Ideal Gas Law Calculator

The ideal gas law and rearranged formulas

PV = nRT, where P is pressure, V is volume, n is the amount of substance in moles, R is the universal gas constant (8.31446 J·mol⁻¹·K⁻¹), and T is absolute temperature in Kelvin. All values must use consistent SI units: Pa, m³, mol, and K.

The law combines Boyle's law (PV = constant at fixed T and n), Charles's law (V/T = constant at fixed P and n), and Avogadro's law (V ∝ n at fixed P and T) into a single unified equation.

The calculator rearranges the same equation depending on the unknown: pressure uses P = nRT / V, volume uses V = nRT / P, moles use n = PV / RT, and temperature uses T = PV / nR. Showing the active rearranged formula matters because many gas-law mistakes come from solving the algebra correctly but using the wrong pressure, volume, or temperature unit with the chosen gas constant.

Worked example: one mole at STP

A standard chemistry benchmark is one mole of gas at 0 °C and 1 atm. Substituting n = 1 mol, T = 273.15 K, and P = 1 atm into PV = nRT gives a volume of about 22.414 L. Running the same values backward through the calculator should return roughly 1 atm, 22.414 L, 1 mol, or 273.15 K depending on which variable you choose to solve for.

That worked example is useful because it checks both the equation and the unit system. If you accidentally enter Celsius where Kelvin is required, or mix litres with cubic metres without converting, the result will be off by a large factor even though the algebra looks correct.

The preset chips use the same idea as a built-in answer key. Start with classic STP, IUPAC STP, SATP, or room-air conditions, then change one known value at a time. If the molar volume changes in the expected direction when pressure or temperature changes, the setup is probably consistent.

Standard conditions, molar volume, and unit choices

At STP (0 °C, 1 atm), one mole of an ideal gas occupies 22.414 litres. At SATP (25 °C, 100 kPa), one mole occupies 24.790 litres. IUPAC-style standard pressure of 100 kPa gives a molar volume near 22.711 L/mol at 0 °C, which is why different textbooks and lab sheets may quote slightly different standard molar volumes.

The calculator reports molar volume in L/mol alongside the solved variable so you can compare your state against familiar reference points. Molar volume is especially helpful when the unknown is not volume: a pressure or moles result can still be checked by asking whether V/n is close to the expected value for the stated temperature and pressure.

You can enter pressure in atm, Pa, kPa, bar, psi, mmHg, or torr; volume in L, mL, m³, cm³, or ft³; and temperature in K, °C, or °F. The internal calculation converts everything to Pa, m³, mol, and K before solving, so you do not need to pick a different numerical R value for every display-unit combination.

Mass, molar mass, and density checks

The ideal gas equation uses moles, not grams. If a problem gives gas mass, convert with n = mass / molar mass before entering the amount of substance. The result panel lists mass estimates for common gases such as hydrogen, helium, nitrogen, oxygen, carbon dioxide, and argon so you can connect the mole result to a practical mass.

Density can also be derived from PV = nRT by combining n = m / M with density = m / V. That gives density = PM / RT, where M is molar mass. The calculator's common-gas density rows are not a substitute for a full gas-property table, but they quickly show why carbon dioxide is denser than nitrogen or oxygen under the same state conditions.

Standard conditions and real gases

At STP (0 °C, 1 atm), one mole of an ideal gas occupies 22.414 litres. At SATP (25 °C, 100 kPa, the newer standard), one mole occupies 24.790 litres.

Real gases deviate from ideal behaviour at high pressures and low temperatures. For most applications involving air, oxygen, nitrogen, and common gases at moderate conditions, the ideal law is accurate to within a few percent.

Use the result note as a model-quality warning rather than a pass/fail verdict. The ideal-gas law assumes point particles with no intermolecular attraction; real gases depart from those assumptions as molecules get crowded together, cool toward condensation, or interact strongly. For high-accuracy process work, use a real-gas equation of state or measured property data rather than relying on a single ideal-gas calculation.

Common mistakes when using a PV nRT calculator

The most common mistake is entering temperature in Celsius as if it were Kelvin. A temperature of 25 °C must be converted to 298.15 K before the equation is evaluated; using 25 K would describe an extremely cold state and produce a wildly different answer. The calculator accepts °C and °F inputs, but the result panel still shows the Kelvin value so the absolute-temperature conversion is visible.

A second mistake is mixing unit systems inside a hand calculation. If R is 8.314 J·mol⁻¹·K⁻¹, pressure-volume work must be in Pa·m³ because 1 joule equals 1 Pa·m³. Chemistry courses often use R = 0.082057 L·atm·mol⁻¹·K⁻¹ instead; that is fine when pressure is in atm and volume is in litres, but it is the same physical constant expressed in a different unit basis.

A third mistake is treating the ideal gas law as a gas-identity calculator. PV = nRT does not say whether the gas is nitrogen, oxygen, carbon dioxide, or a mixture. Gas identity matters for mass and density through molar mass, and it matters for real-gas deviations through molecular size and intermolecular attractions.