Boyle's Law Calculator

Apply Boyle's Law (P1V1 = P2V2) to find how a gas's volume changes with pressure, assuming constant temperature and a fixed amount of gas.

Quick Facts

Formula
P1V1 = P2V2 (constant temperature)
Pressure and volume of a fixed gas amount are inversely proportional when temperature stays constant.

Your Results

Calculated
Final volume (V2)
-
Solved from P1V1 = P2V2
Boyle's constant (k)
-
k = P1V1 = P2V2
Volume change (ΔV)
-
V2 minus V1
Process type
-
Compression or expansion

Ready

Enter P1, V1, and P2, then press Calculate.

Understanding Boyle's Law

Boyle's Law describes how a gas behaves when you change its pressure or volume while keeping its temperature and the amount of gas fixed. Discovered by Robert Boyle in 1662, it says that pressure and volume move in opposite directions: squeeze a gas into a smaller space and its pressure rises; let it expand and its pressure falls. The relationship is precise, not just directional — the product of pressure and volume stays constant.

The formula

Boyle's Law is written P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the pressure and volume after the change. Because the product PV is constant (call it k), any one unknown can be found once the other three values are known:

  • Solving for final volume: V2 = (P1 × V1) / P2
  • Solving for final pressure: P2 = (P1 × V1) / V2
  • Boyle's constant: k = P1 × V1 = P2 × V2, which stays fixed for that sample of gas at that temperature

This calculator takes your initial pressure, initial volume, and final pressure, then solves for the final volume — the most common version of the problem in chemistry and physics courses.

Working with units

  • Pressure must be absolute pressure, not gauge pressure — a tire gauge reading 0 psi is actually at roughly 1 atm absolute, since it measures pressure above atmospheric.
  • Use consistent units on each side of the equation: if P1 and P2 are both in atmospheres, the result is unaffected by switching the pair to kPa or mmHg, as long as both pressures use the same unit.
  • The same logic applies to volume — liters, milliliters, or cubic meters all work as long as V1 and V2 (or the V2 you're solving for) share one unit.

Limits of Boyle's Law

Boyle's Law assumes an ideal gas: a fixed amount of gas, constant temperature (an isothermal process), and no phase change. It closely matches real gases — air, helium, nitrogen — at everyday pressures and temperatures. It breaks down at very high pressure or very low temperature, where intermolecular attractions and the physical volume of gas molecules become significant, and near the point where the gas would condense into a liquid.

Frequently Asked Questions

What is Boyle's Law?
Boyle's Law states that for a fixed amount of gas held at constant temperature, pressure and volume are inversely proportional: P1V1 = P2V2. If you compress a gas into a smaller volume, its pressure rises by the same factor; if you let it expand, its pressure falls.
What units does this calculator use?
Results are labeled in atmospheres (atm) for pressure and liters (L) for volume. Boyle's Law is unit-agnostic as long as both pressures share one unit and both volumes share one unit, so you can enter kPa or mmHg for pressure, or mL or cubic meters for volume, and the ratio still holds.
Does Boyle's Law apply to real gases?
It closely approximates real gases at ordinary pressures and temperatures, away from the point of condensation. At very high pressure or low temperature, intermolecular forces and molecular volume become significant and real gases deviate from the ideal P1V1 = P2V2 relationship.
Can this calculator solve for pressure instead of volume?
This tool solves for the final volume given both pressures and the initial volume. To find a different variable, rearrange the same formula: P2 = (P1 × V1) / V2, or P1 = (P2 × V2) / V1, then divide by hand using your known values.

Related calculators