Combined Gas Law Calculator
Solve Ideal Gas Law, Combined Gas Law, Boyle's Law, Charles's Law, Gay-Lussac's Law, and Avogadro's Law problems. Enter your known values and calculate the unknown instantly with step-by-step solutions.
P₁V₁/T₁ = P₂V₂/T₂
Compares initial and final states when moles remain constant
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Gas Constant (R):
0.08206 L·atm/(mol·K)
8.314 J/(mol·K)
8.314 L·kPa/(mol·K)
62.364 L·mmHg/(mol·K)
Worked Examples
Ideal Gas Law - Find Moles
A gas at 1.00 atm occupies 24.6 L at 298 K. How many moles of gas are present?
Use PV = nRT and solve for n: n = PV / RT
n = (1.00 × 24.6) / (0.08206 × 298)
n = 24.6 / 24.45
n = 1.01 mol
Combined Gas Law - Find P₂
A gas at 0.980 atm and 2.00 L at 300 K is compressed to 3.50 L at 350 K. Find the new pressure.
Use P₁V₁/T₁ = P₂V₂/T₂ and solve for P₂
P₂ = (P₁V₁T₂) / (T₁V₂)
P₂ = (0.980 × 2.00 × 350) / (300 × 3.50)
P₂ = 686 / 1050
P₂ = 0.653 atm
Charles's Law - Find V₂
A gas occupies 1.50 L at 20°C. What is its volume at 100°C if pressure is constant?
Convert temperatures to Kelvin: T₁ = 293.15 K, T₂ = 373.15 K
Use V₁/T₁ = V₂/T₂ and solve for V₂
V₂ = V₁(T₂/T₁)
V₂ = 1.50 × (373.15 / 293.15)
V₂ = 1.91 L
Boyle's Law - Find V₂
A gas at 2.5 atm occupies 4.0 L. What volume does it occupy at 1.0 atm if temperature is constant?
Use P₁V₁ = P₂V₂ and solve for V₂
V₂ = P₁V₁ / P₂
V₂ = (2.5 × 4.0) / 1.0
V₂ = 10.0 L
Gas Laws Formulas and When to Use Them
Each gas law applies to different situations. Here is a quick reference to help you choose the right formula.
How to Use the Combined Gas Law Calculator
Follow these steps to solve any gas law problem quickly and accurately.
Select the Gas Law
Choose from Ideal Gas Law (PV=nRT), Combined Gas Law (P₁V₁/T₁=P₂V₂/T₂), Boyle's Law (P₁V₁=P₂V₂), Charles's Law (V₁/T₁=V₂/T₂), Gay-Lussac's Law (P₁/T₁=P₂/T₂), or Avogadro's Law (V₁/n₁=V₂/n₂).
Choose Your Units
Set your preferred units for pressure (atm, kPa, bar, mmHg, psi), volume (L, mL, m³), and temperature (K, °C, °F). The calculator automatically uses the correct gas constant R for your units.
Select What to Solve For
Click on the variable you want to find. The calculator will disable that input field and highlight it as the target. For combined gas law, you can solve for any of the six variables.
Enter Known Values
Fill in all the values you know. For temperature, you can enter in any unit and the calculator converts to Kelvin internally. Use the Load STP button to quickly set standard conditions (0°C, 1 atm).
Get Your Answer with Steps
The result appears instantly with the formula used and calculation steps. You can share the result or export it as a text file for your homework or lab report.
Why Use Our Gas Law Calculator
All Gas Laws in One Tool
Ideal, Combined, Boyle's, Charles's, Gay-Lussac's, and Avogadro's Law calculators in a single interface. No need to switch between tools.
Instant Results with Steps
Get your answer immediately with the formula and calculation steps shown. Perfect for checking homework or understanding the process.
Automatic Unit Conversion
Enter temperature in Kelvin, Celsius, or Fahrenheit. The calculator converts everything internally and shows results in your chosen units.
Worked Examples Included
Four detailed worked examples show you how to approach different types of gas law problems step by step.
Multiple Pressure Units
Supports atm, kPa, Pa, bar, mmHg, Torr, and psi. The correct gas constant R is automatically selected for your units.
Load Standard Conditions
One-click button to load STP (0°C, 1 atm) values. Save time when working with standard temperature and pressure problems.
Complete Guide to Gas Law Calculations
Understanding the Combined Gas Law
The combined gas law is one of the most useful equations in chemistry and physics. It describes how pressure, volume, and temperature of a gas are related when the amount of gas stays constant. The formula P₁V₁/T₁ = P₂V₂/T₂ lets you calculate any unknown variable when you know five of the six values.
