Combined Gas Law Calculator

Free Combined Gas Law Calculator

This Combined Gas Law Calculator solves for final pressure, final volume, or final temperature whenever a fixed amount of gas moves from one set of conditions to another and more than one property changes at the same time. Enter the starting state, fill in whichever two of the three final values you already know, and the calculator works out the missing one using P₁V₁/T₁ = P₂V₂/T₂. Every answer comes with the full rearrangement, the substitution, the final calculation, three useful ratios, and a labelled two-state diagram so the before-and-after picture is easy to follow.

This calculator is built for chemistry and physics homework, laboratory write-ups, gas-cylinder estimates, and general thermodynamics revision. It assumes a fixed, unchanging amount of ideal gas throughout. If the number of moles is changing too, because gas is being added, removed, or produced by a reaction, the ideal gas law PV = nRT is the better tool. Quick-fill buttons for common starting conditions are included below to save you retyping the same numbers for practice problems.

What Is the Combined Gas Law?

The combined gas law is P₁V₁ / T₁ = P₂V₂ / T₂. It brings together Boyle's Law, which relates pressure and volume at constant temperature, and Charles's Law, which relates volume and temperature at constant pressure, into one formula that works when pressure, volume, and temperature can all move at once. The only requirement is that the amount of gas present, the number of moles, stays exactly the same between the two states being compared.

Because three quantities can change together, the combined gas law is genuinely more useful than Boyle's or Charles's Law on their own for most real situations, where heating a container rarely leaves either pressure or volume perfectly fixed. This calculator lets you solve for whichever of the three final quantities is unknown, so the same formula covers all three common question types.

Solving for Final Pressure

When the final volume and final temperature are known but final pressure is not, the combined gas law rearranges to P₂ = P₁V₁T₂ / (T₁V₂). This is the first mode of this calculator, and it answers the common question of what pressure a gas will reach once it has been compressed, heated, or both, given a known starting pressure, volume and temperature.

A rising temperature pushes the final pressure up, while a shrinking final volume also pushes it up, so when both happen together the pressure increase can be substantial. This is exactly the situation behind warnings on aerosol cans and gas cylinders about keeping them away from heat.

Worked Example: Final Pressure

A gas starts at 101.325 kilopascals, occupies 2 litres, and is at 20 degrees Celsius. It is then heated to 100 degrees Celsius and compressed down to 1.5 litres. Converting both temperatures to kelvin gives T₁ = 293.15 K and T₂ = 373.15 K. Substituting into P₂ = P₁V₁T₂ / (T₁V₂) gives P₂ = 101.325 × 2 × 373.15 divided by 293.15 × 1.5, which comes out to approximately 171.7 kilopascals.

This result makes physical sense: the gas ended up hotter and in a smaller container, so its particles are moving faster and hitting the walls more often within a smaller space, both of which push pressure higher. The calculator's diagram places state 1 and state 2 side by side so this kind of comparison is easy to see at a glance.

Solving for Final Volume

When the final pressure and final temperature are known but final volume is not, the formula rearranges to V₂ = P₁V₁T₂ / (T₁P₂). This is the second mode of this calculator, useful for predicting how much space a gas will take up after both its pressure and temperature have changed, such as gas expanding as it moves from a high-pressure cylinder into a lower-pressure line while also warming up.

A rising temperature tends to expand the gas, pushing final volume up, while a rising pressure tends to compress it, pushing final volume down. Because both effects can happen at once and in opposite directions, the calculator's step-by-step working is especially useful here, since it is easy to guess the wrong overall direction without actually doing the substitution.

Worked Example: Final Volume

Suppose a gas starts at 150 kilopascals, occupies 1.5 litres, and is at 80 degrees Celsius. It then expands into a larger space where the pressure drops to 101.325 kilopascals and the temperature falls to 20 degrees Celsius. Converting to kelvin gives T₁ = 353.15 K and T₂ = 293.15 K. Using V₂ = P₁V₁T₂ / (T₁P₂), the new volume is 150 × 1.5 × 293.15 divided by 353.15 × 101.325, which works out to approximately 1.84 litres.

Here the falling pressure pushes the volume up, while the falling temperature pushes it back down, and the two effects partly cancel, leaving a final volume only modestly larger than the starting 1.5 litres. Working through the substitution, rather than guessing, is the only reliable way to see how two competing changes combine.

Solving for Final Temperature

When the final pressure and final volume are known but final temperature is not, the formula rearranges to T₂ = P₂V₂T₁ / (P₁V₁). This is the third mode of this calculator, and it is the version most often needed when a gas is compressed or expanded under conditions where the resulting temperature is exactly what a lab measurement or a safety check is trying to find.

Because temperature is what comes out of this rearranged formula in kelvin, this calculator automatically subtracts 273.15 to show a Celsius reading as well, since kelvin values are rarely how a temperature change is described outside a physics classroom.

Worked Example: Final Temperature

A gas cylinder holds gas at 100 kilopascals, 2 litres, and 20 degrees Celsius. The gas is then transferred into a smaller 1.5-litre space where the pressure rises to 169.7 kilopascals, and the final temperature needs to be found. Converting the starting temperature to kelvin gives T₁ = 293.15 K. Using T₂ = P₂V₂T₁ / (P₁V₁), the calculation is 169.7 × 1.5 × 293.15 divided by 100 × 2, which comes out to approximately 373.1 K, or about 99.9 degrees Celsius.

