Charles's Law Calculator
Charles's law says that at constant pressure the volume of a fixed amount of gas is directly proportional to its absolute (kelvin) temperature, so V₁/T₁ = V₂/T₂. Enter any three of the four values and leave the unknown blank to solve for it. Work in kelvin, Celsius or Fahrenheit, and optionally add a pressure to find how many moles of gas are present.
Formula
Worked example
A 1 L gas at 0 °C (273.15 K) is heated to 273.15 °C (546.3 K) at constant pressure. Solving for V₂: V₂ = V₁ × T₂/T₁ = 1 × 546.3/273.15 = 2 L. Doubling the kelvin temperature doubles the volume. At 1 atm the 1 L starting state holds n = PV/RT ≈ 0.0446 mol of gas.
What Charles's law describes
Charles's law is one of the simple gas laws and states that, for a fixed amount of gas held at constant pressure, the volume is directly proportional to the absolute temperature measured in kelvin. Written as a ratio it reads V₁/T₁ = V₂/T₂, which means the quantity volume divided by temperature has the same value before and after any change. Discovered by Jacques Charles in the 1780s and later published by Joseph Louis Gay-Lussac, it explains everyday observations such as a balloon expanding when warmed and contracting in the cold. Because the relationship is linear, doubling the kelvin temperature doubles the volume and halving it halves the volume.
Working in any temperature or volume unit
This calculator lets you enter temperatures in kelvin, Celsius or Fahrenheit and converts them to kelvin for you, because the proportionality only holds on an absolute scale that begins at absolute zero. To convert by hand, add 273.15 to a Celsius reading, or for Fahrenheit compute (°F − 32) × 5/9 and then add 273.15. The volume units, by contrast, can be litres, millilitres, cubic metres, cubic feet or gallons, because the units cancel within each ratio as long as both V₁ and V₂ use the same unit. If you solve for a temperature, the answer is given back in the scale you chose, so you never have to convert kelvin results manually.
Rearranging to solve any unknown
Because the law is a single equation linking four quantities, knowing any three lets you solve the fourth by simple algebra, which is exactly what this calculator does when you leave one field blank. To find a final volume, multiply the initial volume by the temperature ratio: V₂ = V₁ × T₂/T₁. To find a final temperature, scale the initial temperature by the volume ratio: T₂ = T₁ × V₂/V₁. The same cross-multiplication recovers either initial value. The calculator also reports the percent change in volume between the two states so you can see at a glance how much the gas expanded or contracted.
Optional: how many moles of gas are present
Charles's law on its own does not need the pressure, but if you switch on the moles option and supply a constant pressure, the calculator applies the ideal gas law n = PV/RT to report how many moles of gas the container holds. It uses the initial state (V₁ and T₁), converts your volume to cubic metres and your pressure to pascals, and divides by the universal gas constant R = 8.314 J per mole per kelvin times the kelvin temperature. This is handy for chemistry problems that ask both how a gas expands and how much of it there is. Pressure can be entered in atmospheres, kilopascals, bar, psi or millimetres of mercury.
Charles's law at constant pressure (starting from 1 L at 273.15 K)
| Temperature (°C) | Temperature (K) | Volume (L) |
|---|---|---|
| -100 | 173.15 | 0.634 |
| 0 | 273.15 | 1 |
| 100 | 373.15 | 1.366 |
| 200 | 473.15 | 1.732 |
| 273.15 | 546.3 | 2 |
Volume scales linearly with kelvin temperature; the ratio V/T stays fixed at about 0.00366 L/K.
Frequently asked questions
What is Charles's law in simple terms?
Charles's law says that if you keep the pressure of a fixed amount of gas constant, its volume changes in direct proportion to its absolute temperature in kelvin. Heat the gas and it expands; cool it and it contracts. Mathematically V₁/T₁ = V₂/T₂, meaning the ratio of volume to kelvin temperature is the same before and after the change. It is why a sealed balloon swells in warm air and shrinks when placed in a freezer.
Why do I have to use kelvin instead of Celsius?
The law only works on an absolute temperature scale that starts at absolute zero, and kelvin is that scale. Celsius and Fahrenheit place zero at arbitrary points, so dividing volumes by those temperatures gives wrong or even negative answers. This calculator converts Celsius (add 273.15) and Fahrenheit ((°F − 32) × 5/9 + 273.15) to kelvin for you, so you can enter temperatures in whichever scale you have and still get a correct result.
Can this calculator find the number of moles of gas?
Yes. Turn on the moles option and enter a constant pressure, and the calculator uses the ideal gas law n = PV/RT on the initial state. It converts your volume to cubic metres and your pressure to pascals, then divides by R = 8.314 J per mole per kelvin times the kelvin temperature. Charles's law itself does not require pressure, so this is an optional extra for chemistry problems that also ask how much gas is present.
How is Charles's law different from the combined gas law?
Charles's law assumes pressure stays constant and links only volume and temperature. The combined gas law, P₁V₁/T₁ = P₂V₂/T₂, lets pressure vary as well, so it accounts for all three state variables at once. If a problem holds pressure fixed, Charles's law is the simpler tool; if pressure changes between the two states, use the combined gas law or the full ideal gas law PV = nRT instead.