What is the Combined Gas Law?

The Combined Gas Law merges Boyle's Law and Charles's Law into a single equation: P1 times V1 divided by T1 equals P2 times V2 divided by T2. It describes how a fixed amount of ideal gas behaves when pressure, volume, and temperature all change simultaneously. Unlike Boyle's Law (which requires constant temperature) or Charles's Law (which requires constant pressure), the Combined Gas Law applies to any change of state where the amount of gas remains constant.

How do you solve for V2 using the Combined Gas Law?

Rearrange P1V1/T1 = P2V2/T2 to isolate V2: V2 = (P1 times V1 times T2) divided by (T1 times P2). Substitute your known values to find V2. For example, P1=1 atm, V1=2 L, T1=300 K, P2=2 atm, T2=400 K gives V2 = (1 times 2 times 400) / (300 times 2) = 800/600 = 1.333 L.

What is the difference between the Combined Gas Law and the Ideal Gas Law?

The Combined Gas Law compares two states of the same fixed amount of gas (P1V1/T1 = P2V2/T2) without needing to know the number of moles. The Ideal Gas Law (PV = nRT) includes the number of moles n and the gas constant R, making it more general: it can find the absolute state of a gas rather than just comparing two states. If the amount of gas changes between states, you need the Ideal Gas Law, not the Combined Gas Law.

Combined Gas Law Calculator

The Combined Gas Law brings together Boyle's Law and Charles's Law into a single equation that describes how a fixed amount of gas behaves when pressure, volume, and temperature all change at the same time. The formula is P1V1 divided by T1 equals P2V2 divided by T2, where the subscripts 1 and 2 refer to the initial and final states of the gas. Unlike the two simpler laws, which each hold one variable constant, the Combined Gas Law works for any change of state as long as the quantity of gas stays the same. You can use it to find any one of the six variables given the other five. The most common use is to find the final volume V2 after a gas has been compressed or expanded and also heated or cooled, but the equation can equally be rearranged to find any pressure or temperature. The only firm requirement is that temperatures must be in kelvin: convert from Celsius by adding 273.15. This calculator lets you choose which variable to solve for, enter the other five values, and get the result immediately. The supporting display shows the ratio P1V1/T1 and P2V2/T2 for verification that the law holds, along with the individual pressure, volume, and temperature ratios. Results are suitable for science coursework and introductory engineering calculations involving ideal gases.

Calculate.co.nz is proud to be partnered with realtor.co.nz, a trusted resource for navigating the New Zealand property market. Their Helpful Articles section offers clear, well-structured insights across buying, selling, and building, making complex real estate topics more accessible. With a focus on up-to-date guidance and practical knowledge, they empower Kiwis to move forward with clarity and confidence in a constantly evolving property landscape.

Solve for

Initial pressure P1

atm

Initial volume V1

Initial temperature T1

Final pressure P2

atm

Final temperature T2

Final volume V2

1.333 L

solved variable

P1V1/T10.006667

P2V2/T20.006667

Pressure ratio P2/P12.00

Volume ratio V2/V10.667

Temperature must be in kelvin (K = °C + 273.15). Assumes ideal gas behaviour and constant amount of gas.

How it works

The Combined Gas Law states P1V1/T1 = P2V2/T2. Rearranging for each variable: V2 = P1V1T2/(T1P2); P2 = P1V1T2/(T1V2); T2 = T1P2V2/(P1V1); V1 = P2V2T1/(T2P1); P1 = P2V2T1/(T2V1); T1 = T2P1V1/(P2V2). Select the variable you want to solve for and the calculator applies the correct form. The constant ratio P1V1/T1 = P2V2/T2 is displayed for verification.

Worked example

A gas starts at P1 = 1 atm, V1 = 2 L, T1 = 300 K. It is compressed to P2 = 2 atm and heated to T2 = 400 K. Using the Combined Gas Law: V2 = (1 × 2 × 400) / (300 × 2) = 800 / 600 = 1.333 L. P1V1/T1 = 2/300 = 0.006667 and P2V2/T2 = (2 × 1.333)/400 = 0.006667. These match the default values pre-filled above.

Related calculators

Boyle's Law Calculator: solve for P or V at constant temperature.
Charles's Law Calculator: solve for V or T at constant pressure.
Ideal Gas Law Calculator: use PV = nRT including the number of moles.
Pressure Converter: convert atm, kPa, Pa, bar, and psi.

If you've found a bug, or would like to contact us, or learn more about James Graham and Calculate.co.nz.

Calculate.co.nz is partnered with Interest.co.nz for New Zealand's highest quality calculators and financial analysis.

Calculate.co.nz is the sister site of CalculatorHub.com, the world's largest calculator website by tool count.

All calculators and tools are provided for educational and indicative purposes only and do not constitute financial advice.

Calculate.co.nz is proudly part of the Realtor.co.nz group, New Zealand's leading property transaction literacy platform, helping Kiwis understand the home buying and selling process from start to finish. Whether you're a first home buyer navigating your first property purchase, an investor evaluating your next acquisition, or a homeowner planning to sell, Realtor.co.nz provides clear, independent, and trustworthy guidance on every step of the New Zealand property transaction journey.

Calculate.co.nz is also partnered with Health Based Building and Premium Homes to promote informed choices that lead to better long-term outcomes for Kiwi households.

Calculate.co.nz is hosted in Auckland via SiteHost new Zealand.

All content on this website, including calculators, tools, source code, and design, is protected under the Copyright Act 1994 (New Zealand). No part of this site may be reproduced, copied, distributed, stored, or used in any form without prior written permission from the owner.

About & trust: Why Calculate is NZ's most comprehensive · By the Numbers · How we compare · Editorial standards · How we keep data current · NZ finance glossary · Research & data · Financial literacy NZ · About · Privacy policy · Terms of use

Reviewed and maintained. Last reviewed 2026-07-02 and checked on a twice-monthly cycle against IRD, RBNZ and Stats NZ. How we keep data current.