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🧪 Ideal Gas Law Calculator

Enter 3 values among Pressure (P), Volume (V), Moles (n), and Temperature (T) to calculate the remaining one.

🧪 Ideal Gas Law Calculator

mol

📈 Isotherm (P-V Curve)

Please enter values to calculate.

Calculator Description

The ideal gas law is a fundamental thermodynamic relation that ties together a gas's pressure, volume, amount (moles), and temperature in a single equation of state. It combines Boyle's, Charles's, and Avogadro's laws and describes most gases well at ordinary temperatures and pressures.

What this calculator finds

Given any three of the four variables P, V, n, and T, this calculator solves for the remaining one using the ideal gas equation of state, supporting a range of units (Pa/atm/psi, m³/L/ft³, and so on).

Why it matters

  • Calculating amounts of gas produced or consumed in reactions (stoichiometry)
  • Predicting gas pressure and volume in tanks and vessels for storage design
  • Estimating gas expansion or contraction with temperature (HVAC, process engineering)

Formula

Ideal Gas Law Equation

The ideal gas law states that the product of pressure and volume equals the product of the number of moles, the gas constant, and the absolute temperature.

PV=nRTP V = n R T
  • PPressure [Pa, atm, psi]
  • VVolume [m³, L, ft³]
  • nNumber of moles [mol]
  • TAbsolute temperature [K]
  • RIdeal gas constant (≈ 8.314 J/(mol·K) or 0.08206 L·atm/(mol·K))

How the formula works

  • At constant temperature T, P and V are inversely related (Boyle's law): compressing the gas raises its pressure.
  • At constant pressure P, V is proportional to absolute temperature T (Charles's law): heating expands the gas.
  • More moles n produce a higher pressure at the same volume and temperature.

Worked example

At 0 °C (273.15 K) and 1 atm, the volume of 1 mol of gas is V = nRT/P = (1 × 0.08206 × 273.15) / 1 ≈ 22.4 L — the familiar molar volume of an ideal gas at standard conditions (22.4 L).

Useful Tips

Practical tips

  • Always use absolute temperature (K). Convert from Celsius with K = °C + 273.15.
  • The value of R must match your unit system (use 8.314 J/(mol·K) in SI).
  • For state changes, comparing two states with P₁V₁/T₁ = P₂V₂/T₂ (the combined gas law) is convenient.

Limitations & cautions

  • The ideal-gas assumption breaks down at high pressure and low temperature; real-gas equations such as van der Waals (accounting for intermolecular forces and molecular volume) are then needed.
  • Errors grow as the gas approaches condensation or its critical point.