Boyle's Law Calculator — P₁V₁ = P₂V₂
Boyle's Law states that at constant temperature the pressure and volume of a fixed amount of ideal gas are inversely proportional: P₁V₁ = P₂V₂. Enter any three of the four values — initial pressure, initial volume, final pressure and final volume — and the calculator solves for the fourth.
kPa
L
kPa
L
At constant temperature: P₁V₁ = P₂V₂ = 200 kPa·L
- 1
Constant k = P₁ × V₁
100 × 2 = 200At constant temperature, P × V is the same before and after compression. - 2
Final volume V₂ = k ÷ P₂
200 ÷ 200 = 1
How does this calculator work?
Boyle's Law: P₁V₁ = P₂V₂ at constant temperature. Doubling pressure halves volume, and vice versa. Enter any three of the four values (P₁, V₁, P₂, V₂) in any consistent units and the calculator solves for the fourth. The product P·V stays constant throughout the process.
Formula
How this is calculated
Boyle's Law (1662) describes how an ideal gas behaves when compressed or expanded at constant temperature (an isothermal process). Because the product P × V is constant throughout, doubling the pressure halves the volume and vice versa. The relationship is strictly valid for ideal gases — real gases deviate at high pressures or near the liquefaction point.
This calculator accepts any consistent pressure unit (kPa by default, but atm, Pa, psi or bar work equally well as long as both pressure inputs use the same unit) and any volume unit for both volumes. Solving for any of the four variables is equivalent — rearrange P₁V₁ = P₂V₂: P₁ = P₂V₂/V₁, V₁ = P₂V₂/P₁, P₂ = P₁V₁/V₂, V₂ = P₁V₁/P₂.
The particle animation scales the displayed density with the computed final pressure relative to the initial pressure, illustrating how the same number of molecules occupy less space at higher pressure. The calculation assumes a sealed container (constant amount of gas, n = const) and a thermostatic environment (constant temperature, T = const). For processes where temperature changes, use the combined gas law P₁V₁/T₁ = P₂V₂/T₂ instead.
Frequently asked questions
If you squeeze a gas into half the volume (and keep the temperature the same), its pressure doubles. Expand it to twice the volume and the pressure halves. Pressure and volume are inversely proportional: P × V = constant.
No, as long as you use the same unit for both pressure values and the same unit for both volume values. The constant k = P·V will carry the combined units (e.g. kPa·L or atm·mL), but the ratio P₂/P₁ and V₂/V₁ are dimensionless.
Boyle's Law is accurate for ideal gases at moderate pressures and temperatures well above the boiling point. At very high pressures, real gas molecules interact with each other and the law overestimates compressibility. Near the liquefaction temperature, the gas begins to condense and the law no longer applies.
Also known as
TG we-Calculate Editorial Team. (2026). Boyle's Law Calculator — P₁V₁ = P₂V₂ [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/boyles-law-calculator
TG we-Calculate Editorial Team. "Boyle's Law Calculator — P₁V₁ = P₂V₂." TG we-Calculate. 2026. https://we-calculate.com/calculator/boyles-law-calculator.
TG we-Calculate Editorial Team, "Boyle's Law Calculator — P₁V₁ = P₂V₂," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/boyles-law-calculator
@misc{wecalculate_boyles_law_calculator, title = {Boyle's Law Calculator — P₁V₁ = P₂V₂}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/boyles-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
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