This equation combines three simpler gas laws into one. Boyle's Law covers pressure and volume at constant temperature. Charles's Law covers volume and temperature at constant pressure. Gay-Lussac's Law covers pressure and temperature at constant volume. The combined gas law works when any of these conditions might change together.
The Ideal Gas Law Explained
The ideal gas law, PV = nRT, is the foundation of gas calculations. It relates four properties: pressure (P), volume (V), moles (n), and temperature (T) through the gas constant (R). Unlike the combined gas law, the ideal gas law works for a single state rather than comparing two states.
The gas constant R has different values depending on your units. When using atmospheres for pressure and liters for volume, R = 0.08206 L·atm/(mol·K). When using kilopascals and liters, R = 8.314 L·kPa/(mol·K). Our calculator automatically selects the correct R value based on your chosen pressure unit.
Real gases deviate from ideal behavior at high pressures and low temperatures, where intermolecular forces become significant. For most classroom and everyday calculations, the ideal gas law gives accurate results. For precise engineering work with real gases, the Van der Waals equation or other equations of state may be needed.
Boyle's Law: Pressure and Volume
Robert Boyle discovered in 1662 that at constant temperature, the pressure and volume of a gas are inversely proportional. Mathematically, P₁V₁ = P₂V₂. If you double the pressure on a gas, its volume halves. If you expand a gas to twice its volume, the pressure drops to half.
Boyle's Law explains many everyday phenomena. When you pump a bicycle tire, compressing air into a smaller volume increases its pressure. Scuba divers must ascend slowly because the air in their lungs expands as water pressure decreases. Syringes work because pulling the plunger increases volume and decreases pressure, drawing in fluid.
Charles's Law: Volume and Temperature
Jacques Charles found in 1787 that at constant pressure, the volume of a gas is directly proportional to its absolute temperature. The formula V₁/T₁ = V₂/T₂ shows this relationship. Heat a gas and it expands; cool it and it contracts.
This law explains why hot air balloons work. Heating the air inside the balloon makes it expand, becoming less dense than the surrounding cool air, creating lift. It also explains why a car tire appears flatter on cold mornings but returns to normal as the day warms up.
Gay-Lussac's Law: Pressure and Temperature
Joseph Gay-Lussac showed in 1808 that at constant volume, pressure is directly proportional to absolute temperature. The formula P₁/T₁ = P₂/T₂ applies when a gas is in a rigid container that cannot expand.
This law is important for safety. A pressurized container heated in a fire will experience rapidly increasing pressure, which can cause an explosion if the container fails. Pressure cookers use this principle productively, raising the boiling point of water by increasing pressure through heating.
Common Mistakes in Gas Law Calculations
The most frequent error is forgetting to convert temperature to Kelvin. Gas laws require absolute temperature because they are based on molecular kinetic energy. Zero Kelvin is absolute zero where theoretically all molecular motion stops. Using Celsius or Fahrenheit gives incorrect results because their zero points are arbitrary.
Another common mistake is mixing units. If pressure is in atm, the gas constant must also use atm. Converting all values to consistent units before calculating prevents this error. Our calculator handles unit consistency automatically.
Students sometimes confuse which law to use. Remember: use the combined gas law when comparing two states with constant moles. Use the ideal gas law when you need to find or use the number of moles. Use the simpler laws (Boyle's, Charles's, Gay-Lussac's) when one variable remains constant.
Practical Applications of Gas Laws
Gas laws have applications across science and engineering. In medicine, respiratory therapy uses these principles to deliver oxygen at correct pressures. Anesthesiologists calculate gas mixtures for surgery. Weather balloons expand as they rise because atmospheric pressure decreases with altitude.
In industry, chemical engineers design reactors that operate at specific temperatures and pressures. HVAC systems rely on gas compression and expansion cycles. Automotive engines use the ideal gas law to model combustion. Scuba equipment must account for pressure changes at different depths.
Even cooking involves gas laws. Pressure cookers raise the boiling point of water by increasing pressure, allowing faster cooking. Baking relies on gases expanding when heated to make bread rise. Understanding these principles helps troubleshoot when things go wrong.
Combined Gas Law Calculator FAQ
Common questions about gas law formulas, calculations, and how to use this calculator.
Disclaimer: This Combined Gas Law Calculator is for educational purposes only. Results assume ideal gas behavior, which may not apply to real gases at extreme conditions. Always verify calculations for critical applications. This tool is not affiliated with any educational institution.