What Charles's law describes
Charles's law tells you how much a gas swells or shrinks when you change its temperature while holding the pressure fixed. Heat a sealed syringe of air with the plunger free to slide, and the plunger moves out; cool it, and the plunger moves in. The law puts a number on that movement: the volume of a fixed quantity of gas is directly proportional to its absolute temperature.
Because it is a proportionality, the two states of the gas share one constant. Write V₁/T₁ for the first state and V₂/T₂ for the second, set them equal, and you can find any one of the four quantities from the other three. That is all this calculator does — but it does the temperature conversion for you, which is where nearly every wrong answer comes from.
The law is one of the three simple gas laws that combine into the ideal gas law. Boyle's law fixes temperature and relates pressure to volume; Gay-Lussac's law fixes volume and relates pressure to temperature; Charles's law fixes pressure and relates volume to temperature. Multiply them together and you get PV = nRT, with Charles's law recovered by holding P and n constant.
Practical uses are everywhere a gas is heated or cooled at atmospheric pressure: a hot-air balloon envelope, a ventilation duct carrying warm supply air, a bag of gas sample warming from a cold-room to a bench, or a lab measurement corrected from room temperature to standard temperature. In each case the pressure stays at whatever the surroundings impose and only the temperature changes.
Why the temperature must be absolute
The single rule that makes Charles's law work is that T is measured on an absolute scale. Kelvin and Rankine qualify; Celsius and Fahrenheit do not.
Here is why. A proportionality V = kT is a straight line through the origin: at T = 0 the volume is zero. That statement is only meaningful on a scale whose zero is the true zero of thermal energy. On the Celsius scale, zero is the freezing point of water, which is a completely arbitrary point as far as a gas is concerned. If you used Celsius, the law would predict that a gas at 0 °C has zero volume and that a gas at −10 °C has a negative one.
The historical route to this insight is worth knowing, because it is how absolute zero was first estimated. Charles and later Gay-Lussac measured gas volume against Celsius temperature and found a straight line with a slope of about 1/273 of the volume at 0 °C per degree. Extrapolate that line back to zero volume and you land at roughly −273 °C. The modern kelvin fixes that offset at exactly 273.15.
So the conversion you perform before anything else is T(K) = T(°C) + 273.15, or T(K) = (T(°F) − 32) × 5/9 + 273.15, or T(K) = T(°R) × 5/9. Once both temperatures are in kelvin the ratio T₂/T₁ is the whole answer: multiply V₁ by it for the new volume, or multiply T₁ by V₂/V₁ for the new temperature.
A quick sanity check on the scale of the effect: heating air from 20 °C to 40 °C is a doubling in Celsius but only 293.15 K → 313.15 K in absolute terms, a 6.8% expansion. Anyone who expects the volume to double has used the wrong scale.
Worked example: 2.00 L of air heated from 25 °C to 100 °C
A 2.00 L gas syringe of dry air sits on a bench at 25 °C with the plunger free, so the gas stays at atmospheric pressure. You place it in a 100 °C oil bath. What volume does it reach?
- Convert both temperatures to kelvin. T₁ = 25 + 273.15 = 298.15 K. T₂ = 100 + 273.15 = 373.15 K.
- Form the absolute ratio. T₂ ÷ T₁ = 373.15 ÷ 298.15 = 1.251551.
- Multiply the starting volume by that ratio. V₂ = 2.00 L × 1.251551 = 2.5031 L.
- Check the direction. You heated the gas, the ratio is greater than 1, and the volume grew. If your answer had come out smaller than 2.00 L you would have inverted the ratio.
Now run it backwards to see the other mode. Suppose the syringe reads 2.50 L and you want to know the bath temperature. T₂ = T₁ × V₂ ÷ V₁ = 298.15 K × 2.50 ÷ 2.00 = 372.69 K, which is 99.5 °C. That is the same problem viewed from the other side, and it is exactly what happens if you select Final temperature T₂ above.
Notice how small the fractional change is compared with the Celsius change. The temperature rose by 75 Celsius degrees — a factor of four on that scale — but the volume rose by only 25%, because in absolute terms the change was 298.15 K to 373.15 K.
How to read the ratio and when the answer is trustworthy
The volume ratio V₂/V₁ is the number worth looking at, because it is identical to T₂/T₁ and it tells you immediately whether you have made a scale error. If you heated the gas and the ratio is below 1, or you cooled it and the ratio is above 1, the inputs are swapped. If the ratio is enormous — say 5 or more — for a modest-looking temperature change, you almost certainly typed Celsius values into a calculator expecting kelvin.
