Combined gas law calculator with worked examples

The combined gas law links the pressure, volume and temperature of a fixed amount of gas before and after a change: P₁V₁/T₁ = P₂V₂/T₂, with temperatures in kelvin. Squeeze 2.0 L of gas at 1.0 atm and 20 °C down to 1.0 L while it warms to 47 °C, and its pressure rises to 2.18 atm. This combined gas law calculator solves for the new pressure, volume or temperature, and converts °C and °F to kelvin for you.

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Gas Laws Calculator

Apply Boyle's law, Charles's law and the ideal gas equation

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How to use the combined gas law calculator

1. Open the Gas Laws Calculator. Under Calculate, choose Combined, then what to find: P₂, V₂ or T₂.
2. Type the starting state, Pressure 1, Volume 1 and Temperature 1, and the two values you know about the end state.
3. Pick each unit from its box: pressure in Pa, kPa, bar, atm, mmHg or psi, volume in cm³, mL, L or m³, and temperature in K, °C or °F. Temperatures are turned into kelvin automatically.
4. Read the answer, with the rearranged formula and your numbers in the steps. The extra result is the amount of gas in moles.
5. The diagram shows a piston before and after, so you can see the gas being squeezed or expanding.

The same calculator has Boyle's law, Charles's law, the pressure law and the ideal gas equation PV = nRT, each under its own name in Calculate.

The combined gas law formula

For a fixed amount of gas, PV ÷ T stays the same, so the value before the change equals the value after. Pressures and volumes can be in any unit as long as both sides use the same one, but the temperatures must be in kelvin: T(K) = T(°C) + 273.15. Rearranged:

Where Boyle's, Charles's and Gay-Lussac's laws come from

Hold one of the three quantities fixed and it cancels from both sides, leaving one of the simpler laws:

Worked examples you can check in the calculator

Example 1: finding the new pressure

2.0 L of gas at 1.0 atm and 20 °C is compressed to 1.0 L, and its temperature rises to 47 °C. First the temperatures: 20 + 273.15 = 293.15 K and 47 + 273.15 = 320.15 K.

The new pressure is 2.18 atm. Halving the volume alone would double it to 2.0 atm, and the warming adds a little more. In the calculator, choose P₂, pick atm, L and °C, and type 1, 2, 20, 1 and 47.

Example 2: finding the new volume

A balloon holds 5.0 L of helium at 1.0 atm and 25 °C. It rises until the pressure is 0.50 atm and the temperature is −10 °C. In kelvin, 298.15 K and 263.15 K:

The balloon grows to 8.83 L. The drop in pressure would double the volume, but the cold shrinks it a little.

Example 3: finding the new temperature

A gas fills 30 L at 200 kPa and 20 °C (293.15 K). It is compressed to 28 L, and its pressure rises to 240 kPa. What temperature is it now?

The gas is at 328.3 K, which is 55.2 °C. The calculator gives the answer in kelvin and lists it in the other temperature units underneath.

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Why the temperature must be in kelvin

Gas pressure and volume are proportional to the absolute temperature, which starts at absolute zero, 0 K or −273.15 °C. Celsius starts at the freezing point of water instead, so its numbers can't be used in ratios. Put 20 and 47 into example 1 as if they were kelvin and you get 1.0 × 2.0 × 47 ÷ (1.0 × 20) = 4.7 atm, more than twice the right answer. Going from 20 °C to 40 °C doesn't double the temperature: in kelvin it rises by only about 7%.

Common mistakes

• Using Celsius. Always convert to kelvin, or let the calculator do it by choosing °C as the unit.
• Mixing units between the two sides. P₁ and P₂ must be in the same unit, and so must V₁ and V₂.
• Using it when gas is added or escapes. The combined gas law is for a fixed amount of gas. If the amount changes, use PV = nRT.
• Rearranging upside down. Check the answer makes sense: a higher temperature at the same volume should mean a higher pressure.
• Rounding the kelvin temperatures. Keep 273.15 unless your course says to use 273.

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