Boyle's Law Calculator (P1V1 = P2V2)
Boyle's law links pressure and volume when temperature and the amount of gas stay the same. Choose the value to find and enter the other three.
Updated
Report a problem
Formula
P1 × V1 = P2 × V2 (constant temperature and amount of gas)
- Solve for each unknown:
V2 = P1 × V1 ÷ P2,P2 = P1 × V1 ÷ V2,V1 = P2 × V2 ÷ P1,P1 = P2 × V2 ÷ V1. - Conversions used: 1 atm = 101325 Pa, 1 bar = 100000 Pa, 1 mmHg = 101325 / 760 Pa, 1 L = 1000 mL = 0.001 m³.
- The product P × V is shown in joules (1 Pa × 1 m³ = 1 J).
Worked example
A 10 L sample of gas at 1 atm is compressed at constant temperature until the pressure is 2.5 atm.
- V2 = P1 × V1 ÷ P2 = 1 × 10 ÷ 2.5
- V2 = 4 L, a 60% decrease in volume.
- Check: 1 × 10 = 10 and 2.5 × 4 = 10 (in atm L), which is 1013.25 J.
Frequently asked questions
What does Boyle's law say?
At constant temperature, the pressure of a fixed amount of gas is inversely proportional to its volume: P1 × V1 = P2 × V2. Double the pressure and the volume halves.
How do I find the new volume after a pressure change?
Use V2 = P1 × V1 ÷ P2. A 10 L sample at 1 atm squeezed to 2.5 atm has V2 = 1 × 10 ÷ 2.5 = 4 L, a 60% drop in volume.
Do I have to convert units for Boyle's law?
Only to keep pressure in one unit and volume in one unit on both sides, since the ratio cancels them. This calculator converts to pascals and cubic metres for you, so 760 mmHg in 4 L compressed into 1 L gives 3040 mmHg.
What is the difference between Boyle's law and Charles's law?
Boyle's law holds temperature constant and relates pressure to volume. Charles's law holds pressure constant and relates volume to temperature. Use the combined gas law when all three change.
Why is the product P × V shown as joules?
Pressure times volume has the units of energy: 1 Pa × 1 m³ = 1 J. At 1 atm and 10 L the product is 101325 × 0.010 = 1013.25 J, and it stays the same on both sides of the equation.