keeping it constant isolates the pressure-volume relationship.

What is standard atmospheric pressure?

Standard atmospheric pressure is defined as exactly 101,325 Pa (Pascals), equivalent to 1 atm, approximately 1.01325 bar, 760 mmHg (Torr), or 14.696 psi. This is the average pressure at sea level on Earth and is used as the reference point in many gas law calculations.

Related Calculators