Ideal Gas Law Calculator

The ideal gas law unifies pressure, volume, temperature, and amount of gas in one equation — the backbone of gas stoichiometry, balloon buoyancy estimates, and HVAC duct sizing at low pressure. Real gases deviate at high pressure or low temperature, but air near room conditions behaves ideally enough for engineering estimates and chemistry homework alike.

Ideal gas law:

PV = nRT

Where P is pressure (Pa or atm), V volume (m³ or L), n moles, T absolute temperature (K), and R is the gas constant (8.314 J/(mol·K) or 0.08206 L·atm/(mol·K)). Solve any variable when the other three are known. Combined gas law for fixed n: P₁V₁/T₁ = P₂V₂/T₂.

Always convert to absolute kelvin before calculating — Celsius misleads badly. 27°C = 300 K, not 27 in PV=nRT. Enter three knowns to find the fourth. One mole of ideal gas at STP (0°C, 1 atm) occupies 22.414 L — a useful sanity check.

Worked example: How many moles in a 10.0 L balloon at 25°C (298 K) and 101.3 kPa? P = 101,300 Pa, V = 0.010 m³, R = 8.314. n = PV/(RT) = 101,300 × 0.010 / (8.314 × 298) = 0.409 mol. Mass of air (M ≈ 29 g/mol): 0.409 × 29 ≈ 11.9 g. Compress isothermally to 2.0 L: P₂ = nRT/V = 0.409 × 8.314 × 298 / 0.002 ≈ 506 kPa ≈ 5 atm.

Connect to pressure calculator for unit context, molar mass for mass-mole conversion, and celsius-to-kelvin for temperature prep. Van der Waals and compressibility corrections matter for CO₂ cylinders and cryogenic storage beyond this ideal model.