This example is effectively the reverse of the earlier final-pressure worked example, and getting back to almost exactly 100 degrees Celsius is a useful check that the combined gas law is self-consistent no matter which of the three quantities is treated as the unknown.

How the Combined Gas Law Relates to Boyle's, Charles's, and Gay-Lussac's Laws

The combined gas law is really a combination of three simpler, named relationships, and it reduces to each of them whenever one quantity happens to stay fixed. If temperature is constant, the equation reduces to Boyle's Law, P₁V₁ = P₂V₂. If pressure is constant, it reduces to Charles's Law, V₁/T₁ = V₂/T₂. If volume is constant, it reduces to Gay-Lussac's Law, P₁/T₁ = P₂/T₂.

Because real problems rarely hold one quantity perfectly fixed on purpose, the combined gas law is usually the more practical starting point, since it works correctly whether one, two, or all three quantities are changing between the two states. Choosing one of the three named laws instead only makes sense when a problem specifically states that a particular quantity is being held constant.

Absolute Pressure and Absolute Temperature

The combined gas law needs both pressure and temperature to be absolute values, not gauge readings. Absolute pressure is measured from a true vacuum, while a gauge, such as a tyre pressure gauge, usually reads relative to atmospheric pressure and needs about 101.325 kilopascals added to convert it to an absolute value before it can be used correctly in this formula.

Absolute temperature, measured in kelvin, is required for the same underlying reason: the formula is built around a scale that starts at absolute zero, where particle motion is at its practical minimum. Using a Celsius value directly, without adding 273.15 first, produces a result that is wrong in a way that is easy to miss, since the arithmetic still runs and produces a number, just the wrong one.

Units and Conversions

This calculator accepts pressure in kilopascals and volume in litres, which is convenient for most classroom and laboratory problems. Common conversions worth remembering are that one atmosphere equals 101.325 kilopascals, and one litre equals 0.001 cubic metres. Whatever units are used for pressure and volume, the same units must be used consistently for both state 1 and state 2, or the ratios will be meaningless.

Temperature always needs converting to kelvin before it enters the formula, regardless of which units are used for pressure and volume, since kelvin is the one non-negotiable unit in every gas law calculation. This calculator performs that conversion automatically from a Celsius input, and displays both the kelvin and Celsius values in the results and the diagram.

Real Gases Versus Ideal Gases

Every formula on this page describes an ideal gas, meaning the gas particles are treated as point-like objects with no volume of their own and no attractive or repulsive forces between them. Real gases behave very close to this ideal model at low pressure and high temperature, when particles are spread far apart and interact with each other only briefly during collisions.

Near the point where a gas would condense into a liquid, typically at high pressure or low temperature, real gases deviate from what the combined gas law predicts, because molecular size and intermolecular attraction start to matter. Engineers working with compressed or refrigerated gases often use more advanced equations of state to account for these effects. This calculator's results are a strong estimate for typical classroom and laboratory conditions, not a substitute for real-gas corrections in demanding engineering work.

Common Mistakes in Combined Gas Law Problems

The single most common error is forgetting to convert one or both Celsius temperatures to kelvin before substituting them into the formula. Because this formula uses two separate temperatures, it is easy to convert one and forget the other, which produces an answer that looks plausible but is still wrong.

Another frequent mistake is mixing pressure or volume units between state 1 and state 2, for instance entering the starting pressure in kilopascals and the final pressure in atmospheres without converting one of them first. A third common error is trying to apply the combined gas law when the amount of gas has actually changed, such as a leak, a gas-producing reaction, or venting gas from a container; in those situations, the ideal gas law PV = nRT, which explicitly accounts for moles, is the correct tool instead.

How to Use This Calculator

Choose which final quantity you need to find: pressure, volume, or temperature. Fill in the starting pressure, volume, and temperature, either by typing them directly or by clicking one of the quick-fill starting-condition buttons, then fill in the two known final quantities. The results panel, ratio values, diagram, and full step-by-step working all update instantly as you type.

This calculator is designed for education, revision, and general estimation. It does not replace container or vessel engineering calculations, industrial process design, or safety assessments involving pressurised or flammable gases. Any situation involving real gas storage, heated sealed containers, or hazardous materials should be handled according to qualified professional guidance and official safety standards rather than a general-purpose online tool.

Combined Gas Law Calculator FAQ Summary

The combined gas law is P₁V₁/T₁ = P₂V₂/T₂, and it applies whenever a fixed amount of gas moves between two states where pressure, volume, and temperature may all change. Rearranged forms give P₂ = P₁V₁T₂/(T₁V₂) for final pressure, V₂ = P₁V₁T₂/(T₁P₂) for final volume, and T₂ = P₂V₂T₁/(P₁V₁) for final temperature. Always convert both temperatures to kelvin, keep pressure and volume units consistent between the two states, and switch to the ideal gas law if the amount of gas itself is changing rather than staying fixed.