Ideal Gas Law
Calculate any variable of the ideal gas law PV = nRT with this free online calculator. Solve for pressure, volume, moles, or temperature with interactive charts and breakdown.
Enter any 3 of the 4 values to calculate the missing variable.
About This Calculator
The Ideal Gas Law Calculator solves any variable in the ideal gas equation PV = nRT. Enter any 3 of the 4 values — pressure (P), volume (V), amount of substance (n), or temperature (T) — and the calculator automatically determines the missing one using the universal gas constant R = 8.314462618 J/(mol·K). This tool is designed for physics and chemistry students, engineers, researchers, and educators working with gas thermodynamics.
The ideal gas law assumes that gas molecules are point particles with no intermolecular forces and perfectly elastic collisions. While no real gas is perfectly ideal, the equation provides excellent approximations at high temperatures and low pressures. The calculator uses the appropriate rearrangement: P = nRT/V to find pressure, V = nRT/P for volume, n = PV/RT for moles, and T = PV/nR for temperature. Results are shown with multiple unit conversions including kPa, atm, liters, and degrees Celsius for practical use.
Regional Notes
India: Indian students and engineers commonly use pascals and bars in thermodynamics coursework. The calculator provides pressure in SI units (Pa, kPa) alongside atm. STP conditions (273.15 K, 101.325 kPa) are used as default values matching the Indian curriculum.
United States: US educators often use atmospheres and psi in chemistry and physics classrooms. This calculator includes atm results for convenience. Default values reflect IUPAC standard conditions used in US textbooks.
United Kingdom: UK A-level and university physics courses use SI units as standard (pascals for pressure, cubic meters for volume). The Kelvin scale is mandatory for gas law calculations in UK curricula, and the calculator enforces this correctly.
Frequently Asked Questions
What is the ideal gas law and how does the calculator work?
The ideal gas law is PV = nRT, where P is pressure in pascals, V is volume in cubic meters, n is the number of moles, R is the universal gas constant (8.314 J/(mol·K)), and T is temperature in Kelvin. This calculator solves for any missing variable — enter any 3 of the 4 values and it computes the fourth using the appropriate rearrangement: P = nRT/V, V = nRT/P, n = PV/RT, or T = PV/nR.
What units does this calculator support?
The calculator accepts pressure in pascals (Pa), volume in cubic meters (m³), amount in moles (mol), and temperature in Kelvin (K). Results display pressure in Pa, kPa, and atm; volume in m³ and liters; temperature in Kelvin and Celsius; and moles in mol. The breakdown table shows all converted units for a complete analysis.
How do I convert Celsius to Kelvin for the ideal gas law?
To convert Celsius to Kelvin, add 273.15 to the Celsius temperature. For example, 25°C = 298.15 K, 100°C = 373.15 K, and 0°C = 273.15 K. The ideal gas law requires absolute temperature in Kelvin because the Kelvin scale starts at absolute zero, where molecular motion theoretically stops.
What is the gas constant R used in the calculation?
This calculator uses R = 8.314462618 J/(mol·K), which is the SI value of the universal gas constant. It is the same for all ideal gases regardless of chemical composition. The gas constant can also be expressed as R = N_A × k, where N_A is Avogadro's number (6.022 × 10²³ mol⁻¹) and k is Boltzmann's constant (1.381 × 10⁻²³ J/K).
When do real gases behave like an ideal gas?
Real gases approximate ideal gas behavior at high temperatures and low pressures, where intermolecular forces become negligible and the volume of gas particles is insignificant compared to container volume. Common gases like oxygen, nitrogen, and carbon dioxide show near-ideal behavior at standard temperature and pressure (STP: 273.15 K, 101.325 kPa). At high pressures or low temperatures, real gases deviate significantly from the ideal gas law due to intermolecular attractions and finite molecular volume.
What is standard temperature and pressure (STP)?
Standard temperature and pressure (STP) is defined as 273.15 K (0°C) and 101.325 kPa (1 atm). At STP, one mole of an ideal gas occupies approximately 22.414 liters (0.022414 m³). This reference point is widely used in chemistry and physics for comparing gas volumes and calculating gas properties across different conditions.
Can I solve for any variable in the ideal gas law with this calculator?
Yes, this calculator can solve for pressure, volume, moles, or temperature — whichever value is missing. Simply enter the three known values and leave the fourth field empty. The calculator automatically detects which variable to compute using the ideal gas law PV = nRT. This makes it a versatile tool for thermodynamics homework, lab work, and engineering calculations.
How does the Ideal Gas Law calculator differ from other ideal gas calculators?
This general calculator solves for any unknown variable in PV = nRT. For calculators that focus on a single variable, use Ideal Gas Pressure (solves P from V, T, n), Ideal Gas Temperature (solves T from P, V, n), Ideal Gas Volume (solves V from P, T, n), or Ideal Gas Density (solves gas density from pressure, temperature, and molar mass). All use the same gas constant R = 8.314 J/(mol·K) and the ideal gas law.