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Ideal Gas Law Calculator PV=nRT
The ideal gas law is one of the most fundamental equations in physics and chemistry, relating the four state variables of a gas: pressure (P), volume (V), amount of substance (n in moles) and absolute temperature (T). The formula PV = nRT, where R = 8.314 J/(mol·K) is the universal gas constant, allows any one of these quantities to be calculated when the other three are known. This calculator lets you solve for any of the four variables. Choose which quantity you want to find, enter the three known values in SI units (Pa, m³, mol, K) and click "Calculate". The result is shown immediately, along with the PV and nRT products — they should be equal, providing a built-in check of your inputs. The tool is ideal for high school and university students studying chemistry and physics, as well as engineers working with technical gases and gas mixtures.
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How the ideal gas law calculator works
Base formula: PV = nRT. Solve for pressure: P = nRT/V. Solve for volume: V = nRT/P. Solve for moles: n = PV/(RT). Solve for temperature: T = PV/(nR). Gas constant R = 8.314462618 J/(mol·K). Temperature must be in kelvins (K = °C + 273.15). Results are rounded to 6 decimal places.
Example: volume of 1 mole of gas at STP
At standard temperature and pressure (STP): P = 101 325 Pa, n = 1 mol, T = 273.15 K. V = nRT/P = 1 × 8.314 × 273.15 / 101 325 ≈ 0.02241 m³ = 22.41 litres. This is the molar volume of an ideal gas at 0 °C and atmospheric pressure.
Frequently asked questions
What is the ideal gas law?
The ideal gas law is PV = nRT, where P is pressure (Pa), V is volume (m³), n is the number of moles, R is the universal gas constant (8.314 J/(mol·K)) and T is absolute temperature (K). It describes the behaviour of an ideal gas — one whose molecules have no volume and do not interact with each other.
What is the value of the gas constant R?
The universal gas constant R = 8.314462618 J/(mol·K). It can also be expressed as 8.314 Pa·m³/(mol·K), 0.08206 L·atm/(mol·K) or 62.36 L·mmHg/(mol·K), depending on the unit system used.
Why must temperature be in kelvins?
The ideal gas law requires absolute temperature because at 0 K (absolute zero) the kinetic energy of molecules is zero and the gas volume theoretically reaches zero. Using Celsius would give incorrect results because 0 °C ≠ 0 K. Convert: K = °C + 273.15.
What units should I use for pressure and volume?
In SI units: pressure in pascals (Pa) and volume in cubic metres (m³). 1 atm = 101 325 Pa, 1 bar = 100 000 Pa, 1 litre = 0.001 m³. Make sure all inputs are consistent — mixing units leads to incorrect results.
What is the molar volume of an ideal gas at STP?
At STP (0 °C = 273.15 K, 101 325 Pa), the molar volume of an ideal gas is approximately 22.414 litres per mole (0.022414 m³/mol). At SATP (25 °C = 298.15 K, 100 000 Pa), it is approximately 24.789 litres per mole.
When does the ideal gas law fail?
The ideal gas law is a good approximation at low pressures and high temperatures, where intermolecular forces are negligible and the volume of molecules is small compared to the container. It breaks down near the condensation point of the gas, at very high pressures (above ~10 atm) or at very low temperatures. For real gases, use the van der Waals equation: (P + a·n²/V²)(V − nb) = nRT.
How do I calculate the number of moles?
From the ideal gas law: n = PV/(RT). For example, if P = 200 000 Pa, V = 0.01 m³ and T = 300 K, then n = (200 000 × 0.01) / (8.314 × 300) = 2000 / 2494.2 ≈ 0.802 mol.
What is Boyle's law and how does it relate to PV=nRT?
Boyle's law states that at constant temperature, the pressure and volume of a gas are inversely proportional: P₁V₁ = P₂V₂. This is a special case of the ideal gas law with n and T constant, so PV = nRT = constant.
What is Charles's law?
Charles's law states that at constant pressure, the volume of a gas is directly proportional to its absolute temperature: V/T = constant. This follows from PV = nRT when P and n are fixed: V = (nR/P) × T.
Can this calculator be used for gas mixtures?
Yes, but only under Dalton's law of partial pressures: each gas in a mixture behaves as if it were alone in the container. Enter the total pressure and the number of moles of the component of interest, or use partial pressures for individual gases.
This calculator is for educational and reference purposes. The ideal gas law is an approximation — for real gases at high pressures or low temperatures, use the van der Waals equation or other real-gas models.