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What does the ideal gas law give?

Pick the value you want, then type the other three. The ideal gas law calculator solves PV = nRT for pressure, volume, amount of gas or temperature, and takes the amount as moles or as a mass and molar mass.

Your numbers

Units
Find
Amount as
Answer
V = 1019.17 L

The answer is V = 1019.17 L.

Pressure (atm)
0.980263
Pressure (kPa)
99.3252
Volume (L)
1,019.17
Amount (mol)
40.8354
Mass (g)
655
Temperature (K)
298.15
Temperature (°C)
25

Answer: V = 1019.17 L. The answer is V = 1019.17 L.

How to calculate

Solves the ideal gas law PV = nRT for pressure, volume, moles or temperature, from moles or from a mass and molar mass, in atm, kPa, torr, liters, °C and kelvins.

Example with the default inputs (Find Volume, Pressure (P) 0.980263157894737 atm, Amount as Mass, Mass of gas 655 g, Molar mass, g/mol 16.04, Temperature (T) 76.9999999999999 °F): The answer is V = 1019.17 L.

Method: PV = nRT with R = 8.31446261815324 J/(mol·K) (0.0820574 L·atm/(mol·K)). P = nRT ÷ V; V = nRT ÷ P; n = PV ÷ RT; T = PV ÷ nR. From a mass: n = mass ÷ molar mass.

  • The gas behaves as an ideal gas: a fair model at ordinary pressures and temperatures, less so near condensation or at high pressure.
  • Pressure is absolute pressure; temperature is absolute (K = °C + 273.15).

Machine-readable copies: Markdown, JSON.

Worked examples

Each example is checked against the calculator on every build.

  1. Find Volume, Pressure (P) 0.9803 atm, Amount as Mass, Mass of gas 655 g, Molar mass, g/mol 16.04, Temperature (T) 77 °F gives Volume (L) 1,019.170025, Answer V = 1019.17 L.Source: OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law (PV = nRT), https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Example 9.9 Using the Ideal Gas Law: 1.02 × 10³ L
  2. Find Pressure, Volume (V) 10 L, Amount as Moles, Amount (n), mol 0.0025, Temperature (T) 95 °F gives Pressure (atm) 0.006321.Source: OpenStax, Chemistry 2e, §9.3 Stoichiometry of Gaseous Substances, Mixtures, and Reactions, https://openstax.org/books/chemistry-2e/pages/9-3-stoichiometry-of-gaseous-substances-mixtures-and-reactions, Example 9.14 The Pressure of a Mixture of Gases: P(H₂) = 6.32 × 10⁻³ atm
  3. Find Moles, Pressure (P) 1 atm, Volume (V) 22.4 L, Molar mass, g/mol 28.01, Temperature (T) 32 °F gives Amount (n), mol 0.999377.Source: OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law (PV = nRT), https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law (standard molar volume about 22.4 L at STP)
  4. Find Temperature, Pressure (P) 1 atm, Volume (V) 22.4 L, Amount as Moles, Amount (n), mol 1 gives Temperature (K) 272.979759.Source: OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law (PV = nRT), https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law

How it works

Pick what to find, then type the other three:

  • Pressure: P = nRT ÷ V
  • Volume: V = nRT ÷ P
  • Amount: n = PV ÷ (RT)
  • Temperature: T = PV ÷ (nR)

R = N_A × k = 6.02214076 × 10²³ × 1.380649 × 10⁻²³ = 8.31446261815324 J/(mol·K), exact. The page works in pascals, cubic meters, moles and kelvins, where 1 Pa·m³ = 1 J.

Amount as a mass. n = mass in grams ÷ molar mass in g/mol. When you solve for the amount and give a molar mass, the page also shows the mass: n × molar mass.

Unit sizes: 1 atm = 101,325 Pa; 1 kPa = 1,000 Pa; 1 bar = 100,000 Pa; 1 torr = 101,325 ÷ 760 Pa; 1 mmHg = 13.5951 × 9.80665 = 133.322387415 Pa; 1 psi = 4.4482216152605 ÷ 0.00064516 Pa. 1 L = 0.001 m³; 1 mL = 10⁻⁶ m³; 1 ft³ = 0.028316846592 m³; 1 gal = 0.003785411784 m³. K = °C + 273.15; K = (°F + 459.67) × 5/9. 1 lb = 453.59237 g; 1 oz = 28.349523125 g.

Exact arithmetic. Each value is read as the exact decimal you typed, in its unit, and every unit size and R are exact, so each result is an exact fraction until it is rounded for display.

Output format. The answer line shows the solved value to 6 significant figures with no thousands separators: P = … atm, V = … L, n = … mol (with (… g) when a molar mass is known) or T = … K (… °C). A negative Celsius value uses the true minus sign. The value rows show 6 significant figures; values of 10¹⁵ or more, or below 10⁻⁶, show in scientific form.

When there is no answer.

  • A mass and molar mass that give an amount below 10⁻¹⁵ mol or above 10¹⁵ mol.
  • A solved value outside the page's range: pressure 10⁻⁹ to 10¹² Pa, volume 10⁻¹² to 10⁹ m³, amount 10⁻¹⁵ to 10¹⁵ mol, temperature 10⁻⁶ to 10⁹ K.

Assumptions

  • The gas is ideal.
  • Pressure is absolute pressure, not a gauge reading.

Worked examples by hand

Methane volume (OpenStax Example 9.9). n = 655 ÷ 16.04 = 40.8354 mol; T = 298.15 K; P = 745 × 101,325 ÷ 760 = 99,325.3 Pa. V = 40.8354 × 8.31446 × 298.15 ÷ 99,325.3 = 1.01917 m³ = 1,019.17 L (the book: 1.02 × 10³ L).

Hydrogen pressure (OpenStax Example 9.14). P = 0.0025 × 8.31446 × 308.15 ÷ 0.0100 = 640.53 Pa = 0.00632149 atm (the book: 6.32 × 10⁻³ atm).

Moles in 22.4 L at STP. n = 101,325 × 0.0224 ÷ (8.31446 × 273.15) = 0.999377 mol.

Temperature of 1 mol in 22.4 L at 1 atm. T = 101,325 × 0.0224 ÷ 8.31446 = 272.980 K.

Other questions people ask

What is the ideal gas law?

PV = nRT links the pressure P, volume V, amount n (in moles) and absolute temperature T of a gas. R is the gas constant, 8.314 J/(mol·K) or 0.08206 L·atm/(mol·K).

Which value of R should I use?

Any value works if its units match the others. This page works in SI units with R = 8.31446261815324 J/(mol·K), the exact product of the Avogadro and Boltzmann constants, and converts every unit you type.

How do I find the volume of a gas from its mass?

Divide the mass by the molar mass to get moles, then V = nRT ÷ P. 655 g of methane (16.04 g/mol) at 25 °C and 745 torr fills about 1,019 L.

Why must the temperature be in kelvins?

The law uses absolute temperature, which starts at absolute zero. 25 °C is 298.15 K. You can type °C or °F; the page converts to kelvins first.

What is the molar volume at STP?

One mole of an ideal gas at 0 °C and 1 atm fills about 22.4 L. Type 22.4 L, 0 °C and 1 atm and solve for moles to see it.

When does the ideal gas law not work well?

At high pressure or low temperature, near the point where a gas turns to liquid. There the molecules’ own size and their pull on each other matter, and real gases differ from the ideal model.