Boyle's Law Calculator (P₁V₁ = P₂V₂)
Boyle's Law Calculator (P₁V₁ = P₂V₂)
Boyle's law describes how a gas's pressure and volume are inversely related at constant temperature - squeeze a gas into half its volume and its pressure doubles, which is exactly why a bicycle pump gets harder to push as you compress the air inside. Choose the variable you need, enter the other three known values (an initial pressure/volume pair and one final value), and this calculator solves for the fourth, with a P-V curve showing both states.
- P₁V₁ = P₂V₂, so a gas at 2 atm occupying 4 L, compressed down to 2 L, reaches a pressure of P₂ = (2×4)/2 = 4 atm - the pressure doubled when the volume halved.
- This only holds at constant temperature - Boyle's law is a special case of the more general ideal gas law (PV=nRT) where temperature and the amount of gas don't change, only pressure and volume trade off against each other.
- The P-V graph below is a hyperbola - as volume increases, pressure drops off increasingly slowly, which is why compressing an already-small volume of gas takes much more force than compressing a large one by the same amount.
How do I use Boyle's law to find a new pressure?
Use P₂ = P₁V₁ / V₂. A gas at 2 atm and 4 L, compressed to 2 L, reaches P₂ = (2×4)/2 = 4 atm.
Does Boyle's law apply if the temperature changes?
No - Boyle's law strictly assumes constant temperature and a fixed amount of gas. If temperature also changes, you need the combined gas law or the full ideal gas law (PV=nRT) instead.
Boyle's Law Calculator (P₁V₁ = P₂V₂)
Boyle's law describes how a gas's pressure and volume are inversely related at constant temperature - squeeze a gas into half its volume and its pressure doubles, which is exactly why a bicycle pump gets harder to push as you compress the air inside. Choose the variable you need, enter the other three known values (an initial pressure/volume pair and one final value), and this calculator solves for the fourth, with a P-V curve showing both states.
- P₁V₁ = P₂V₂, so a gas at 2 atm occupying 4 L, compressed down to 2 L, reaches a pressure of P₂ = (2×4)/2 = 4 atm - the pressure doubled when the volume halved.
- This only holds at constant temperature - Boyle's law is a special case of the more general ideal gas law (PV=nRT) where temperature and the amount of gas don't change, only pressure and volume trade off against each other.
- The P-V graph below is a hyperbola - as volume increases, pressure drops off increasingly slowly, which is why compressing an already-small volume of gas takes much more force than compressing a large one by the same amount.
How do I use Boyle's law to find a new pressure?
Use P₂ = P₁V₁ / V₂. A gas at 2 atm and 4 L, compressed to 2 L, reaches P₂ = (2×4)/2 = 4 atm.
Does Boyle's law apply if the temperature changes?
No - Boyle's law strictly assumes constant temperature and a fixed amount of gas. If temperature also changes, you need the combined gas law or the full ideal gas law (PV=nRT) instead.