Solve the ideal gas law PV = nRT for pressure, volume, moles, or temperature, with units (atm, kPa, L, mL, K, °C) and the steps.
Pick an example, then enter your own values.
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The ideal gas law, PV = nRT, ties together the four properties of a gas: pressure (P), volume (V), the amount in moles (n), and temperature (T), linked by the gas constant R. Know any three and you can solve for the fourth — which is exactly what this calculator does. Choose what to solve for, enter the other three values in whatever units you have (atmospheres, kilopascals, mmHg, liters, milliliters, Kelvin, Celsius, and more), and it returns the answer along with the full gas state, a pressure–volume curve, and the steps. It even gives the mass of the gas if you add a molar mass. Everything is converted to SI internally and solved with R = 8.314 J/(mol·K), so you never have to match R to your units.
Rearrange PV = nRT to solve for the unknown: pressure P = nRT/V, volume V = nRT/P, moles n = PV/(RT), or temperature T = PV/(nR). The gas constant R depends on your units — it's 0.08206 L·atm/(mol·K) for atmospheres and liters, or 8.314 J/(mol·K) in SI (pascals and cubic meters). Temperature must always be absolute (Kelvin); convert Celsius by adding 273.15. A classic example is the molar volume at STP (standard temperature and pressure, 0 °C and 1 atm): for 1 mole, V = nRT/P = (1 × 0.08206 × 273.15) / 1 ≈ 22.4 liters — the well-known result that one mole of any ideal gas occupies about 22.4 L at STP. The law assumes gas particles have no volume and no intermolecular forces, so it's most accurate at low pressure and high temperature; real gases deviate under extreme conditions.
Ideal Gas Law
Solve PV = nRT problems with the full working shown.
Determine how many moles a gas sample contains from P, V, and T.
Confirm the 22.4 L molar volume or work out volumes at other conditions.
Find the pressure or volume of a gas collected in an experiment.
Get the mass of a gas from its moles and molar mass.
Practice solving the ideal gas law for every variable and unit.
Find pressure, volume, moles, or temperature from the other three.
Mix atm, kPa, mmHg, bar, liters, mL, Kelvin, or Celsius — conversions are handled for you.
Everything is normalized to SI internally, so you never pick the wrong gas constant.
Add a molar mass and it returns the mass of the gas, not just the moles.
See the inverse P–V relationship at constant temperature and amount.
Shows the rearranged formula and the working — great for homework.
The ideal gas law is PV = nRT, relating a gas's pressure (P), volume (V), amount in moles (n), and absolute temperature (T) through the gas constant R. It describes how an ideal gas behaves and lets you solve for any one property given the other three.
Rearrange it for the unknown: P = nRT/V, V = nRT/P, n = PV/(RT), or T = PV/(nR). Make sure temperature is in Kelvin and that R matches your pressure and volume units — this calculator converts everything for you automatically.
R is the universal gas constant. Its value depends on units: 0.08206 L·atm/(mol·K) when using atmospheres and liters, or 8.314 J/(mol·K) in SI units (pascals and cubic meters). This tool uses 8.314 internally after converting your inputs to SI.
Use n = PV/(RT). Enter the pressure, volume, and temperature, set 'solve for' to moles, and the calculator returns the amount in moles. Add a molar mass and it also gives the mass.
About 22.4 liters. At standard temperature and pressure (0 °C and 1 atm), V = nRT/P = (1 × 0.08206 × 273.15) / 1 ≈ 22.414 L — the molar volume of an ideal gas at STP.
Pressure in atm, kPa, mmHg, bar, or Pa; volume in liters, milliliters, or cubic meters; and temperature in Kelvin, Celsius, or Fahrenheit. You can mix units freely — the calculator converts to SI before solving.
The math requires absolute temperature (Kelvin), but you can enter Celsius or Fahrenheit and the calculator converts it. Temperature must be above absolute zero (0 K, −273.15 °C), or the result is undefined.
It's an approximation that assumes gas molecules have no volume and don't attract each other. Real gases deviate at high pressure and low temperature, where those assumptions fail; equations like van der Waals give better results under those conditions.