Ideal Gas Law Calculator

Solve the PV=nRT equation to find any missing variable in gas calculations.

Calculate pressure, volume, temperature, or number of moles using the ideal gas law. Enter three known values and find the fourth unknown variable.

Examples

Click on any example to load it into the calculator.

Standard Temperature and Pressure (STP)

Standard Temperature and Pressure (STP)

One mole of any ideal gas at STP (0°C, 1 atm) occupies 22.4 L.

Pressure: 1.0 atm

Volume: 22.4 L

Moles: 1.0 mol

Temperature: 273.15 K

Room Temperature and Pressure

Room Temperature and Pressure

One mole of gas at room temperature (25°C, 1 atm) occupies about 24.5 L.

Pressure: 1.0 atm

Volume: 24.5 L

Moles: 1.0 mol

Temperature: 298.15 K

High Pressure Gas Tank

High Pressure Gas Tank

A compressed gas tank with 10 moles at high pressure and room temperature.

Pressure: 200.0 atm

Volume: 1.0 L

Moles: 10.0 mol

Temperature: 298.15 K

Low Pressure Laboratory

Low Pressure Laboratory

A vacuum chamber with very low pressure gas at standard temperature.

Pressure: 0.001 atm

Volume: 100.0 L

Moles: 0.01 mol

Temperature: 273.15 K

Other Titles
Understanding the Ideal Gas Law Calculator: A Comprehensive Guide
Master the fundamental equation of gas behavior and learn how to apply it to real-world chemistry and physics problems. This guide covers everything from basic concepts to advanced applications.

What is the Ideal Gas Law?

  • The PV=nRT Equation
  • Ideal vs. Real Gases
  • The Gas Constant R
The Ideal Gas Law is one of the most fundamental equations in chemistry and physics, describing the relationship between pressure (P), volume (V), number of moles (n), temperature (T), and the universal gas constant (R). Expressed as PV = nRT, this equation provides a mathematical model for how gases behave under various conditions. While no gas is truly 'ideal,' most gases at moderate temperatures and pressures follow this relationship closely enough for practical calculations.
The Components of PV = nRT
Each variable in the ideal gas law has a specific physical meaning: Pressure (P) is the force exerted by gas molecules colliding with container walls, measured in atmospheres (atm), Pascals (Pa), or bars. Volume (V) is the space occupied by the gas, typically in liters (L) or cubic meters (m³). Moles (n) represent the amount of gas substance, with one mole containing 6.022 × 10²³ molecules (Avogadro's number). Temperature (T) must be in Kelvin (K) for the equation to work correctly, as it represents the average kinetic energy of gas molecules.
The Universal Gas Constant R
The gas constant R is a fundamental physical constant that relates the energy scale to the temperature scale. Its value depends on the units used: R = 0.0821 L·atm/(mol·K) when using liters and atmospheres, R = 8.314 J/(mol·K) when using SI units, or R = 0.0831 L·bar/(mol·K) when using bars. This constant ensures that the units on both sides of the equation balance correctly and provides the proper scaling between macroscopic gas properties and molecular behavior.
When is the Ideal Gas Law Valid?
The ideal gas law works best under specific conditions: moderate temperatures (not too close to the gas's condensation point), moderate pressures (not extremely high), and for gases that don't have strong intermolecular forces. At very high pressures, gas molecules are forced close together and their finite size becomes significant. At very low temperatures, intermolecular attractions become important. For most practical applications involving common gases like nitrogen, oxygen, carbon dioxide, and noble gases at room temperature and atmospheric pressure, the ideal gas law provides excellent accuracy.

Common Gas Constant Values:

  • R = 0.0821 L·atm/(mol·K) - Most common for chemistry problems
  • R = 8.314 J/(mol·K) - SI units, used in physics and engineering
  • R = 0.0831 L·bar/(mol·K) - When using bar as pressure unit
  • R = 62.4 L·mmHg/(mol·K) - When using mmHg as pressure unit

Step-by-Step Guide to Using the Calculator

  • Identifying Known Variables
  • Unit Conversions
  • Interpreting Results
Using the ideal gas law calculator is straightforward, but requires careful attention to units and ensuring you have exactly three known variables to solve for the fourth unknown.
1. Determine Your Known Variables
Start by identifying which three variables you know from your problem. You might be given pressure and volume and asked to find temperature, or given moles and temperature and asked to find pressure. Make sure you have exactly three known values - if you have fewer, you'll need additional information. If you have more than three, you can choose which three to use or verify your calculations with the extra data.
2. Pay Attention to Units
Units are crucial in gas law calculations. Temperature must always be in Kelvin - if given in Celsius, add 273.15 to convert. Pressure can be in atm, Pa, or bar, but be consistent. Volume is typically in liters or cubic meters. The calculator handles unit conversions automatically, but understanding the relationships helps you verify your results. Remember: 1 atm = 101,325 Pa = 1.013 bar, and 1 m³ = 1000 L.
3. Enter Values and Calculate
Input your three known values in the appropriate fields, leaving the unknown variable empty. Select the correct units for each variable. Click 'Calculate' to find the missing value. The calculator will also provide additional useful information like gas density and molar mass if applicable. Always double-check that your result makes physical sense - for example, temperatures should be positive, and pressures and volumes should be reasonable for your situation.
4. Verify and Apply Your Results
Once you have your calculated value, verify it makes sense in the context of your problem. Is the pressure reasonable for the conditions? Is the volume appropriate for the amount of gas? Use the additional calculated values like gas density to gain more insight into your system. Remember that the ideal gas law is an approximation, so real-world results may vary slightly from calculated values.

