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Combined Gas Law Calculator

Find the missing pressure, volume or temperature when a gas changes from one state to another, by solving P₁V₁/T₁ = P₂V₂/T₂.

Level: Grades 10–11

Printable worksheet

Combined Gas Law Calculator

Know the answer you need? Pick an input to work backward.

Inputs
Temperature scale (both temperatures)

Absolute pressure: add atmospheric pressure to a gauge reading.

Converted to kelvins. It must be above absolute zero, the coldest possible temperature.

Absolute pressure: add atmospheric pressure to a gauge reading.

Converted to kelvins. It must be above absolute zero, the coldest possible temperature.

Result

Final volume (V₂)

1.2516 L

Final volume is 1.2516 L.

Pressure ratio (P₂ ÷ P₁)
2
Volume ratio (V₂ ÷ V₁)
0.6258
Absolute temperature ratio (T₂ ÷ T₁)
1.2516
Constant PV ÷ T
0.0067 atm·L/K

See the step-by-step solution ↓

Step-by-step solution

  1. Put the initial temperature in kelvins. The law needs a scale that starts at absolute zero, so add 273.15

    25 °C+273.15=298.15 K

  2. Put the final temperature in kelvins. The law needs a scale that starts at absolute zero, so add 273.15

    100 °C+273.15=373.15 K

  3. PV ÷ T stays the same before and after. So rearrange P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂ to get the final volume

    1 atm×2 L×373.15 K298.15 K×2 atm=1.2515512326 L

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Find the missing pressure, volume or temperature when a gas is squeezed, heated or allowed to expand. For a fixed amount of gas, those three change together in a predictable way. Pressure times volume, divided by absolute temperature (PV ÷ T), stays the same. That's the combined gas law. It rolls three simpler laws into one equation. They are Boyle's law (pressure and volume), Charles's law (volume and temperature) and Gay-Lussac's law (pressure and temperature).

The calculator solves for whichever of the six values you don't know. Enter the other five, using any pressure and volume units, and Celsius, Fahrenheit or kelvins. Temperatures are turned into kelvins first, and every step is shown. The ratios between the two states are listed too, so you can see what changed.

Where it's used

Why this math matters outside the classroom:

  • Weather balloons. Meteorology students predict how much a balloon swells as pressure and temperature both fall with altitude.
  • Chemistry homework. Students find that 2 L of gas at 1 atm and 25 °C becomes about 1.25 L at 2 atm and 100 °C.
  • Tire pressure. A driver estimates how a tire's absolute pressure rises from 46.7 psi at 20 °C after warming to 40 °C.
  • Gas cylinders. Technicians check that a sealed cylinder's pressure stays safe when it sits in a hot vehicle.
  • Lab corrections. Students convert a gas volume measured at room conditions to standard temperature and pressure.

Grade level and standards: Grades 10–11; Common Core State Standards for Mathematics HSA.CED.A.4. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose which value to solve for: a final or an initial pressure, volume or temperature.
  2. Choose one pressure unit and one volume unit for both states, and the temperature scale.
  3. Enter the five known values. Pressures must be absolute, not gauge readings.
  4. Read the missing value, the ratios between the states and the constant PV ÷ T.

What the inputs mean

Pressure unit (both pressures)
Both pressures use the same unit, so any unit works. But they must be absolute pressures. A tire or tank gauge reads the pressure above the air around it, so add atmospheric pressure to the gauge reading.
Temperature scale (both temperatures)
The law needs absolute temperature, counted up from absolute zero (the coldest possible temperature). Celsius and Fahrenheit values are converted to kelvins. Anything at or below absolute zero is rejected.
Initial pressure (P₁)
Absolute pressure: add atmospheric pressure to a gauge reading.
Initial temperature (T₁)
Converted to kelvins. It must be above absolute zero, the coldest possible temperature.
Final pressure (P₂)
Absolute pressure: add atmospheric pressure to a gauge reading.
Final temperature (T₂)
Converted to kelvins. It must be above absolute zero, the coldest possible temperature.

Formula and method

P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂
V₂ = P₁V₁T₂ ÷ (T₁P₂)
P₂ = P₁V₁T₂ ÷ (T₁V₂)
T₂ = P₂V₂T₁ ÷ (P₁V₁)
T(K) = T(°C) + 273.15

P is pressure, V is volume and T is absolute temperature in kelvins. The small 1 marks the initial (starting) state and the 2 marks the final state. So P₁ is the initial pressure and V₂ is the final volume.

For a fixed amount of ideal gas, PV = nRT. Here n is the amount of gas and R is a fixed number called the gas constant. With n and R unchanged, PV ÷ T = nR is the same before and after the change. That gives the combined law. To solve for one value, you rearrange that balance.

Because the law is a ratio, pressure and volume can be in any units, as long as each pair matches. Temperature is different. Its zero point matters, so it has to be absolute.

Worked example

A 2 L sample of gas at 1 atm and 25 °C is heated to 100 °C and compressed to 2 atm. What is its new volume?

  1. Convert temperatures: 25 + 273.15 = 298.15 K and 100 + 273.15 = 373.15 K.
  2. V₂ = P₁V₁T₂ ÷ (T₁P₂) = (1 × 2 × 373.15) ÷ (298.15 × 2).
  3. V₂ = 1.2515512326 L.

Result: The gas ends up at about 1.2516 L. Doubling the pressure alone would halve the volume, but heating it by 75 °C expands it by about 25%.

Understanding the result

Raising the pressure shrinks the volume. Raising the absolute temperature expands the gas or raises its pressure. The ratio results show each effect separately.

If two of the values don't change, the combined law shrinks to one of the simpler laws. So you can use this calculator for Boyle's, Charles's or Gay-Lussac's problems too.

Assumptions and limitations

  • The gas behaves ideally, and none of it leaks in or out or reacts.
  • Pressures are absolute, and the temperature is the same throughout the gas in each state.
  • Real gases stray from the law at high pressure or close to turning into liquid, such as steam close to boiling.
  • The law says nothing about how fast the change happens or the heat involved.

Frequently asked questions

What is the combined gas law?

It says that P × V ÷ T stays constant for a fixed amount of gas, so P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂. Know five of the six values and you can find the sixth.

Why must temperature be in kelvins?

The law is proportional to temperature measured from absolute zero. Going from 10 °C to 20 °C doesn't double anything. It raises the absolute temperature from 283.15 K to 293.15 K, only about 3.5%.

How is it related to the ideal gas law?

The ideal gas law, PV = nRT, includes the amount of gas, n. The combined law is the special case where n doesn't change. So n and R cancel out between the two states.

Can I use psi from a tire gauge?

Only after adding atmospheric pressure, about 14.7 psi at sea level. A tire reading 32 psi on the gauge is about 46.7 psi absolute, and that's the number the law needs.

How this calculator is checked

Method: Combined gas law P₁V₁/T₁ = P₂V₂/T₂, from the ideal gas equation with a fixed amount of gas; K = °C + 273.15. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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