Ideal Gas Law Calculator

Solve PV = nRT for pressure, volume, moles or temperature in any units. The gas constant and kelvin conversion are handled for you.

PV = nRT
Solve for
V
Volume
22.414L
1 sig figs: 20
≡
Same value in
22,410 mL
22,410,000 µL · 0.02241 m³ · 22,410 cm³
  1. Rearrange: V = nRT ÷ P
  2. Substitute: P = 1.00 atm, n = 1.00 mol, T = 0 °C (converted to SI units first).
  3. Result: V = 22.414 L, rounded to 1 significant figures because the least precise input has 1.

R = 8.314 J/(mol·K) = 0.08206 L·atm/(mol·K). Temperatures are converted to kelvin before solving.

Hold one thing constant: the three gas laws

Each named gas law is PV = nRT with two variables frozen. Pick which one to hold, then drag the slider.

V × 1.00P × 1.00T × 1.00n fixed

Boyle's law. At constant temperature, squeezing the gas into half the volume doubles the pressure: P ∝ 1/V.

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0/1500

Worked example

What volume does 1.00 mol of gas occupy at 0 °C and 1.00 atm? V = nRT ÷ P = 1.00 × 0.08206 × 273.15 ÷ 1.00 = 22.4 L. That is the familiar molar volume at STP.

Combine with molar mass to get gas density: ρ = PM ÷ RT. Or with the stoichiometry calculator to find the volume of gas a reaction releases.

Frequently asked questions

What is the ideal gas law?
PV = nRT, where P is pressure, V volume, n moles of gas, T absolute temperature in kelvin and R the gas constant, 8.314 J/(mol·K) or 0.08206 L·atm/(mol·K).
Which value of R should I use?
Match R to your units: 0.08206 L·atm/(mol·K) with litres and atmospheres, 8.314 J/(mol·K) with pascals and cubic metres (or kPa and litres), 62.36 L·torr/(mol·K) with torr. This calculator converts everything to SI internally, so any units work.
Why must temperature be in kelvin?
Gas laws are proportionalities that start from absolute zero. At 0 °C a gas does not have zero volume; at 0 K an ideal gas would. Add 273.15 to a Celsius temperature.
What is the molar volume of a gas at STP?
At IUPAC STP (0 °C, 1 bar) one mole of ideal gas occupies 22.71 L. Many textbooks use the older 0 °C and 1 atm, giving 22.41 L. Room conditions (25 °C, 1 atm) give 24.47 L.
When does the ideal gas law fail?
At high pressure and low temperature, where molecules are close together, their own volume and attractions matter. The van der Waals equation corrects for both.