Charles's Law Calculator
Find the final volume or final temperature of a gas at constant pressure using V1/T1 = V2/T2 with automatic Kelvin conversions.
Isobaric Gas State Transformation (Constant Pressure: P₁ = P₂)
V₂ = (V₁ × T₂) / T₁ V₂ = (2.0 L × 353.15 K) / 293.15 K = 2.4093 L This Charles's law calculator finds the final volume or final temperature of a gas when pressure and the amount of gas stay constant. Enter three of the four values (V1, T1, V2, T2), leave the unknown blank, and the tool solves V1/T1 = V2/T2 with full steps. It accepts L, mL, and m³ for volume and K, °C, and °F for temperature, and it converts every temperature to Kelvin automatically, so you avoid the most common error in gas law problems.
Quick Reference
| Item | Value |
|---|---|
| Formula | V1/T1 = V2/T2 |
| Relationship | Volume and absolute temperature are directly proportional |
| Held constant | Pressure and amount of gas (moles) |
| Solves for | V1, T1, V2, or T2 |
| Temperature scale required | Kelvin (K = °C + 273.15) |
What Is Charles's Law?
Charles's law is a gas law stating that the volume of a fixed amount of gas is directly proportional to its absolute temperature when pressure stays constant. If you double the Kelvin temperature of a gas, its volume doubles. If you cool it to half its Kelvin temperature, its volume halves.
The law is named after the French scientist Jacques Charles, who studied how gases expand when heated in the 1780s. Charles never published his results. The French chemist Joseph Louis Gay-Lussac published the relationship in 1802 and credited Charles for the original work, which is why the law carries Charles's name today. Charles is also known for launching the first hydrogen balloon flight in 1783, a few months before the Montgolfier brothers carried passengers in a hot air balloon.
Charles's law is one of the three classic gas laws, along with Boyle's law and Gay-Lussac's law. Together they form the combined gas law, and all of them follow from the ideal gas law.
Why the Law Works
According to the kinetic molecular theory, temperature measures the average kinetic energy of gas particles. Heating a gas makes its particles move faster, so they hit the container walls harder and more often. If the container can expand, such as a balloon or a piston cylinder, the gas pushes the walls outward until the pressure returns to its original value. The result is a larger volume at a higher temperature.
The Link to Absolute Zero
If you plot the volume of a gas against temperature in Celsius, the data forms a straight line. Extending that line back, it reaches zero volume at about −273.15 °C. That point is absolute zero, which is 0 K. Real gases condense into liquids before reaching it, but the extrapolation is the reason the Kelvin scale exists and why gas laws must use it.
Charles's Law Formula
The formula is:
You can also write it as V/T = k, where k is a constant for a given gas sample at a given pressure.
Where the Formula Comes From
Start with the ideal gas law:
Rearrange it to isolate V/T:
When the amount of gas (n) and pressure (P) are constant, and R is the universal gas constant, nR/P is a constant. That means V/T is the same in the initial and final states:
Variable Table
| Variable | Meaning | Common Units |
|---|---|---|
| V1 | Initial volume | L, mL, m³ |
| T1 | Initial absolute temperature | K |
| V2 | Final volume | L, mL, m³ |
| T2 | Final absolute temperature | K |
How to Use This Charles's Law Calculator
Select what to solve for
Choose V1, T1, V2, or T2.
Enter the three known values
Fill in the initial volume, initial temperature, and one final value.
Pick the units
Choose L, mL, or m³ for volume, and K, °C, or °F for temperature.
Click Calculate
The tool converts temperatures to Kelvin, rearranges V1/T1 = V2/T2, and returns the missing value.
Read the steps
Check the substituted equation to see how the answer was found.
Run a sense check
If temperature went up, volume must have gone up. If temperature went down, volume must have gone down.
What Can This Calculator Calculate?
Final volume (V2)
How much space a gas occupies after it is heated or cooled.
Final temperature (T2)
The temperature a gas must reach to fill a target volume.
Initial volume (V1)
The starting volume when you know the final state.
Initial temperature (T1)
The starting temperature when you know the final state.
If pressure and volume change together at constant temperature, use the Boyle's Law Calculator. If pressure and temperature change at constant volume, use the Gay-Lussac's Law Calculator. If all three change, use the Combined Gas Law Calculator.