Unit Conversion Examples:

  • Temperature: 25°C = 25 + 273.15 = 298.15 K
  • Pressure: 1 atm = 101,325 Pa = 1.013 bar
  • Volume: 1 m³ = 1000 L
  • Pressure: 760 mmHg = 1 atm

Real-World Applications of the Ideal Gas Law

  • Industrial Processes
  • Environmental Science
  • Medical Applications
The ideal gas law finds applications across numerous fields, from industrial chemistry to environmental monitoring and medical technology.
Chemical Manufacturing and Industrial Processes
In chemical manufacturing, the ideal gas law is essential for designing reactors, calculating gas flow rates, and optimizing production processes. Engineers use it to determine how much gas is needed for reactions, how pressure affects reaction rates, and how to safely handle compressed gases. For example, when producing ammonia via the Haber process, precise control of pressure and temperature is crucial, and the ideal gas law helps engineers calculate the exact conditions needed for optimal yield.
Environmental Monitoring and Climate Science
Environmental scientists use the ideal gas law to understand atmospheric composition, calculate greenhouse gas concentrations, and model climate change scenarios. By measuring pressure, temperature, and volume of air samples, they can determine the number of moles of various gases present. This is crucial for monitoring air quality, tracking emissions, and understanding how gases behave in the atmosphere. The law also helps in designing air pollution control systems and calculating gas diffusion rates.
Medical and Biological Applications
In medicine, the ideal gas law is fundamental to respiratory physiology and medical device design. It helps calculate lung volumes, determine oxygen requirements for patients, and design ventilators and anesthesia equipment. Blood gas analyzers use the principles of gas solubility and the ideal gas law to measure oxygen and carbon dioxide levels in blood. The law also applies to hyperbaric medicine, where patients are treated with high-pressure oxygen, and to the design of medical gas delivery systems.

Industrial Applications:

  • Chemical reactors: Calculating gas feed rates and reaction conditions
  • Compressed gas storage: Determining tank capacities and safety limits
  • Air separation: Producing pure oxygen and nitrogen from air
  • Refrigeration: Understanding gas behavior in cooling systems

Common Misconceptions and Correct Methods

  • Temperature Units
  • Pressure Variations
  • Gas Behavior Assumptions
Several common misconceptions can lead to errors when using the ideal gas law. Understanding these pitfalls helps ensure accurate calculations.
Misconception: Temperature Can Be in Celsius
This is one of the most common errors. The ideal gas law requires absolute temperature in Kelvin. Using Celsius directly will give incorrect results because the relationship between pressure and temperature is not linear on the Celsius scale. Always convert Celsius to Kelvin by adding 273.15. For example, 25°C = 298.15 K. This conversion is crucial because the gas law is based on the relationship between molecular kinetic energy and temperature, which is absolute.
Misconception: All Gases Behave Ideally
While the ideal gas law is a good approximation for many gases under normal conditions, it's not perfect. Real gases deviate from ideal behavior at high pressures, low temperatures, or when molecules have strong intermolecular forces. For example, water vapor deviates significantly from ideal behavior due to hydrogen bonding. Carbon dioxide also shows deviations near its critical point. For precise work, more complex equations like the van der Waals equation may be needed.
Misconception: Pressure is Always Atmospheric
Many students assume gas pressure is always 1 atm, but this is only true at sea level under standard conditions. Pressure varies with altitude, weather conditions, and the specific experimental setup. In laboratories, gases are often stored in pressurized cylinders or used under vacuum conditions. Always use the actual pressure of your system, not assumed values. This is especially important in industrial applications where gases may be at very high or very low pressures.

Common Error Examples:

  • Using 25 instead of 298.15 K for room temperature
  • Assuming all gases behave ideally at all conditions
  • Using 1 atm pressure without considering actual conditions
  • Forgetting to account for gas solubility in liquids

Mathematical Derivation and Examples

  • Historical Development
  • Derivation from Kinetic Theory
  • Advanced Applications
The ideal gas law didn't emerge fully formed but developed through centuries of experimental work and theoretical insights, culminating in a unified equation that describes gas behavior.
Historical Development of Gas Laws
The ideal gas law combines several earlier discoveries: Boyle's Law (1662) showed that pressure and volume are inversely related at constant temperature (P₁V₁ = P₂V₂). Charles's Law (1787) established that volume and temperature are directly proportional at constant pressure (V₁/T₁ = V₂/T₂). Gay-Lussac's Law (1802) showed that pressure and temperature are directly proportional at constant volume (P₁/T₁ = P₂/T₂). Avogadro's Law (1811) stated that equal volumes of gases contain equal numbers of molecules at the same temperature and pressure. The ideal gas law unifies all these relationships into one equation.
Derivation from Kinetic Theory
The ideal gas law can be derived from the kinetic theory of gases, which models gas molecules as point particles in constant random motion. The theory assumes that molecules have negligible volume compared to the container, exert no forces on each other except during collisions, and that collisions are perfectly elastic. From these assumptions, we can derive that the pressure exerted by a gas is proportional to the number of molecules, their average kinetic energy, and inversely proportional to the volume. This leads directly to the PV = nRT relationship.
Advanced Applications and Extensions
Beyond basic calculations, the ideal gas law forms the foundation for more complex gas behavior models. The van der Waals equation adds correction terms for molecular volume and intermolecular forces. The virial equation expands the ideal gas law as a power series in density. For mixtures, Dalton's Law of partial pressures states that the total pressure is the sum of individual gas pressures. These extensions allow scientists to model real gas behavior more accurately in industrial and research applications.

Mathematical Relationships:

  • Boyle's Law: P₁V₁ = P₂V₂ (constant T, n)
  • Charles's Law: V₁/T₁ = V₂/T₂ (constant P, n)
  • Gay-Lussac's Law: P₁/T₁ = P₂/T₂ (constant V, n)
  • Avogadro's Law: V₁/n₁ = V₂/n₂ (constant P, T)