What this calculator does
Charles' law describes how a gas expands or contracts as its temperature changes, provided the pressure stays constant and nothing escapes the container. It states that volume divided by temperature is constant: V1/T1 = V2/T2, with temperature measured in kelvin, not Celsius. This calculator applies the charles law formula directly, solving for whichever side of that ratio you do not already know.
Charles' law is a special case of the more general ideal gas law, PV = nRT, with pressure and the amount of gas both held fixed. It is named after French physicist Jacques Charles, who documented the relationship in the 1780s. Enter a starting volume and temperature, then either a target temperature to find the resulting volume, or a target volume to find the resulting temperature.
The formula
The calculator converts both Celsius readings to kelvin by adding 273.15, since the V/T ratio only holds on an absolute temperature scale that starts at true zero. It then rearranges V1/T1 = V2/T2 to solve for whichever value you asked for, and converts the answer back to Celsius for the final temperature if that is what you solved for.
| Term | Meaning |
|---|---|
| V1, T1 | The initial volume and temperature of the gas, before the change. |
| V2, T2 | The final volume and temperature of the gas, after the change, at the same pressure. |
| Kelvin | The absolute temperature scale used in the calculation, equal to Celsius + 273.15, with 0 K being absolute zero. |
The inputs explained
| Field | What to enter |
|---|---|
| Initial volume (L) | The volume the gas starts at, in any consistent unit; only the ratio between V1 and V2 matters, so litres, millilitres or cubic metres all give the same percentage change. |
| Initial temperature (°C) | The starting temperature of the gas, in degrees Celsius. This is converted to kelvin automatically. |
| Solve for | Choose whether you know the final temperature and want the resulting volume, or know the final volume and want the resulting temperature. |
| Final temperature (used when solving for V2) (°C) | The temperature you are heating or cooling the gas to, used when solving for the final volume. |
| Final volume (used when solving for T2) (L) | The volume you want the gas to reach, used when solving for the final temperature. |
When to use it
Heating a gas in a flexible container
A balloon, piston or weather balloon at constant atmospheric pressure expands as it warms. Charles’ law gives the new volume directly from the temperature change, without needing to know the pressure or the amount of gas.
Working through a chemistry problem set
Charles’ law questions are a standard part of introductory gas-law coursework. Entering the known values checks a worked answer, or shows the working for one that only gives the final figure.
Estimating how much a gas sample will shrink on cooling
Cooling a fixed amount of gas at constant pressure shrinks its volume in direct proportion to the drop in absolute temperature, which the calculator shows as a new, smaller volume.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How does the volume of 2 litres of gas at 20°C change as it is heated?
The same 2-litre starting volume, heated to a range of final temperatures.
| Final temperature | Final volume (V2) | Final temperature (T2) |
|---|---|---|
| 30°C | 2.068 L | 303.15 K |
| 40°C | 2.136 L | 313.15 K |
| 60°C | 2.273 L | 333.15 K |
| 80°C | 2.409 L | 353.15 K |
| 100°C | 2.546 L | 373.15 K |
| 150°C | 2.887 L | 423.15 K |
What temperature is needed to shrink 5 litres of gas down to a target volume?
The same starting point, solved backwards for the temperature that gives a range of smaller final volumes.
| Target final volume | Final temperature (T2) | In kelvin |
|---|---|---|
| 4.5 L | -4.81 °C | 268.34 K |
| 4 L | -34.63 °C | 238.52 K |
| 3.5 L | -64.45 °C | 208.70 K |
| 3 L | -94.26 °C | 178.89 K |
| 2.5 L | -124.07 °C | 149.08 K |
| 2 L | -153.89 °C | 119.26 K |
Questions
What is Charles' law?
Charles' law states that at constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature: V1/T1 = V2/T2, with temperature in kelvin. Heating the gas expands it; cooling it contracts it.
What is the Charles' law formula?
The charles law formula is V1/T1 = V2/T2. Given any three of the four values, initial volume, initial temperature, final volume and final temperature, the fourth can be found by rearranging this equation.
Why does the calculator use kelvin instead of Celsius?
The V/T ratio in Charles’ law only stays constant on a scale where zero means zero volume, which is absolute zero, 0 K or -273.15°C. Celsius has an arbitrary zero point, so a Celsius-based ratio would not hold; the calculator converts to kelvin internally and only shows Celsius in the final answer for convenience.
How is Charles' law different from the general ideal gas law?
The ideal gas law, PV = nRT, covers pressure, volume, temperature and amount of gas all at once. Charles’ law is the special case where pressure and the amount of gas are both held fixed, leaving only volume and temperature to vary against each other.
For the full pressure-volume-temperature relationship, including changes in pressure or in the amount of gas, see the ideal gas law calculator.