Why Temperature Must Be in Kelvin
Charles's law only works with absolute temperature. The Kelvin scale, named after Lord Kelvin (William Thomson), starts at absolute zero, where particle motion is at its minimum. Celsius and Fahrenheit have arbitrary zero points, so using them gives wrong ratios. For example, going from 10 °C to 20 °C looks like a doubling in Celsius, but in Kelvin the change is only from 283.15 K to 293.15 K, about 3.5%. Gas volume follows the Kelvin change.
Convert to Kelvin with these formulas:
| Celsius | Fahrenheit | Kelvin |
|---|---|---|
| 0 °C | 32 °F | 273.15 K |
| 20 °C | 68 °F | 293.15 K |
| 25 °C | 77 °F | 298.15 K |
| 37 °C | 98.6 °F | 310.15 K |
| 100 °C | 212 °F | 373.15 K |
Charles's Law Rearranged Formulas
Each variable can be isolated with one step of algebra. Keep all temperatures in Kelvin.
| Solve For | Formula |
|---|---|
| Final volume | V2 = (V1 × T2) / T1 |
| Final temperature | T2 = (V2 × T1) / V1 |
| Initial volume | V1 = (V2 × T1) / T2 |
| Initial temperature | T1 = (V1 × T2) / V2 |
Charles's Law Examples
Solve for Final Volume (V2)
Problem: A balloon holds 2.0 L of air at 27 °C. It is heated to 127 °C at constant pressure. Find the new volume.
The Kelvin temperature increased by one third, so the volume increased by one third.
Solve for Final Temperature (T2)
Problem: A gas occupies 5.0 L at 20 °C. At what temperature will it occupy 6.0 L at constant pressure?
Cooling a Gas
Problem: A 500 mL gas sample at 25 °C is cooled to 0 °C at constant pressure. Find the new volume.
The volume drops by about 8.4% because the Kelvin temperature drops by the same fraction. The mL unit carries through because both volumes use the same unit.
Fahrenheit Input
Problem: A 3.0 L gas sample at 68 °F is heated to 104 °F at constant pressure. Find the final volume.
Solve for Initial Volume (V1)
Problem: A gas ends at 8.0 L and 400 K after being heated at constant pressure. It started at 300 K. What was the initial volume?
Charles's Law Units
Volume
| Unit | Equivalent |
|---|---|
| 1 L | 1000 mL |
| 1 mL | 1 cm³ |
| 1 L | 1 dm³ |
| 1 m³ | 1000 L |
Use the same volume unit for V1 and V2. Because the law is a ratio, volume units cancel, and any consistent pair works.
Temperature must be in Kelvin (K). Convert from Celsius or Fahrenheit before calculating, or let the calculator do it for you.
Pressure is not in the formula, but it must stay constant. This is called an isobaric process.
Charles's Law Graph: The Direct Relationship
Plotting volume against absolute temperature gives a straight line that passes through the origin. This is what "directly proportional" means. The slope of the line depends on the pressure and the amount of gas. A lower pressure gives a steeper line, because the same temperature rise produces a larger volume increase.
| Kelvin Temperature Change | Volume Change |
|---|---|
| Temperature doubles | Volume doubles |
| Temperature halves | Volume halves |
| Temperature increases by 10% | Volume increases by 10% |
| Temperature drops to one third | Volume drops to one third |
Plotting volume against Celsius temperature also gives a straight line, but it does not pass through the origin. It crosses the temperature axis at −273.15 °C, which is why Kelvin is needed for ratio calculations.
Real-World Examples of Charles's Law
Hot air balloons
Burners heat the air inside the envelope, which expands and becomes less dense than the surrounding air, creating lift.
Inflated balloons in cold weather
A balloon left in a freezer shrinks because the air inside contracts as it cools.
Car tires and basketballs
Cold air lowers the volume or pressure of the air inside, so a ball feels softer on a winter day.
Baking
Gas bubbles in dough expand in the oven as they heat, helping bread rise.
Weather balloons
Temperature changes with altitude affect balloon volume along with pressure changes.
Engines
Hot combustion gases expand and push pistons.
When Can You Use Charles's Law?
