Solve the ideal gas law for pressure, volume, moles, or temperature. Supports multiple pressure units (atm, kPa) and temperature in °C or Kelvin. Volume is expressed in liters (L). Visualize the molar volume at STP (22.414 L/mol) and get instant results with precise gas constant handling.
The ideal gas law (PV = nRT) combines Boyle's, Charles's, and Avogadro's laws into a single equation describing the behavior of most gases under moderate conditions. STP (Standard Temperature and Pressure) is a reference state defined by IUPAC as 0°C (273.15 K) and 105 Pa (1 bar), though many textbooks still use 1 atm = 101.325 kPa. This calculator adopts the classic chemistry convention: 1 atm and 273.15 K for STP, yielding the well-known molar volume of 22.414 L/mol.
The ideal gas law evolved from Émile Clapeyron's 1834 formulation, building on Robert Boyle’s (1662), Jacques Charles’ (1787), and Amedeo Avogadro’s (1811) discoveries. Avogadro’s hypothesis that equal volumes of gases at the same T and P contain equal numbers of molecules laid the groundwork for the mole concept. The universal gas constant R was later determined experimentally with high precision. Today, the ideal gas law remains a cornerstone in thermodynamics, chemical engineering, and atmospheric science.
Based on your chosen target variable, the calculator rearranges PV = nRT:
Temperature is automatically converted to Kelvin if provided in Celsius (K = °C + 273.15). The gas constant R is selected based on pressure unit: 0.082057 L·atm/(mol·K) for atmospheres or 8.3145 L·kPa/(mol·K) for kilopascals. All results are displayed with 4 decimal precision, suitable for academic use.
At STP (1 atm, 273.15 K), one mole of an ideal gas occupies exactly V = nRT/P = (1 mol * 0.082057 * 273.15 K) / 1 atm = 22.414 L. This value is fundamental in stoichiometry: given a gas volume at STP, you can instantly determine moles (n = V/22.414). Real gases like O2, N2, and CO2 approximate this within ~0.1–0.5% deviation at STP. The calculator includes a specific molar volume indicator for reference.
A chemical plant stores nitrogen in a 500 L tank at 25°C and 150 atm. To estimate the mass of gas, engineers first solve for moles: n = PV/(RT) with R = 0.082057. n = (150 * 500) / (0.082057 * 298.15) ≈ 3065 mol. Mass = 3065 mol × 28.0134 g/mol ≈ 85.8 kg. Using our calculator, you can replicate this workflow and adjust parameters for safety checks or different storage temperatures. The ideal gas law offers a quick, reliable estimate before applying real‑gas corrections (e.g., van der Waals).
| Scenario | Input (P,V,n,T) | Solved for | Result |
|---|---|---|---|
| Molar volume STP | P=1 atm, n=1 mol, T=273.15 K | Volume | 22.414 L |
| Balloon helium | n=2 mol, T=298 K, P=1 atm | Volume | 48.90 L |
| Scuba tank | V=10 L, T=300 K, n=5 mol | Pressure | 12.31 atm |
| Moles from 44.8 L at STP | V=44.8 L, P=1 atm, T=273.15 K | Moles | 2.000 mol |
For high‑accuracy work (e.g., natural gas metering, cryogenics), the van der Waals equation [ (P + a(n/V)²)(V - nb) = nRT ] introduces correction factors for molecular attraction and finite volume. While our calculator focuses on the ideal gas law, we encourage users to apply it as a first‑order approximation. For most educational and many engineering tasks, PV = nRT provides remarkable accuracy.