Charles's Law Calculator

What Charles's law says

Charles's law describes gases that are free to expand. Hold the pressure steady and keep the amount of gas fixed, and the volume climbs or falls in step with the temperature on the Kelvin scale. Warm a gas and its molecules move faster, strike the walls harder, and push the container outward until the inside pressure matches the outside pressure again. Cool it and the opposite happens, with the gas taking up less room.

Jacques Charles measured the effect with hydrogen balloons in the 1780s but never published. Joseph Gay-Lussac set the law out in 1802 and credited Charles with the earlier work, which is why some older textbooks attach both names to it. The NASA Glenn pages on the gas laws tell that story alongside the equations.

Two cautions come with the definition. The law concerns a gas that can change size, so a sealed rigid tank does not qualify: heat that tank and the pressure rises instead, which is Gay-Lussac's pressure law. And the temperature must be absolute, measured in Kelvin, or the ratios compare the wrong things. The next section shows why.

The formula, and why the temperature must be in Kelvin

V1 / T1 = V2 / T2, with both temperatures in Kelvin and both volumes in the same unit. The law is often written as V / T = constant. Solving for a missing piece is one cross multiplication: V2 = V1 x T2 / T1, T2 = T1 x V2 / V1, and so on.

The Kelvin requirement is not a formality. Zero on the Celsius scale is the freezing point of water, not the point where a gas volume would vanish, so a ratio of Celsius readings has no physical meaning. Kelvin starts at absolute zero, where the law's straight line reaches zero volume, so a temperature ratio in Kelvin is a true ratio of the gas's thermal state. The NIST page on the kelvin explains how the unit is anchored.

To come from Fahrenheit, convert to Celsius first with (F - 32) x 5 / 9. A reading of 68 °F gives (68 - 32) x 5 / 9 = 20 °C, which is 293.15 K.

Each unknown has its own rearrangement, and all four come from the same cross multiplication. V2 = V1 x T2 / T1 solves for the final volume, V1 = V2 x T1 / T2 recovers the starting volume, T2 = T1 x V2 / V1 predicts where the temperature lands, and T1 = T2 x V1 / V2 works backward from a measured result. Keep the pairing straight: each volume sits over its own temperature, never mixed across the two states.

Worked example: a balloon warming up

A party balloon holds 2.50 L indoors at 20 °C, or 273.15 + 20 = 293.15 K. Carry it out on a 50 °C day and the gas inside warms to 273.15 + 50 = 323.15 K. The new volume is 2.50 x 323.15 / 293.15 = 2.76 L, a gain of about 0.26 L, or roughly 10 percent.

The rubber imposes little back pressure here, so the pressure inside stays close to atmospheric the whole time, which is exactly the constant pressure condition the law assumes. Run the same balloon the other way, into a freezer at -18 °C or 255.15 K, and it shrinks to 2.50 x 255.15 / 293.15 = 2.18 L.

Cooling down: the same rule in reverse

Run the algebra the other direction and the law predicts shrinking just as neatly. A 6.00 L flexible bag of air sits at 25 °C, or 298.15 K. Night falls and the temperature drops to -5 °C, which is 268.15 K. The volume becomes 6.00 x 268.15 / 298.15 = 5.40 L, so the bag gives up about a tenth of its size to the cold night air, with no leak involved.

Fahrenheit readings work the same once converted. A 4.00 L inflatable pool toy goes from 68 °F to 104 °F on a hot deck. Those readings are 20 °C and 40 °C, so 293.15 K and 313.15 K, and the volume becomes 4.00 x 313.15 / 293.15 = 4.27 L. The swing looks large in Fahrenheit degrees, but the Kelvin ratio 313.15 / 293.15 is a rise of only 6.8 percent, which is the number that sets the size change.

Absolute zero and the Kelvin scale

Extrapolate the straight line of volume against Celsius temperature backward and it crosses zero volume at -273.15 °C. That intercept is absolute zero, the floor of the Kelvin scale, and it is the reason the law takes Kelvin inputs. Doubling a Kelvin temperature doubles the volume; doubling the Celsius reading does not. A sample at 0 °C warmed until its Kelvin reading doubles sits at 2 x 273.15 = 546.30 K, which is 273.15 °C, and its volume has doubled too.

No real gas makes the full trip down. Helium, the last holdout, condenses near -269 °C, and every other gas turns liquid sooner, so measured points stop well above the intercept and the last stretch is an extrapolation. The intercept itself is genuine physics: measurements on different gases, extrapolated back, all agree on the same -273.15 °C, and that agreement is how the value was pinned down in the first place.

The cost of skipping the conversion is easy to see with numbers. Warm a sample from 10 °C to 20 °C and the Celsius ratio 20 / 10 suggests the volume doubles. In Kelvin the same day reads 283.15 K to 293.15 K, and 293.15 / 283.15 = 1.0353, an expansion of 3.5 percent. The Celsius answer is off by a factor of nearly 2, which is exactly the mistake the Kelvin rule exists to prevent.

When the law stops holding

Charles's law is a limiting case. It is accurate for gases at everyday temperatures and pressures and wrong at the edges, so it pays to know where the edges are.

Near condensation the picture changes. As a gas approaches the temperature where it turns liquid, its molecules attract one another and the volume falls faster than the law predicts. Steam on its way to water and refrigerants near their dew point both need real-gas corrections, not a two-value ratio.

A sealed rigid container breaks the constant pressure assumption outright. With no room to expand, heating raises the pressure instead of the volume, and Gay-Lussac's pressure law takes over the bookkeeping.

When pressure moves along with temperature, the combined gas law is the safe tool, since it reduces to Charles's law whenever P1 and P2 turn out to be equal.

Where you see it day to day

A basketball left outside on a cold night goes soft. The leather gives a little, so the volume drops with the temperature and the pressure dips along with it. The same effect deflates a pool ring on a cool morning and plumps it back up by noon, with no air added on either end. Bringing the object somewhere warm undoes the shrinkage, exactly as the law says.

Bakers meet the law in the oven, where gas pockets trapped in dough expand as the loaf heats and contribute to the spring in the first minutes of baking. Car tires show the pressure side of the story: their volume is nearly fixed, so the seasonal swing of 20 to 30 °C arrives as a pressure change instead of a size change, which is why tire pressure should be checked when the seasons turn.

For volume questions the calculator above handles the Kelvin conversions directly. To bring pressure and the amount of gas into the picture, the ideal gas law calculator covers all four variables at once, and the volume calculator works out container sizes before any heating starts.

How far the shortcut can be trusted

For ordinary air at room temperature and atmospheric pressure, the two-temperature ratio lands within a fraction of a percent of careful measurements, which is well inside the precision a balloon or a bag calls for. Three effects nudge real gases away from the textbook line: molecules take up a small share of the container space themselves, they attract one another slightly, and humid air behaves a touch differently from dry air. All three grow as the gas gets denser or colder, which is why the law is described as accurate for gases far from condensing.

A second limit is procedural rather than physical. The ratio assumes the amount of gas stays fixed, so a balloon that leaks, a bag that pops open, or a container that vents moisture will not follow the prediction no matter how carefully the temperatures are taken. Where the answer matters, take the temperatures in Kelvin, keep the sample sealed, and treat the result as the center of a small range rather than a guarantee. For most household questions the spread is smaller than the measurement error anyway.