Ideal Gas Law Calculator — PV = nRT · Solve for P, V, n or TPV = nRT · R = 8.314 J/mol·K · atm · kPa · L · mol · Kelvin
Use this free Ideal Gas Law Calculator to instantly solve any unknown variable in the fundamental Ideal Gas Law equation: PV = nRT — where P is the gas pressure in atm, kPa, or mmHg, V is the gas volume in litres (L) or m³, n is the number of moles of gas (mol), R is the universal gas constant (8.314 J/mol·K or 0.08206 L·atm/mol·K), and T is the absolute temperature in Kelvin (K). Enter any three known gas parameters to automatically solve the fourth — computing: gas pressure (P) in atm, kPa, bar, or mmHg · gas volume (V) in litres or m³ · number of moles (n) from mass & molar mass · temperature (T) in Kelvin, Celsius & Fahrenheit — with automatic unit conversion across all standard pressure, volume, and temperature units.
The PV = nRT Ideal Gas Law is the single most important equation in gas chemistry and physical chemistry, applied extensively across science and engineering disciplines: chemistry stoichiometry — moles, mass & gas volume problems · STP & NTP gas volume calculations (22.4 L/mol at STP) · molar mass and gas density determination · partial pressure & Dalton's Law of partial pressures · thermodynamic cycle & heat engine analysis · atmospheric science & meteorology pressure calculations · industrial gas cylinder pressure & storage volume sizing. Trusted by A-Level and AP Chemistry students, undergraduate chemistry and chemical engineering learners, physics researchers, thermodynamics engineers, and science educators for precise ideal gas behavior calculations grounded in Boyle's Law, Charles' Law, Gay-Lussac's Law, and Avogadro's Law.
⚠ Chemistry Disclaimer: This Ideal Gas Law calculator assumes ideal gas behavior — where gas molecules have no intermolecular attractive or repulsive forces and negligible molecular volume relative to the container. These assumptions break down for real gases at high pressure (above 10 atm), low temperature (near condensation or liquefaction point), and for polar molecules (NH₃, H₂O vapor) and heavy gases. For real gas calculations, apply the van der Waals equation: (P + a/V²)(V − b) = nRT. Always use absolute temperature in Kelvin (K = °C + 273.15) — never Celsius or Fahrenheit — to avoid calculation errors. Verify results with a qualified chemistry or chemical engineering professional for safety-critical industrial gas applications.
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Ideal Gas Calculator — PV = nRT Solved for Any Variable
The ideal gas law PV = nRT connects four state variables: pressure (P), volume (V), moles of gas (n), and temperature (T), through the universal gas constant R = 8.314 J/(mol·K). Knowing any three variables allows calculation of the fourth. One mole of an ideal gas at 0°C and 1 atmosphere occupies 22.4 liters — this is STP (Standard Temperature and Pressure) and serves as a reference point for all gas volume calculations. The ideal gas calculator solves for the unknown variable given any three inputs with automatic unit conversion between atm, bar, Pa, and kPa.
Combined gas law problems — comparing gas state before and after a process — use P₁V₁/T₁ = P₂V₂/T₂. A gas at 25°C and 1 atm occupying 5 liters, when heated to 100°C at constant volume, reaches 1.25 atm. When compressed from 5 liters to 2 liters at constant temperature, pressure rises to 2.5 atm. These calculations underlie compressor design, scuba tank sizing, autoclave validation, and engine combustion analysis. The calculator handles all four constraint cases: isothermal, isobaric, isochoric, and the general combined law.
Ideal gas law accuracy degrades at high pressures and low temperatures where intermolecular forces become significant. At 100 atm, real gases deviate from ideal behavior by 5-30% depending on the gas. The van der Waals equation corrects for molecular volume (b) and intermolecular attraction (a): (P + a/V²)(V - b) = nRT. The calculator provides the ideal gas result and optionally applies van der Waals correction for common gases (N₂, O₂, CO₂, H₂, CH₄, H₂O vapor) where the correction constants are known.