The Charles's law calculator above handles the relationship between the volume of a gas and its absolute temperature when pressure is held constant. Heat a fixed quantity of gas without letting the pressure change and its volume rises in direct proportion to its absolute temperature; cool it and the volume falls the same way. Enter any three of the four quantities and the tool returns the fourth, converting your temperatures to kelvin first so the proportion is taken on the scale where it is actually true.
Arb Digital builds free calculators that make the failure modes visible rather than silently producing a plausible wrong answer. Almost every mistake with this law is a temperature-scale mistake, so this page shows both kelvin values alongside the result and states the boundary against its neighbours: Boyle's law holds temperature constant and varies pressure, while the combined gas law calculator lets pressure, volume and temperature all change at once.
What This Charles's Law Calculator Does
It solves the proportion V₁/T₁ = V₂/T₂ in all four directions. The default mode finds the final volume after a temperature change, which is the question most people arrive with. The reverse modes are just as useful: find the temperature that would produce a required volume, or work backwards from a measured expansion to the starting conditions.
Volume units cancel out of the ratio, so litres, millilitres, cubic metres and cubic feet all give the same numerical answer as long as both volumes use the same one. Temperature units emphatically do not cancel, which is why the tool converts before it divides and then reports both absolute values in the result grid. If you can see 298.15 K and 373.15 K on screen, the ratio 1.2516 stops looking mysterious.
The result grid also gives the volume ratio and the absolute change, because those are frequently what the question is really about. A container that expands by half a litre may or may not matter; a gas whose volume rises by twenty-five per cent almost certainly does.
How to Use It
- Choose which quantity is unknown. The hero label names it, so there is never doubt about which figure was computed.
- Enter the two volumes you know, in a single unit. Mixing litres and millilitres between the two fields will produce a wrong answer that looks perfectly reasonable.
- Enter the temperatures and pick their scale. Celsius, kelvin and Fahrenheit are all accepted and all converted internally.
- Read the kelvin values in the grid. They are the numbers the proportion actually used, and checking them catches most input errors immediately.
- Check the assumption still holds. Constant pressure and a fixed amount of gas are required; if either changes, this is the wrong equation.
The Formula: How Charles's Law Is Calculated
At constant pressure and constant amount of gas, volume is directly proportional to absolute temperature: V ∝ T, so V₁/T₁ = V₂/T₂. Rearranged for the common case, V₂ = V₁ × T₂/T₁. OpenStax University Physics Volume 2, section 2.1 on the molecular model of an ideal gas, sets out this proportionality alongside Boyle's law and states plainly that the temperature must be expressed in kelvin and the pressure must be absolute pressure.
Work the defaults. A 2.000 L sample at 25 °C is at 298.15 K, and heating it to 100 °C takes it to 373.15 K. The temperature ratio is 373.15 ÷ 298.15 = 1.25155, so the final volume is 2.000 × 1.25155 = 2.5031 L. The volume rose by 25.16 per cent, exactly matching the rise in absolute temperature. Had you divided 100 by 25 instead, you would have predicted 8 L — a fourfold error from one scale mistake.
Charles's law is not an independent law so much as one face of the ideal gas equation pV = nRT, in which R is the molar gas constant, given as 8.314 462 618 J mol−1 K−1 and exact in the NIST CODATA value for the molar gas constant. Hold p and n fixed and V/T must equal nR/p, a constant — which is precisely the statement above. Our ideal gas law calculator works the single-state version where the amount of gas is one of the quantities in play.
Why Kelvin, and Why Celsius Breaks the Proportion
A proportional relationship requires a scale with a true zero, where zero means none of the quantity. Absolute temperature has that: zero kelvin is the point at which the extrapolated volume of an ideal gas would vanish. Celsius does not — zero degrees Celsius is the freezing point of water, an arbitrary landmark, and a gas at that temperature has plenty of volume left.
The consequence is that ratios in Celsius are meaningless while differences are fine. Twenty degrees Celsius is not twice ten degrees Celsius in any physical sense, but a twenty-degree rise is a twenty-kelvin rise regardless of scale, because the two scales share a degree size. That is why the kelvin appears throughout gas calculations and why the temperature converter is worth keeping open beside them.
Fahrenheit adds a second problem: its degree is a different size, five-ninths of a kelvin. Both the offset and the scaling must be undone, which the tool does automatically. The definition of the kelvin itself is now fixed through the Boltzmann constant rather than through any material property, as described in the SI Brochure published by the BIPM.
What Constant Pressure Actually Requires
The law's condition is easy to state and easy to violate. Constant pressure means the gas is free to change volume against a fixed external pressure — a piston that moves, a balloon that stretches, a syringe with the plunger unrestrained. If the gas is instead sealed in a rigid container, its volume cannot change at all and heating raises the pressure instead. That is a different relationship entirely, and using this calculator for it will give an answer that has nothing to do with the experiment.