Use Charles's law when all of the following are true:
Constant pressure
The process is isobaric, such as a gas in a flexible container open to the atmosphere.
Constant amount of gas
No gas is added, removed, or lost, and nothing reacts.
A gas sample
The law applies to gases, not liquids or solids.
Absolute temperature
Both temperatures are expressed in Kelvin.
Charles's Law vs Other Gas Laws
| Gas Law | Formula | Held Constant | Relationship |
|---|---|---|---|
| Charles's law | V1/T1 = V2/T2 | Pressure, moles | Volume and temperature are directly related |
| Boyle's law | P1V1 = P2V2 | Temperature, moles | Pressure and volume are inversely related |
| Gay-Lussac's law | P1/T1 = P2/T2 | Volume, moles | Pressure and temperature are directly related |
| Avogadro's law | V1/n1 = V2/n2 | Pressure, temperature | Volume and moles are directly related |
| Combined gas law | P1V1/T1 = P2V2/T2 | Moles | All three change together |
| Ideal gas law | PV = nRT | None | Links P, V, T, and moles |
Common Charles's Law Mistakes
| Mistake | Why It Fails | Fix |
|---|---|---|
| Using °C or °F | Gas laws need absolute temperature | Convert with K = °C + 273.15 |
| Letting pressure change | Charles's law needs constant pressure | Use the combined gas law instead |
| Swapping T1 and T2 | Puts the initial temperature in the final slot | Label all four values before solving |
| Swapping V1 and V2 | Inverts the volume ratio | Pair each volume with its temperature |
| Unit mismatch for volume | mL and L in the same equation break the ratio | Convert to one unit first |
| Treating the relationship as inverse | Volume and temperature move in the same direction | Remember: hotter means larger |
| Changing the amount of gas | Moles must stay constant | Use the ideal gas law |
| Rounding too early | Small errors grow through the calculation | Keep extra digits and round at the end |
Charles's Law FAQs
Frequently asked questions about isobaric gas behavior, absolute zero, Kelvin temperature ratios, and balloon physics.
What is Charles's law?
Charles's law states that the volume of a fixed amount of gas is directly proportional to its absolute temperature at constant pressure. The formula is V1/T1 = V2/T2.
What is the formula for Charles's law?
The formula is V1/T1 = V2/T2, where V1 and T1 are the initial volume and temperature, and V2 and T2 are the final volume and temperature in Kelvin.
How do you use a Charles's law calculator?
Enter any three of the four values (V1, T1, V2, T2), choose your units, leave the unknown blank, and click Calculate. The tool converts temperature to Kelvin and returns the missing value with steps.
Why must temperature be in Kelvin for Charles's law?
Kelvin is an absolute scale that starts at absolute zero. Gas volume is proportional to absolute temperature, so Celsius and Fahrenheit give incorrect results.
What does directly proportional mean in Charles's law?
It means that when one quantity increases, the other increases by the same factor. Doubling the Kelvin temperature doubles the volume.
Who discovered Charles's law?
Jacques Charles discovered the relationship in the 1780s but did not publish it. Joseph Louis Gay-Lussac published it in 1802 and credited Charles.
What is an isobaric process?
An isobaric process is one in which pressure stays constant. Charles's law describes gas behavior during an isobaric change.
What units can I use for Charles's law?
Any volume unit works if it matches between the initial and final states. Common choices are liters and milliliters. Temperature must be in Kelvin, though the calculator accepts Celsius and Fahrenheit and converts them.
What is absolute zero and why does it matter here?
Absolute zero is 0 K (−273.15 °C), the lowest possible temperature. Extending the Charles's law line to zero volume points to this value, which is why the Kelvin scale is used for gas laws.
Is Charles's law accurate for real gases?
It is accurate for real gases at low to moderate pressure and temperatures well above their boiling points. Near condensation, real gases deviate from ideal behavior.
How is Charles's law related to the combined gas law?
Charles's law is the special case of the combined gas law where pressure is constant. Setting P1 = P2 in P1V1/T1 = P2V2/T2 gives V1/T1 = V2/T2.
Why does a balloon shrink in the cold?
Cooling lowers the average kinetic energy of the gas particles, so they push less on the balloon walls. The balloon contracts until the internal pressure matches the outside pressure again.