Combined Gas Law Explained: One Equation for Pressure, Volume, and Temperature

Most chemistry students meet the gas laws as a stack of three rules with three names: Boyle's law, Charles's law, Gay-Lussac's law. Each comes with its own formula, its own diagram, its own flashcard. That framing makes them harder than they are. All three are the same relationship seen from three angles, and once you write that relationship down in full, the three names collapse into one equation you never have to memorize separately again.

That equation is the combined gas law:

P1V1 / T1 = P2V2 / T2

It says that for a fixed amount of gas, the quantity (pressure × volume ÷ absolute temperature) is the same in state 1 as it is in state 2. Squeeze the gas, heat it, move it to a higher altitude, and the individual values of P, V, and T all change. Their combination does not. That single invariant is enough to solve a huge range of problems.

What the equation actually relates

The combined gas law compares two states of one gas sample, the "before" and the "after." It is not describing a single snapshot. That distinction matters because it tells you when to reach for this equation instead of the ideal gas law calculator and its PV = nRT.

PV = nRT describes one absolute state and needs two extra pieces of information: the gas constant R and the amount n in moles. The combined gas law describes a change between two states of the same fixed sample, so n and R appear on both sides and cancel cleanly. You never need to know how much gas you have. You only need the ratio between where it started and where it ended up.

So the rule of thumb is simple. If a problem mentions moles or asks for an absolute pressure from scratch, use PV = nRT. If it describes a gas that goes from one condition to another and asks for a missing quantity, the combined gas law is the right tool, and it spares you a constant you were never given.

Why temperature has to be in Kelvin

This is the single most common way to get a wrong answer, so it deserves its own section. The equation divides by temperature. Division by temperature only behaves correctly when temperature is measured on an absolute scale that starts at true zero, which means Kelvin.

Celsius and Fahrenheit put their zero points in arbitrary places. Water freezing is a fine reference for everyday life, but it is not "no thermal energy." If you drop 25 into the equation because the gas is at 25 °C, you are telling the math that the gas is barely above absolute zero, and every ratio that follows is corrupted. The correct value is 298.15 K.

The conversion is one addition:

Kelvin = Celsius + 273.15

So 0 °C is 273.15 K, 25 °C is 298.15 K, and a balloon at −10 °C is sitting at 263.15 K. The combined gas law calculator ships with a built-in Celsius-to-Kelvin helper and an inline reminder for exactly this reason, because the algebra is the easy part and this conversion is where people lose marks. If you ever want to spot-check a temperature swap by hand, the temperature converter does the same job across all three scales.

The three classic laws fall right out

Here is the payoff for writing the full equation. Each of the three named laws is just the combined gas law with one quantity held constant.

Hold temperature constant, so T1 = T2. The temperatures cancel and you are left with P1V1 = P2V2. That is Boyle's law: at fixed temperature, pressure and volume are inversely proportional. Push the pressure up and the volume drops by the same factor.

Hold pressure constant, so P1 = P2. The pressures cancel and you get V1/T1 = V2/T2. That is Charles's law: at fixed pressure, volume rises in step with absolute temperature. Warm a gas and it expands.

Hold volume constant, so V1 = V2. The volumes cancel and you get P1/T1 = P2/T2. That is Gay-Lussac's law: at fixed volume, pressure rises with temperature. This is why a sealed aerosol can thrown into a fire can burst, and why a car tire reads higher pressure after a long highway run.

Three laws, one equation, three things you can hold still. You do not memorize them. You derive each one in two seconds by deciding which quantity stays the same.

A worked example: solve for the final volume

Let me work a problem the way I do when I'm sanity-checking the tool, because it shows how little you actually have to do.

A sealed syringe holds 2.0 L of gas at 1.0 atm and 300 K. You hold the plunger so the pressure stays at 1.0 atm, then warm the gas to 600 K. What is the new volume?

List what you know:

P1 = 1.0 atm, V1 = 2.0 L, T1 = 300 K
P2 = 1.0 atm, T2 = 600 K
V2 = the unknown

Rearrange P1V1/T1 = P2V2/T2 for V2:

V2 = (P1 × V1 × T2) / (T1 × P2)

Substitute:

V2 = (1.0 × 2.0 × 600) / (300 × 1.0) = 1200 / 300 = 4.0 L

The volume doubled, which is the answer you'd expect: pressure was constant, the absolute temperature doubled from 300 K to 600 K, so by Charles's law the volume doubles too. The combined gas law gives the same result without you having to recall that Charles's law exists. Feed those five numbers into the calculator, leave V2 blank, and you'll read 4 directly, with a shareable URL that reproduces the exact setup so a classmate can open the identical problem.

The first time I built this kind of solver, I was surprised how often the "hard" part was not the physics at all but keeping units straight and remembering to convert Celsius. That's why the tool refuses to be clever about it: one absolute-temperature rule, one unit per quantity pair, and the answer falls out.

Keeping units honest

One more practical point. The ratios only cancel when each quantity uses one consistent unit across both states. If V1 is in liters, V2 must be in liters. If P1 is in atmospheres, so is P2. The combined gas law does not care which unit you pick, only that you pick one and stay with it, because the units divide out of the ratio along with R and n.

That gives you freedom: pressures in kPa, mmHg, or atm all work, as long as both pressures match. If your inputs are in mismatched units, convert them first with a unit converter before they touch the equation, and you'll avoid the second most common error after the Kelvin mistake.

Put those two habits together: absolute temperature, consistent units. Get those right and the combined gas law is one of the most forgiving equations in introductory chemistry. It solves for any of the six quantities, it absorbs Boyle, Charles, and Gay-Lussac into a single expression, and it never asks you for the amount of gas. One equation, three laws, six solvable unknowns.

Made by Toolora · Updated 2026-06-13