Quick answer
Charles's law says V₁ ÷ T₁ = V₂ ÷ T₂ for a fixed amount of gas at constant pressure, with temperature in kelvin. A gas of 2 L at 300 K heated to 450 K expands to 3 L.
Enter any three of the four values and leave one blank. The calculator returns the missing value.
Related tools: Boyle's Law Calculator: P₁V₁ = P₂V₂ at constant temperature. Coulomb's Law Calculator: Electrostatic force between two point charges. Density Calculator: Solve mass, density or volume.
How to use the Charles's Law Calculator
- Optionally, enter initial volume (V₁) (L) (above 0).
- Optionally, enter initial temperature (T₁) (K) (above 0).
- Optionally, enter final volume (V₂) (L) (above 0).
- Optionally, enter final temperature (T₂) (K) (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Initial volume (V₁) (optional) | A number, in L. Leave exactly one blank | > 0 |
| Initial temperature (T₁) (optional) | A number, in K. Leave exactly one blank | > 0 |
| Final volume (V₂) (optional) | A number, in L. Leave exactly one blank | > 0 |
| Final temperature (T₂) (optional) | A number, in K. Leave exactly one blank | > 0 |
Formula and method
Formula
V₁ ÷ T₁ = V₂ ÷ T₂
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 volume (V₁) = 2; Initial temperature (T₁) = 300; Final temperature (T₂) = 450.
| Result | Value |
|---|---|
| Final volume | 3 L |
Example 2
Inputs: Initial volume (V₁) = 5; Final volume (V₂) = 10; Final temperature (T₂) = 600.
| Result | Value |
|---|---|
| Initial temperature | 300 K |
The first line is the headline result (final volume). IEEE-754 double precision; shown to at most 6 decimal places.
Worked example
V₂ = V₁ × T₂ ÷ T₁ = 2 × 450 ÷ 300 = 3 L. Volume is proportional to absolute temperature, so a 50% rise in kelvin gives 50% more volume.
Use kelvin
Temperatures must be absolute: K = °C + 273.15. Using Celsius gives wrong answers, since 20 °C is not twice 10 °C. For pressure changes use Boyle's law, and the combined gas law when both vary.
How the result changes with initial volume
Holding every other input at the first worked example, this table changes only initial volume. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Initial volume | Final volume |
|---|---|
| 1 | 1.5 L |
| 2 | 3 L |
| 4 | 6 L |
| 8 | 12 L |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Initial volume (V₁): entering "1" shows "Leave exactly one field blank." beside that field and no result.
Choosing between the Charles'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 |
|---|---|---|
| [Boyle's Law Calculator](/science/boyles-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 volume (V₁) to confirm this.
Frequently asked questions
What is 27 °C in kelvin?
27 °C + 273.15 = 300.15 K, usually rounded to 300 K.
Why must temperature be absolute?
Volume extrapolates to zero at absolute zero.
Who discovered it?
Jacques Charles, around 1787.
What does the Charles's Law Calculator calculate?
V₁/T₁ = V₂/T₂ at constant pressure. It returns Final volume.
What formula does the Charles's Law Calculator use?
V₁ ÷ T₁ = V₂ ÷ T₂. Leave one value blank to solve for it.
What do I need to enter in the charles's Law Calculator?
You enter . Optional: Initial volume (V₁) (L), Initial temperature (T₁) (K), Final volume (V₂) (L) and Final temperature (T₂) (K).
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 charles's Law result?
With initial volume (V₁) 2, initial temperature (T₁) 300 and final temperature (T₂) 450, the final volume is 3 L.
Where does the method come from?
The method follows: Charles's law (Gay-Lussac, 1802).
Related calculators
- Boyle's Law Calculator — P₁V₁ = P₂V₂ at constant temperature.
- 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
- Charles's law (Gay-Lussac, 1802)
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.