Ideal Gas Law Calculator (PV = nRT)
Ideal gas law calculator. Solve PV = nRT for pressure, volume, moles or temperature, in SI or L-atm units. Educational only.
Ideal Gas Law Calculator
How to use the ideal gas law calculator
Pick your units
Choose atm · L · K (which uses R = 0.082057) or SI Pa · m³ · K (R = 8.314). The calculator uses the matching gas constant.
Select the unknown
Choose whether to solve for pressure, volume, moles, or temperature. The corresponding input is hidden.
Enter the other three
Type the known values. Temperature must be absolute — in kelvin — so add 273.15 to a Celsius temperature first.
Read the result
The unknown is computed from PV = nRT, along with the molar volume. Remember the ideal-gas assumption breaks down at high pressure or low temperature.
The ideal gas law — one equation for four variables
Pressure, volume, moles, temperature
The ideal gas law, PV = nRT, ties together the four quantities that describe a gas: its pressure P, volume V, amount in moles n, and absolute temperature T, linked by the universal gas constant R. It is one of the most useful relationships in chemistry and physics because it lets you find any one of those four from the other three. The law is really a synthesis of three earlier observations: Boyle's law (at fixed temperature, pressure and volume are inversely related), Charles's law (at fixed pressure, volume rises with temperature), and Avogadro's law (equal volumes of gas at the same conditions contain equal numbers of molecules). Combined, they say that the product of pressure and volume is proportional to the amount of gas and its absolute temperature. The proportionality constant, R, has the same value for every ideal gas — 8.314 joules per mole per kelvin in SI units, or 0.082057 litre-atmospheres per mole per kelvin when pressure is in atmospheres and volume in litres. Choosing the right value of R for your units is the only real subtlety in using the equation.
A famous consequence is the molar volume: one mole of an ideal gas at 0 °C (273.15 K) and 1 atm occupies 22.414 litres, a number worth remembering. At the more modern standard of 0 °C and 1 bar it is about 22.711 litres, and at 25 °C and 1 bar around 24.79 litres — which is why "standard conditions" must always be specified. The law underpins everyday calculations from the amount of gas in a cylinder to the volume change of air as it heats, and it is the foundation on which more accurate real-gas equations are built.
"PV = nRT folds Boyle, Charles, and Avogadro into one line. Know any three of pressure, volume, moles, and temperature, and the fourth follows — provided you keep temperature in kelvin."
When gases stop being ideal
The "ideal" in ideal gas law is a reminder that it's a model with assumptions: that gas molecules have negligible volume of their own and exert no forces on one another except during instantaneous, perfectly elastic collisions. Real molecules do take up space and do attract one another, so the law is an approximation that works best where those effects are smallest — at low pressure and high temperature, where molecules are far apart and moving fast. It becomes unreliable at high pressure (where the molecules' own volume matters) and at low temperature near condensation (where intermolecular attractions matter), which is exactly when gases are about to become liquids. For those conditions, equations such as van der Waals' add correction terms for molecular volume and attraction. Two practical rules prevent most errors: always convert temperature to kelvin, since the law uses absolute temperature and a Celsius value would give nonsense; and match the gas constant to your pressure and volume units. Within its valid range the ideal gas law is remarkably accurate for common gases under everyday conditions. Use this calculator to solve PV = nRT quickly and to build intuition for how the variables trade off, and reach for a real-gas equation when you're far from ideal.
10 Facts About the Ideal Gas Law
PV = nRT links pressure, volume, moles, temperature.
R = 8.314 J/mol·K or 0.082057 L·atm/mol·K.
It combines Boyle, Charles, and Avogadro.
Temperature must be in kelvin (°C + 273.15).
One mole at 0 °C, 1 atm fills 22.414 L.
R is the same for every ideal gas.
It assumes molecules have no volume or attraction.
Most accurate at low pressure, high temperature.
Fails near condensation (high P, low T).
Van der Waals corrects for real-gas behaviour.
Frequently asked questions
It is the equation PV = nRT, relating a gas's pressure (P), volume (V), amount in moles (n), and absolute temperature (T) through the gas constant R. Knowing any three lets you calculate the fourth. It combines Boyle's, Charles's, and Avogadro's laws into a single relationship and is the workhorse equation for gas calculations in chemistry and physics, accurate for common gases under ordinary conditions.
It depends on your units. Use R = 0.082057 L·atm/mol·K when pressure is in atmospheres and volume in litres, or R = 8.314 J/mol·K (equivalently Pa·m³/mol·K) for SI units. There are other forms (for example with pressure in mmHg or kPa). The key is that R must match the units of pressure and volume you use. The calculator picks the right R for the unit system you select.
Because the law uses absolute temperature, which starts at absolute zero. The Celsius and Fahrenheit scales have arbitrary zero points, so using them would give wrong — even negative or infinite — results. Convert by adding 273.15 to a Celsius temperature to get kelvin. For instance, 25 °C is 298.15 K. Forgetting this conversion is the single most common error in gas-law problems, so the calculator expects temperature in kelvin.
It's the volume one mole of gas occupies at specified conditions. At 0 °C (273.15 K) and 1 atm, one mole of an ideal gas fills 22.414 litres — a classic reference value. At the modern standard of 0 °C and 1 bar it's about 22.711 litres, and at 25 °C and 1 bar around 24.79 litres. Because the value depends on the chosen "standard," always state the temperature and pressure. The calculator reports the molar volume for your inputs.
At high pressure and low temperature — conditions where a gas is dense and close to condensing. There, the assumptions that molecules have no volume of their own and don't attract each other break down: their finite size and mutual attractions become significant. The law works best at low pressure and high temperature, where molecules are far apart and fast-moving. For non-ideal conditions, equations such as van der Waals' add corrections for molecular volume and attractive forces.
"Standard temperature and pressure" is a reference condition, but its definition has changed. The older STP was 0 °C and 1 atm, giving a molar volume of 22.414 L. The current IUPAC definition uses 0 °C and 1 bar, giving about 22.711 L. "Standard ambient" conditions are sometimes 25 °C and 1 bar (about 24.79 L). Because these differ, always state which standard you mean. The calculator works at whatever conditions you enter.
No — that's the remarkable thing. The ideal gas law uses the same constant R for every gas, so an ideal mole of hydrogen, oxygen, or carbon dioxide all occupy the same volume at the same temperature and pressure (Avogadro's insight). The identity of the gas matters only through its molar mass if you're converting between moles and mass. Real gases deviate slightly from this universality, more so for larger, more strongly interacting molecules.
Yes. For a mixture, n is the total moles of all gases combined, and the law gives the total pressure or volume. Dalton's law of partial pressures then says each gas contributes a partial pressure proportional to its mole fraction, and the partial pressures sum to the total. So you can apply PV = nRT to the whole mixture using total moles, and split into partial pressures afterward. This calculator handles a single n; for partial pressures, scale by mole fraction.
For everyday conditions it's accurate and reliable. For high-pressure, low-temperature, or high-precision work, use a real-gas equation that accounts for molecular volume and interactions. As always, keep temperature in kelvin and match R to your units. This tool runs the exact PV = nRT relationship and is educational; for engineering or research near non-ideal conditions, apply the appropriate corrected equation.
No. The values you enter are processed entirely in your browser. Nothing is sent to a server, stored, or shared, and no account is required. The calculation runs on your device only.
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