Charles's Law Calculator

About the Charles's Law Calculator

Warm a gas and it expands; cool it and it shrinks. Charles's law describes exactly how much: at constant pressure, the volume of a fixed amount of gas is proportional to its absolute temperature. Double the temperature in kelvin and the volume doubles. It explains why a party balloon shrinks in the cold, why hot air balloons rise and why car tyres look a little flat on a frosty morning.

This Charles's law calculator solves V₁ ÷ T₁ = V₂ ÷ T₂ for the final volume, the final temperature, or either starting value. Temperatures can be entered in Celsius, kelvin or Fahrenheit; the calculator converts them to kelvin for the calculation, then converts the answer back into your chosen unit. It also shows the percentage change and checks that the two ratios match.

How to Use the Charles's Law Calculator

Choose which value to find: V₂, T₂, V₁ or T₁.

Enter the three values you know.

Choose the temperature unit — °C, K or °F — and the volume unit. Both volumes must use the same unit.

The Formula

  V₁ ÷ T₁ = V₂ ÷ T₂       (T in kelvin)

  V₂ = V₁ × T₂ ÷ T₁       T₂ = T₁ × V₂ ÷ V₁

  T(K) = T(°C) + 273.15
  T(K) = (T(°F) − 32) × 5 ÷ 9 + 273.15

Step-by-Step Examples

Heating a gas. Two litres of gas at 25 °C are heated to 100 °C at constant pressure.

  T₁ = 25 + 273.15 = 298.15 K
  T₂ = 100 + 273.15 = 373.15 K
  V₂ = 2 × 373.15 ÷ 298.15 = 2.5031 L

The gas grows by about 25 percent — not fourfold, as the Celsius numbers 25 and 100 might suggest.

A balloon in the freezer. A 5 L balloon at 20 °C is cooled to −18 °C.

  V₂ = 5 × 255.15 ÷ 293.15 = 4.3519 L

Doubling the volume. To double the volume of a gas starting at 0 °C (273.15 K), the absolute temperature must double to 546.3 K, which is 273.15 °C.

Why Temperature Must Be in Kelvin

Charles's law is a proportion, and proportions only work on a scale that starts at zero. The Celsius and Fahrenheit scales have arbitrary zero points — the freezing point of water and a cold winter's day in eighteenth-century Europe — so doubling a Celsius reading does not double anything physical. The kelvin scale starts at absolute zero, the lowest possible temperature, where an ideal gas would have no thermal motion. On that scale, doubling the number does double the average energy of the molecules and, at constant pressure, the volume. Forgetting to convert to kelvin is the most common mistake in gas law problems.

Why Gases Expand When Heated

Heating a gas makes its molecules move faster, so they hit the walls of the container harder and more often. If the container can stretch or has a movable piston, the gas pushes it outwards until the pressure inside again matches the pressure outside. At that point the gas occupies a larger volume at the same pressure. In a rigid container the volume cannot change, so the pressure rises instead — the relationship known as Gay-Lussac's law.

Charles's Law in Everyday Life

Hot air balloons are the classic example. Burners heat the air inside the envelope, which expands; some is pushed out through the opening at the bottom, so the air left inside is less dense than the cooler air outside. The difference in density creates lift. Tyres lose a few percent of their volume and pressure on a cold morning, which is why pressures should be checked when tyres are cold. Bread and cakes rise partly because gas bubbles in the dough expand as they heat in the oven. Even a table-tennis ball with a small dent can be restored by warming it in hot water, as the air inside expands and pushes the dent out.

Absolute Zero

When scientists in the eighteenth and nineteenth centuries plotted the volume of different gases against temperature, each gave a straight line. Extended backwards, all the lines pointed to zero volume at roughly the same temperature, about −273 °C. No real gas reaches that point, since gases turn to liquids long before, but the pattern suggested a natural lower limit for temperature. Absolute zero is now defined as exactly −273.15 °C, or −459.67 °F, and it is the zero point of the kelvin scale.

A Brief History

The law is named after the French physicist Jacques Charles, who studied it in the 1780s and was also a pioneer of hydrogen balloons. He did not publish his results; Joseph Louis Gay-Lussac published the relationship in 1802 and credited Charles's earlier work. In some countries it is known as Gay-Lussac's law, a name more often used today for the pressure–temperature relationship.

Understanding Your Result

The headline is the volume or temperature you asked for, in your chosen unit.

The temperatures in kelvin line shows both temperatures on the absolute scale.

The change line gives the percentage change in volume and the temperature ratio.

The check line shows that V₁ ÷ T₁ and V₂ ÷ T₂ are equal.

When Should You Use This Calculator?

Use it for physics and chemistry homework on the gas laws.

Use it to estimate how much a balloon, tyre or container of gas will expand or shrink.

Use it to understand why temperatures in gas calculations must be in kelvin.

Common Mistakes

Using Celsius directly. Always convert to kelvin first; the calculator does it for you.

Letting the pressure change. Charles's law assumes constant pressure.

Mixing volume units. Both volumes must use the same unit.

Entering a temperature below absolute zero. No temperature can be lower than 0 K.