Charles' Law Calculator
Solve V₁/T₁ = V₂/T₂ for any missing volume or temperature at constant pressure. Leave one field blank, enter the other three, and get an instant result with full step-by-step working.
Charles' Law Solver
What Is Charles' Law?
Charles' Law describes how gas volume responds to temperature when pressure is held steady. As you heat a gas, its molecules move faster and collide with the walls of their container more forcefully; if the container is free to expand (like a balloon or a piston that can slide), the gas pushes outward until pressure returns to the surrounding level, and volume grows to accommodate the extra molecular motion.
The relationship is a direct proportion: V₁/T₁ = V₂/T₂, always using absolute (Kelvin) temperature. Plotted on a graph of volume against temperature, this traces a straight line that, if extended, would reach zero volume exactly at absolute zero (0 K), the theoretical basis for the Kelvin scale itself.
Charles' Law is the constant-pressure case of the combined gas law. If pressure changes too, use the full combined gas law calculator on the homepage instead.
Volume rises in a straight line with absolute temperature. The line would hit zero volume at 0 K.
Real-World Examples of Charles' Law
The same balloon holds less volume in the cold and more once warmed, at roughly the same pressure.
A hot air balloon is Charles' Law put to work directly: heating the air inside the envelope makes it expand and become less dense than the cooler air outside, generating lift. No pressure difference is needed. Just the volume change that comes from a temperature change at roughly constant (atmospheric) pressure.
A car tire after a long highway drive feels firmer partly because the air inside has warmed from friction. Though tires are a closed, rigid volume, so this example is closer to Gay-Lussac's Law. A better everyday illustration of Charles' Law itself is a party balloon brought from a warm room out into cold winter air: it visibly shrinks as the gas inside cools and contracts.
In the lab, Charles' Law is used to predict how much a fixed mass of gas in a piston-cylinder apparatus will expand when heated, which is foundational to understanding engines, weather balloons, and industrial gas storage systems.
How the Calculator Works
Worked Example: Charles' Law in Practice
Problem: A hot air balloon envelope holds 2,200 m³ of air at 15°C before heating. What volume would the same mass of air occupy once heated to 100°C, at constant (atmospheric) pressure?
In a real hot air balloon, the envelope's physical volume is actually fixed by its fabric, so instead of the volume growing, some of the original air is pushed out through the open bottom as it heats and expands, lowering the average density of the air remaining inside and generating lift. This calculation shows how much volume that heated air would occupy if it were free to expand, which is the volume of air effectively displaced.
Common Mistakes When Applying Charles' Law
By far the most common error is plugging a Celsius or Fahrenheit temperature directly into V₁/T₁ = V₂/T₂ without converting to Kelvin first. Since the relationship is a direct proportion, using a non-absolute scale gives a completely wrong ratio. For example, treating 20°C as if it were "twice" 10°C, when in absolute terms 293.15 K is nowhere near twice 283.15 K. Always convert with K = °C + 273.15 before substituting anything.
A second mistake is assuming Charles' Law applies when pressure is not actually constant, for instance, a gas heated inside a container that is simultaneously being squeezed or released to a different external pressure. If pressure changes at all during the process, Charles' Law alone will not capture the full picture, and you should use the combined gas law instead.
A third pitfall is confusing volume ratios with temperature ratios when rearranging the formula. A common algebra slip is writing V₂ = V₁T₁/T₂ instead of the correct V₂ = V₁T₂/T₁. A quick sanity check: heating a gas at constant pressure should always increase its volume, so if your rearranged formula predicts a decrease when T₂ > T₁, you've almost certainly inverted the ratio.