Quick answer
Boyle's law says P₁V₁ = P₂V₂ for a fixed amount of gas at constant temperature. Compressing 2 L at 100 kPa to 200 kPa leaves 1 L.
Enter any three of the four values and leave one blank. The calculator returns the missing value.
Related tools: Charles's Law Calculator: V₁/T₁ = V₂/T₂ at constant pressure. Coulomb's Law Calculator: Electrostatic force between two point charges. Density Calculator: Solve mass, density or volume.
How to use the Boyle's Law Calculator
- Optionally, enter initial pressure (P₁) (kPa) (above 0).
- Optionally, enter initial volume (V₁) (L) (above 0).
- Optionally, enter final pressure (P₂) (kPa) (above 0).
- Optionally, enter final volume (V₂) (L) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Initial pressure (P₁) (optional) | A number, in kPa. Leave exactly one blank | > 0 |
| Initial volume (V₁) (optional) | A number, in L. Leave exactly one blank | > 0 |
| Final pressure (P₂) (optional) | A number, in kPa. Leave exactly one blank | > 0 |
| Final volume (V₂) (optional) | A number, in L. Leave exactly one blank | > 0 |
Formula and method
Formula
P₁ × V₁ = P₂ × V₂
IEEE-754 double precision; shown to at most 6 decimal places.
Leave one value blank to solve for it. Temperatures must be absolute (kelvin).
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Initial pressure (P₁) = 100; Initial volume (V₁) = 2; Final pressure (P₂) = 200.
| Result | Value |
|---|---|
| Final volume | 1 L |
Example 2
Inputs: Initial volume (V₁) = 3; Final pressure (P₂) = 150; Final volume (V₂) = 6.
| Result | Value |
|---|---|
| Initial pressure | 300 kPa |
The first line is the headline result (final volume). IEEE-754 double precision; shown to at most 6 decimal places.
Worked example
P₁V₁ = 100 × 2 = 200; with P₂ = 200, V₂ = 200 ÷ 200 = 1 L. Doubling the pressure halves the volume.
Conditions
Temperature and amount of gas must stay constant, and the gas should behave ideally. Pressure can be absolute only in the ideal gas laws. Use Charles's or the combined gas law when temperature changes.
How the result changes with initial pressure
Holding every other input at the first worked example, this table changes only initial pressure. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Initial pressure | Final volume |
|---|---|
| 50 | 0.5 L |
| 100 | 1 L |
| 200 | 2 L |
| 400 | 4 L |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Initial pressure (P₁): entering "1" shows "Leave exactly one field blank." beside that field and no result.
Choosing between the Boyle's Law Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Charles's Law Calculator](/science/charles-law/) | Final volume | |
| [Coulomb's Law Calculator](/science/coulombs-law-charge/) | charge 1, charge 2 and distance | Force |
| [Density Calculator](/science/density-calculator/) | Mass | |
| [Kinetic Energy Calculator](/science/kinetic-energy-calculator/) | mass and speed | Kinetic energy |
| [Speed Distance Time Calculator](/science/speed-distance-time-calculator/) | Distance |
Background: motion and mechanics
For constant acceleration the standard relations are v = u + at, s = ut + ½at², v² = u² + 2as and s = ½(u + v)t. Pick the equation that contains your three known quantities and the one you want. Use SI units (metres, seconds, kilograms, newtons, joules) throughout or the answer will be off by a factor.
These equations stop applying when acceleration changes during the motion, as with a rocket burning fuel; that needs calculus or numerical methods.
Assumptions and limitations
- Exactly one field blank
- Absolute temperature only for Charles's law
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for initial pressure (P₁) to confirm this.
Frequently asked questions
What is the relationship?
Pressure and volume are inversely proportional.
Who discovered it?
Robert Boyle, in 1662.
Does it work for liquids?
No. Boyle's law is for gases; liquids are nearly incompressible, so their volume barely changes with pressure.
What does the Boyle's Law Calculator calculate?
P₁V₁ = P₂V₂ at constant temperature. It returns Final volume.
What formula does the Boyle's Law Calculator use?
P₁ × V₁ = P₂ × V₂. Leave one value blank to solve for it.
What do I need to enter in the boyle's Law Calculator?
You enter . Optional: Initial pressure (P₁) (kPa), Initial volume (V₁) (L), Final pressure (P₂) (kPa) and Final volume (V₂) (L).
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Exactly one field blank.
What are the limits of this calculator?
Exactly one field blank. Absolute temperature only for Charles's law.
What is an example of a boyle's Law result?
With initial pressure (P₁) 100, initial volume (V₁) 2 and final pressure (P₂) 200, the final volume is 1 L.
Where does the method come from?
The method follows: Boyle R, A Defence of the Doctrine Touching the Spring and Weight of the Air (1662).
Related calculators
- Charles's Law Calculator — V₁/T₁ = V₂/T₂ at constant pressure.
- Coulomb's Law Calculator — Electrostatic force between two point charges.
- Density Calculator — Solve mass, density or volume.
- Kinetic Energy Calculator — Kinetic energy and momentum of a moving mass.
- Speed Distance Time Calculator — Solve distance, speed or time.
Sources
- Boyle R, A Defence of the Doctrine Touching the Spring and Weight of the Air (1662)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.