Ideal Gas Law Calculator
The ideal gas law PV = nRT is one of the most fundamental equations in chemistry and thermodynamics. It relates pressure P, volume V, amount of substance n (in moles), and absolute temperature T through the universal gas constant R = 8.314462618 J/(mol K), as published by NIST. This calculator solves for any one of the four variables when the other three are known. Pressure can be entered in pascals (Pa) or atmospheres (atm, where 1 atm = 101,325 Pa). Volume can be entered in cubic metres (m³) or litres (L, where 1 L = 0.001 m³). Temperature can be in kelvin (K) or degrees Celsius (where T_K = T_C + 273.15). The result panel also shows the solved quantity converted to alternative units. The ideal gas law is an approximation that works well at low pressures and high temperatures; it becomes less accurate near the condensation point of the gas or at very high pressures. For educational, laboratory, and engineering estimates under moderate conditions, it is widely used and reliable.
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Ideal gas law formula
PV = nRT
P = nRT / V (pressure in Pa)
V = nRT / P (volume in m³)
n = PV / (RT) (moles)
T = PV / (nR) (temperature in K)
R = 8.314462618 J/(mol·K) (NIST CODATA 2018)
1 atm = 101,325 Pa
1 L = 0.001 m³
T(K) = T(°C) + 273.15
Worked example: molar volume at 0 °C and 1 atm
- P = 101,325 Pa, n = 1 mol, T = 273.15 K
- V = nRT / P = 1 × 8.314 × 273.15 / 101,325
- V = 2,271.15 / 101,325 = 0.022414 m³ = 22.414 L
Worked example: pressure of 2 mol gas at 25 °C in 10 L
- n = 2 mol, T = 298.15 K, V = 0.010 m³
- P = nRT / V = 2 × 8.314 × 298.15 / 0.010
- P = 4,958.07 / 0.010 = 495,807 Pa = 4.894 atm
Ideal gas law: frequently asked questions
What is the ideal gas law?
The ideal gas law PV = nRT relates four properties of a gas: pressure P (Pa), volume V (m³), amount of substance n (moles), and absolute temperature T (kelvin). R = 8.314 J/(mol K) is the universal gas constant, published by NIST. The law combines Boyle's Law (P inversely proportional to V at constant T and n), Charles's Law (V proportional to T at constant P and n), and Avogadro's Law (V proportional to n at constant P and T) into a single equation.
When does the ideal gas law break down?
The ideal gas law assumes gas molecules have negligible volume and no intermolecular forces. These assumptions fail at high pressures (where molecules are forced close together and volume matters) and low temperatures (where intermolecular attractions become significant). Real gas behavior is better described by the van der Waals equation or other equations of state. For most engineering and chemistry calculations at moderate pressures and temperatures, the ideal gas law provides a good approximation.
What is the universal gas constant R?
R = 8.314462618 J/(mol K) is the universal (molar) gas constant. It appears in the ideal gas law PV = nRT and in many other thermodynamic equations. The value of R is defined exactly in the 2019 redefinition of the SI through the Boltzmann constant k and Avogadro's number NA: R = k * NA. Its value is published in the NIST Chemistry WebBook and CODATA recommended values of fundamental physical constants.
What are Standard Temperature and Pressure (STP) conditions?
IUPAC defines Standard Temperature and Pressure (STP) as 0°C (273.15 K) and 100,000 Pa (100 kPa, approximately 0.9869 atm). Under these conditions, 1 mole of an ideal gas occupies 22.711 L. Note that some older texts and US sources use 0°C and 1 atm (101,325 Pa) as STP, giving 22.414 L/mol. This calculator uses the user's entered values; check which STP definition applies to your problem.
What is the molar volume of an ideal gas at STP?
Under the IUPAC STP (0°C, 100,000 Pa), 1 mole of an ideal gas occupies V = nRT/P = 1 * 8.314 * 273.15 / 100,000 = 0.022711 m³ = 22.711 L. Under the older US/chemistry STP (0°C, 101,325 Pa), the molar volume is 22.414 L/mol. At 25°C (298.15 K) and 100,000 Pa, it is 24.790 L/mol. These standard molar volumes are commonly used in stoichiometry and gas calculations.
Official sources
- NIST Chemistry WebBook: webbook.nist.gov (gas constant and thermodynamic data).
- NIST SP 330 (2019): The International System of Units (SI).
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology. For educational use only.