Gases expand when they warm and contract when they cool. Jacques Charles noticed in the 1780s that, at constant pressure, the change follows a strikingly simple rule: volume is proportional to temperature measured from absolute zero. This calculator solves Charles’s law for whichever of the four values you need, initial or final volume or temperature, converts any temperature scale to kelvin, and plots the straight line that runs from absolute zero through both states.
How to use the Charles’s law calculator
- Under Solve for, choose the initial volume, initial temperature, final volume or final temperature.
- Enter the known volumes in L, mL, m³, cm³, ft³, in³ or US gallons.
- Enter the known temperatures in °C, °F, K or °R. Every temperature must be above absolute zero.
- Pick the unit of the answer.
- Read the result, the percentage volume change, the constant V ÷ T, the volume the sample would have at 0 °C and the change per degree. The graph shows volume against kelvin temperature.
Charles’s law formula
Convert first: T(K) = T(°C) + 273.15, or T(K) = (T(°F) − 32) × 5/9 + 273.15. Pressure and the amount of gas must stay constant; a balloon or a piston that is free to move keeps the pressure equal to the surroundings.
Worked example
A balloon in the freezer
A party balloon holds 2.5 L of air at room temperature, 25 °C, and is placed in a freezer at −18 °C.
Convert: T1 = 298.15 K, T2 = 255.15 K.
V2 = 2.5 L × 255.15 ÷ 298.15 = 2.139 L
The balloon loses 0.36 L, or 14.4% of its volume. The rubber's own tension changes the inside pressure slightly, so a real balloon shrinks a little differently.
Finding a temperature. How hot must the same 2.5 L of air get to fill 3.0 L? Solve for the final temperature: T2 = 298.15 × 3.0 ÷ 2.5 = 357.78 K = 84.6 °C.
Fahrenheit inputs. One liter of air heated from 68 °F to 212 °F (20 °C to 100 °C) expands to 1.273 L, a 27.3% increase, because 373.15 K ÷ 293.15 K = 1.273.
Volume of 1 L of gas at other temperatures
| Temperature | Kelvin | Volume (from 1 L at 0 °C) |
|---|---|---|
| −40 °C | 233.15 K | 0.854 L |
| 0 °C | 273.15 K | 1.000 L |
| 25 °C | 298.15 K | 1.092 L |
| 100 °C | 373.15 K | 1.366 L |
| 200 °C | 473.15 K | 1.732 L |
The changes are modest for everyday temperatures but add up: a hot-air balloon heated to about 100 °C holds roughly 21% less air than it would at 20 °C (293.15 ÷ 373.15 = 0.79), which is what makes it lighter than the air around it.
Where Charles’s law appears
Tires and footballs go soft on cold mornings, bread rises partly because the gas in the dough expands in the oven, and hot-air balloons fly because heated air is less dense. The straight-line V–T relationship was also the first clue to absolute zero: extrapolated lines for every gas meet at −273.15 °C. In reality, gases liquefy well before then, so the law applies only while the substance stays a gas.
For a change in pressure as well as temperature, use the combined gas law calculator. The Boyle’s law calculator covers constant-temperature changes, and the Celsius to Kelvin converter handles the temperature conversion on its own.
Frequently asked questions
What does Charles's law say?
At constant pressure, the volume of a fixed amount of gas is directly proportional to its absolute temperature: V₁/T₁ = V₂/T₂. Double the kelvin temperature and the volume doubles.
Why can't I use Celsius directly?
Because the proportionality is to absolute temperature. Heating a gas from 10 °C to 20 °C does not double its volume; in kelvin that is 283.15 K to 293.15 K, a 3.5% increase. Enter °C, °F or °R and the calculator converts to kelvin before solving.
How much does a gas expand per degree?
About 1/273 of its volume at 0 °C for every degree Celsius, which is 0.366% per degree. Relative to a gas at room temperature (298 K) it is about 0.34% per degree. The calculator lists the change per degree for your sample.
How did Charles's law lead to absolute zero?
Plotting volume against temperature for different gases gives straight lines that all point to zero volume at the same temperature, about −273 °C. That extrapolation suggested an absolute zero of temperature, now defined as 0 K = −273.15 °C. Real gases liquefy long before reaching it.
Why does a balloon shrink in the freezer?
Its gas cools at nearly constant pressure, so its volume falls in proportion to the kelvin temperature. A 2.5 L balloon at 25 °C shrinks to about 2.14 L at −18 °C, a 14% drop, and recovers when it warms up again.