Even a balloon is only approximately constant-pressure, because the stretched rubber contributes its own pressure that varies with how inflated it is. For classroom-scale demonstrations the approximation is usually good enough; for anything where the number matters, check whether the confining pressure is genuinely fixed before trusting the result.
The amount of gas must also be constant. A leaking container, a reaction that produces or consumes gas, and a liquid that evaporates into the headspace all change the number of moles, and none of them are covered here. If moles are changing, you need the full ideal gas equation rather than a two-state ratio.
Where the Ideal Gas Assumption Starts to Fail
Charles's law describes an ideal gas: point-like particles with no attraction between them. Real gases follow it closely at ordinary temperatures and modest pressures, and depart from it as conditions approach liquefaction. Near the condensation point, intermolecular attraction pulls molecules together and the real volume falls below the prediction; at very high pressure the finite size of the molecules themselves pushes the volume above it.
Practically, this means the law works well for air in a room, for a balloon in a freezer, and for most laboratory work at atmospheric pressure. It works poorly for a gas close to its boiling point, for steam near saturation, and for anything under tens of atmospheres. The linear extrapolation to absolute zero that the law implies never actually happens, because every real gas condenses long before it gets there.
That extrapolation is nonetheless how absolute zero was first estimated. Plot the volume of a gas against Celsius temperature at constant pressure, extend the straight line down until volume reaches zero, and the intercept lands near −273 °C regardless of which gas you used. The universality of that intercept is the historical evidence that absolute temperature is a property of nature rather than of any particular substance.
How This Differs From the Neighbouring Gas Laws
The boundary in one sentence each. Charles's law fixes pressure and relates volume to temperature. Boyle's law fixes temperature and relates pressure to volume inversely. The combined gas law calculator fixes nothing but the amount of gas and handles all three quantities changing together, which makes it the tool to reach for when a real process changes both pressure and temperature. The ideal gas law calculator is different again: it is a single-state equation including the number of moles and the gas constant, rather than a comparison between two states.
Choose by asking what is held constant. If the container is open to the atmosphere and only the temperature changes, this page is the right one. If a pump or a piston is changing the pressure as well, use the combined law. If you need moles, mass or density, use the full ideal gas equation, with the molar mass calculator to get from grams to moles first.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Using Celsius or Fahrenheit in the ratio — the proportion only holds on an absolute scale, and this single error produces the largest mistakes in gas calculations.
- Mixing volume units between the two fields — the unit cancels only if both volumes use the same one, and a litre-to-millilitre mismatch is a factor of a thousand.
- Applying it to a rigid sealed container — with volume fixed, heating changes pressure instead, which is a different relationship.
- Forgetting that the amount of gas must be constant — leaks, evaporation and gas-producing reactions all invalidate the two-state comparison.
- Trusting it near condensation — real gases deviate from ideal behaviour as they approach liquefaction or very high pressure.
Related Free Tools From Arb Digital
For the constant-temperature case use the Boyle's law calculator, and when pressure and temperature both change use the combined gas law calculator. The ideal gas law calculator handles single-state problems involving moles, and the partial pressure calculator covers mixtures. Prepare inputs with the temperature converter, the volume converter and the molar mass calculator. The full free online tools hub lists everything.
Frequently Asked Questions
That the volume of a fixed amount of gas at constant pressure is directly proportional to its absolute temperature. Double the temperature in kelvin and the volume doubles; halve it and the volume halves.
Because proportionality needs a scale with a true zero. Celsius and Fahrenheit have arbitrary zero points, so their ratios carry no physical meaning even though their differences do. The tool converts before dividing.
Only for display. The law is a ratio, so the unit cancels as long as both volumes are expressed in the same one. Mixing units between the two fields, however, produces a wrong answer that looks plausible.
No. A rigid container fixes the volume, so heating raises the pressure instead. Charles's law requires the gas to be free to expand or contract against a constant external pressure.
Charles's law holds pressure constant and relates only volume and temperature. The combined gas law allows pressure, volume and temperature to change together, so it is the tool for processes where more than one of them moves.
Closely, at ordinary temperatures and modest pressures. Deviations grow as a gas approaches its condensation point or very high pressure, where intermolecular forces and molecular volume stop being negligible.
Because the air inside cools toward the freezer temperature while the outside pressure stays the same, so the volume falls in proportion to the drop in absolute temperature. The effect is real but smaller than intuition suggests, since the temperature change is small in kelvin.
This tool is provided for educational and estimating use. It assumes ideal gas behaviour with constant pressure and a fixed amount of gas, and does not model real-gas deviations, phase change or container elasticity.
