Last updated: 2026-07-01

Understanding Charles's law

Charles's law describes how a fixed amount of gas expands when it is warmed and contracts when it is cooled, as long as the pressure stays constant. It is one of the simple gas laws that together build up to the ideal gas law, and it captures a familiar effect: warm air takes up more room than the same air when cold.

The Charles's law formula

At constant pressure the volume of a gas is directly proportional to its absolute temperature. Rearranging the relationship lets you solve for whichever of the four quantities is unknown:

Always use absolute temperature

Charles's law is a direct proportion, so it is only valid on a temperature scale that begins at true zero. The Celsius and Fahrenheit scales place their zero points arbitrarily, so ratios taken on them are physically meaningless — warming a gas from 10 °C to 20 °C does not double its volume, even though the Celsius number doubled.

The Kelvin scale starts at absolute zero (−273.15 °C), so a doubling of kelvin corresponds to a genuine doubling of volume. Convert every temperature to kelvin before applying the law: $T(\text{K}) = T(^{\circ}\text{C}) + 273.15$. This calculator accepts Celsius or Fahrenheit and performs the conversion to kelvin before taking the ratio.

Worked example

A balloon holds 2.0 L of air at 27 °C. It is carried outside on a cold day and cools to −23 °C. What is its new volume at the same pressure?

First convert both temperatures to kelvin: 27 °C = 300.15 K and −23 °C = 250.15 K. Then apply the law:

The balloon shrinks to about 1.67 L. Notice that the ratio 250.15/300.15 is roughly 0.83, so the volume drops by about 17% — the same fraction as the drop in absolute temperature.

Where Charles's law appears

• A balloon left in a cold car looks underinflated, then swells again as it warms back up indoors.
• Bread and cakes rise in part because trapped gas expands as the oven heats it.
• A hot-air balloon lifts because heating the enclosed air expands it and lowers its density relative to the surrounding air.

Each of these happens at roughly constant pressure, which is what makes Charles's law the right description.

Charles's law and the other gas laws

Charles's law is the constant-pressure special case of the combined gas law, $P_1 V_1 / T_1 = P_2 V_2 / T_2$. Setting $P_1 = P_2$ cancels the pressure terms and leaves $V_1/T_1 = V_2/T_2$. Boyle's law is the constant-temperature case relating pressure and volume, and Gay-Lussac's law is the constant-volume case relating pressure and temperature. For a problem where pressure also changes, use the Combined Gas Law Calculator instead; when you need an absolute quantity such as the number of moles, use the Ideal Gas Law Calculator.