Rules of thumb that come straight from the arithmetic: near room temperature, air expands by about 0.34% per Celsius degree, because 1 ÷ 293 = 0.0034. A 10 °C swing is a 3.4% volume change. Going from 20 °C to 200 °C, a realistic flue-gas problem, gives 473.15 ÷ 293.15 = 1.614, a 61% expansion.
The result is trustworthy whenever the gas is far from condensing and the pressure is genuinely constant. Two conditions break it. First, if the container is rigid, the pressure is not constant and the volume cannot change — that is Gay-Lussac's law territory, and you should use the ideal gas law with V fixed instead. Second, near the boiling point of the gas the molecules interact strongly enough that the ideal-gas proportionality fails; steam near 100 °C at 1 atm and carbon dioxide near its critical point both misbehave.
Note also what stays constant that people forget: the amount of gas. If your system leaks, or if a reaction consumes or produces gas, n changes and Charles's law does not apply. Confirm the mass or the mole count is fixed before trusting the ratio.
Volume of 1.000 L of gas at 0 °C when heated at constant pressure
| Temperature (°C) | Temperature (K) | T₂/T₁ | Volume (L) |
|---|---|---|---|
| −100 | 173.15 | 0.6339 | 0.6339 |
| −50 | 223.15 | 0.8170 | 0.8170 |
| 0 | 273.15 | 1.0000 | 1.0000 |
| 20 | 293.15 | 1.0732 | 1.0732 |
| 25 | 298.15 | 1.0915 | 1.0915 |
| 50 | 323.15 | 1.1831 | 1.1831 |
| 100 | 373.15 | 1.3661 | 1.3661 |
| 200 | 473.15 | 1.7322 | 1.7322 |
| 300 | 573.15 | 2.0983 | 2.0983 |
| 500 | 773.15 | 2.8305 | 2.8305 |
The ratio and volume columns are numerically identical here only because V₁ is exactly 1.000 L at T₁ = 273.15 K. Change either and they part company.
Mistakes that produce a wrong answer
- Leaving the temperature in Celsius. The proportionality passes through the origin, so it needs a scale whose zero is absolute zero. Celsius values give nonsense, and negative Celsius values give negative volumes.
- Assuming the pressure is constant when the vessel is rigid. A sealed steel cylinder cannot expand. Heating it raises pressure, not volume, and Charles's law does not apply to it at all.
- Mixing volume units between the two states. V₁ in millilitres and V₂ in litres gives an answer wrong by a factor of 1,000. The unit selectors above normalise both to litres before dividing.
- Applying it to a gas near condensation. Within a few tens of kelvin of the boiling point the ideal-gas assumption breaks down and the measured expansion falls short of the prediction.
- Forgetting that the amount of gas must be fixed. A leaking syringe, an open flask, or a reaction that generates gas all change n, which sits outside the two-state ratio.
- Rounding 273.15 to 273 in precise work. It shifts a room-temperature answer by about 0.05%, which is invisible in a classroom problem and significant in a calibration.
Where Charles's law sits among the gas laws
Charles's law is the constant-pressure slice of a bigger relation. If both pressure and temperature change, use the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, which reduces to Charles's law when P₁ = P₂. If you also need the amount of substance — moles, mass, or density — go straight to PV = nRT with the ideal gas law calculator, which handles all four variables and reports molar volume and density.
For work where a gas is a solute rather than the whole system, the relevant tools change entirely: osmotic pressure uses the same RT product but for dissolved particles, and boiling point elevation and freezing point depression handle the phase-behaviour side of the same molecular picture.
One historical footnote that matters for laboratory conventions. Because gas volume depends so strongly on temperature, quoted gas volumes are meaningless without a stated reference state. IUPAC's standard temperature and pressure is 0 °C and 100 kPa, giving a molar volume of 22.711 L/mol; the older 0 °C and 1 atm convention gives 22.414 L/mol; and much industrial data is quoted at “normal” or “standard” conditions that vary by industry and country. Convert your own measurement to whichever reference your report demands, using exactly the ratio this calculator produces, and state which one you used.
Key terms
- Isobaric
- At constant pressure. Charles's law is the isobaric relation between volume and temperature; a free piston, a flexible balloon, or an open-to-atmosphere system are all isobaric.
- Absolute temperature
- Temperature measured from absolute zero. The kelvin (SI) and the Rankine (imperial) are the two absolute scales; K = °C + 273.15 and °R = °F + 459.67.
- Absolute zero
- 0 K, equal to −273.15 °C or −459.67 °F. The temperature at which the extrapolated volume of an ideal gas reaches zero; unreachable in practice.
- Combined gas law
- P₁V₁/T₁ = P₂V₂/T₂. The general two-state relation for a fixed amount of ideal gas, of which Charles's, Boyle's and Gay-Lussac's laws are the constant-T, constant-P and constant-V special cases.