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Charles's Law Calculator

Solve Charles's law, V₁/T₁ = V₂/T₂, to find a gas's volume or temperature when the pressure stays the same. Temperatures are converted to kelvins for you.

Level: Grades 10–11

Printable worksheet

Charles's Law Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Solve for
Temperature scale (both temperatures)

Converted to kelvins; it must be above absolute zero.

Converted to kelvins; it must be above absolute zero.

Result

Final volume (V₂)

2.5031 L

The final volume is 2.5031 L.

Volume change (V₂ − V₁)
0.5031 L
Constant V ÷ T
0.0067 L/K

See the step-by-step solution ↓

Step-by-step solution

  1. Put the starting temperature in kelvins, a scale that starts at absolute zero: add 273.15

    25 °C+273.15=298.15 K

  2. Put the final temperature in kelvins, a scale that starts at absolute zero: add 273.15

    100 °C+273.15=373.15 K

  3. Find the final volume V₂. Volume goes up in step with temperature, so multiply the starting volume by T₂ ÷ T₁

    2 L×373.15 K298.15 K=2.5031024652 L

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find how much a gas expands or shrinks when it warms up or cools down. Charles's law says that if the pressure and the amount of gas stay the same, its volume rises and falls in step with its absolute temperature. Absolute temperature is measured in kelvins, a scale that starts at absolute zero, the coldest possible temperature. Warm a balloon and it swells; chill it and it shrinks. Double the temperature in kelvins and the volume doubles too.

This calculator finds whichever of the four values you don't know. That can be the starting volume, the starting temperature, the final volume or the final temperature. You can work in Celsius, Fahrenheit or kelvins. The calculator turns each temperature into kelvins before using it, because the law only works on a scale that starts at absolute zero. Both volumes use one unit. You can choose liters, milliliters, cubic meters, cubic centimeters, cubic feet, cubic inches or US gallons.

Where it's used

Why this math matters outside the classroom:

  • Hot-air balloons. Balloon pilots heat the air in the envelope so it expands, pushing some out and making the balloon lighter than the air around it.
  • Chemistry labs. Chemistry students heat 2.0 L of gas from 300 K to 450 K at constant pressure and predict a new volume of 3.0 L.
  • Why kelvin matters. Students see why kelvin is needed: warming a gas from 10 °C to 20 °C raises its volume only about 3.5%, not 100%.
  • Freezer balloons. A balloon taken from a 25 °C room into a −18 °C freezer shrinks to about 86% of its volume.
  • Baking bread. Bakers rely on gas bubbles in dough expanding in the oven's heat, which helps a loaf rise as it bakes.

Grade level and standards: Grades 10–11; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose which value to solve for.
  2. Pick the volume unit and temperature scale used for both the starting and final gas.
  3. Enter the three values you know.
  4. Read the answer, along with the change in volume or temperature and the ratio V ÷ T, which stays constant.

What the inputs mean

Volume unit (both volumes)
The law compares two volumes, so the unit cancels out. Whatever unit you choose for the known volume is the unit of the answer.
Temperature scale (both temperatures)
Any scale works, but each temperature is turned into kelvins first. Putting Celsius straight into V₁/T₁ = V₂/T₂ is the most common mistake with this law.
Initial temperature (T₁)
Converted to kelvins; it must be above absolute zero.
Final temperature (T₂)
Converted to kelvins; it must be above absolute zero.

Formula and method

V₁ ÷ T₁ = V₂ ÷ T₂   (constant pressure and amount)
V₂ = V₁ × T₂ ÷ T₁
T₂ = T₁ × V₂ ÷ V₁
T(K) = T(°C) + 273.15

In the formulas, V₁ and T₁ are the starting volume and temperature, and V₂ and T₂ are the final ones. T(K) is a temperature in kelvins and T(°C) is the same temperature in Celsius.

The law comes from the ideal gas law, PV = nRT. There, P is pressure, n is the amount of gas, R is a fixed number (the gas constant), and V and T are volume and temperature. If P and n don't change, V ÷ T always equals nR ÷ P, which is a constant. So the ratio of volume to absolute temperature is the same before and after the change.

The temperatures must be absolute, because the law measures from absolute zero. Going from 10 °C to 20 °C doesn't double the volume. It raises the absolute temperature from 283.15 K to 293.15 K, an increase of only about 3.5%.

Worked example

A sealed syringe holds 2 L of air at 25 °C. It's warmed to 100 °C while the plunger moves freely, so the pressure stays constant. What is the new volume?

  1. Convert the temperatures: T₁ = 25 + 273.15 = 298.15 K and T₂ = 100 + 273.15 = 373.15 K.
  2. V₂ = V₁ × T₂ ÷ T₁ = 2 × 373.15 ÷ 298.15.
  3. V₂ = 2.5031 L.

Result: The air expands to about 2.503 L, an increase of roughly 0.503 L or 25%.

Understanding the result

The ratio V ÷ T stays fixed the whole time, so any volume and temperature pair on the same line follows the law. If you plot volume against temperature in kelvins, you get a straight line through zero.

In the nineteenth century, scientists extended that line backwards for real gases. That led them to the idea of an absolute zero near −273 °C, where an ideal gas would have no volume at all.

Assumptions and limitations

  • The pressure stays constant. Examples are a gas under a freely moving piston, or inside a loose, unstretched balloon.
  • No gas escapes or is added, and no chemical reaction takes place.
  • The gas behaves ideally, meaning it follows the simple gas laws exactly.
  • Real gases stray from the law near the point where they turn to liquid, and at high pressures. A gas will turn to liquid long before it reaches zero volume.
  • A rigid container can't change volume, so heating it raises the pressure instead. For that case, use Gay-Lussac's law or the ideal gas law.
  • If the pressure also changes, use the combined or ideal gas law instead.

Frequently asked questions

Why must temperatures be in kelvins?

Charles's law says volume and temperature rise and fall in step. That only works on a scale that starts at absolute zero. With Celsius, a gas at 0 °C would seem to have zero volume, which makes no sense. The calculator handles the conversion for you.

How is Charles's law different from Boyle's law?

Charles's law links volume and temperature when the pressure stays the same. Boyle's law links pressure and volume when the temperature stays the same. Both are special cases of the ideal gas law.

Does it work for any gas?

It works for any gas that behaves close to ideally. That includes air, nitrogen, oxygen, helium and carbon dioxide at everyday temperatures and pressures. The type of gas doesn't matter, only that the amount stays the same.

Why does a balloon shrink in the cold?

Taking a balloon from a 20 °C room into −10 °C air cuts its absolute temperature from 293.15 K to 263.15 K. Its volume falls by the same proportion, about 10%.

How this calculator is checked

Method: Charles's law V₁/T₁ = V₂/T₂ for an ideal gas at constant pressure and amount; K = °C + 273.15 and °C = (°F − 32) × 5/9 (exact). The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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