Calculate pressure, volume, moles, or temperature using the ideal gas law: PV = nRT. Free online thermodynamics calculator for physics, chemistry, and engineering with multiple unit support.
Calculate pressure, volume, moles, or temperature using PV = nRT
Formula:
PV = nRT
Copy the code below to embed this calculator on your website
The Ideal Gas Law is one of the most fundamental equations in physics and chemistry, describing the relationship between pressure, volume, temperature, and the number of moles of an ideal gas. Whether you're studying thermodynamics, working on chemical reactions, or designing systems involving gases, understanding the ideal gas law is essential. Our Ideal Gas Law Calculator makes it easy to calculate any variable in the equation PV = nRT, making it perfect for various applications in physics, chemistry, and engineering.
The ideal gas law combines several gas laws (Boyle's Law, Charles's Law, and Avogadro's Law) into a single equation. It provides an excellent approximation for the behavior of gases under most conditions, especially at low pressures and high temperatures where gases behave most ideally.
Our Ideal Gas Law Calculator is designed for simplicity and accuracy. Follow these steps to get your calculation:
The calculator uses the fundamental ideal gas law formula: PV = nRT, where P is pressure, V is volume, n is the number of moles, R is the gas constant, and T is temperature.
The ideal gas law is expressed as:
PV = nRT
Where: P = pressure, V = volume, n = number of moles, R = gas constant, T = temperature
You can rearrange this formula to solve for any variable:
The gas constant (R) has different values depending on the units used:
The ideal gas law is used in countless real-world applications:
It's crucial to use consistent units in your ideal gas law calculations:
Tip: Our calculator automatically converts between different units and handles the gas constant selection. When using L·atm/(mol·K), pressure should be in atm and volume in L. When using SI units, pressure should be in Pa and volume in m³.
What volume does 2.5 moles of gas occupy at 1.0 atm and 273 K?
V = nRT / P = (2.5 mol × 0.0821 L·atm/(mol·K) × 273 K) / 1.0 atm = 56.0 L
What is the pressure of 0.5 moles of gas in a 10 L container at 300 K?
P = nRT / V = (0.5 mol × 0.0821 L·atm/(mol·K) × 300 K) / 10 L = 1.23 atm
How many moles of gas are in a 5.0 L container at 2.0 atm and 298 K?
n = PV / RT = (2.0 atm × 5.0 L) / (0.0821 L·atm/(mol·K) × 298 K) = 0.409 mol
At what temperature will 1.0 mole of gas at 1.0 atm occupy 22.4 L?
T = PV / nR = (1.0 atm × 22.4 L) / (1.0 mol × 0.0821 L·atm/(mol·K)) = 273 K (0°C)
The ideal gas law provides an excellent approximation for most gases under normal conditions, but it has limitations:
For most practical applications at standard temperature and pressure (STP), the ideal gas law provides accurate results. For more precise calculations at extreme conditions, equations like the Van der Waals equation may be needed.
Standard Temperature and Pressure (STP) is a common reference point:
At STP, one mole of any ideal gas occupies 22.4 liters. This is a useful reference point for many calculations.
The ideal gas law (PV = nRT) describes the relationship between pressure, volume, temperature, and the number of moles of an ideal gas. It's used extensively in physics, chemistry, and engineering to calculate gas properties. It works best for gases at low pressure and high temperature where intermolecular forces and particle volume are negligible.
The gas constant value depends on your units. Use R = 0.0821 L·atm/(mol·K) when working with liters and atmospheres (common in chemistry). Use R = 8.314 J/(mol·K) or Pa·m³/(mol·K) when working with SI units (common in physics). Our calculator automatically handles the correct R value based on your selection.
The ideal gas law requires absolute temperature (Kelvin) because the relationship between temperature and other gas properties is based on absolute zero. Celsius and Fahrenheit scales have negative values, but temperature in the gas law must be positive. Our calculator automatically converts to Kelvin internally.
Yes, the ideal gas law provides a good approximation for real gases under most conditions, especially at low pressure and high temperature. At high pressures or low temperatures, real gases deviate from ideal behavior, and more complex equations (like Van der Waals) may be needed for accuracy.
Moles (n) represent the amount of substance. One mole contains Avogadro's number (6.022 × 10²³) of particles (atoms, molecules, etc.). The ideal gas law uses moles, not individual molecules, because it's more convenient for calculations involving macroscopic amounts of gas.
Our calculator automatically handles unit conversions. Simply select your preferred units for pressure and volume, and the calculator will convert everything internally to perform the calculation correctly. You can mix different units (e.g., atm and L, or Pa and m³) as long as you select the appropriate gas constant.
Understanding the ideal gas law is fundamental to thermodynamics, chemistry, and engineering. Our Ideal Gas Law Calculator simplifies these calculations, making it easy to solve problems involving gas pressure, volume, temperature, and moles.
Ready to explore more thermodynamics concepts? Check out our other calculators like the Charles's Law Calculator for temperature-volume relationships, or the Enthalpy Calculator for heat content calculations that often complement gas law analysis.
Get instant results with our optimized calculation engine
Precise calculations you can trust for any project
Works perfectly on all devices and screen sizes