Enter three of the four variables — pressure (P), volume (V), moles (n), or temperature (T) — and this Ideal Gas Law Calculator solves for the missing one using PV = nRT. Choose your calculation type, pick your preferred units for each variable, and get the result with the universal gas constant R = 8.31446 J·mol⁻¹·K⁻¹ applied automatically.
Calculated Result
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Variable Solved
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Pressure in Pa
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Volume in m³
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Temperature in K
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The Ideal Gas Law is expressed as PV = nRT, where P is pressure, V is volume, n is the number of moles of gas, R is the universal gas constant, and T is absolute temperature. It combines Boyle's Law, Charles's Law, and Avogadro's Law into one equation.
The universal gas constant R = 8.31446261815324 J·mol⁻¹·K⁻¹ (or equivalently m³·Pa·K⁻¹·mol⁻¹). Its numerical value changes depending on the unit system used — for example, R = 0.082057 L·atm·mol⁻¹·K⁻¹ when using liters and atmospheres.
The Ideal Gas Law requires an absolute temperature scale because it is based on the average kinetic energy of gas molecules, which is proportional to absolute temperature. Kelvin starts at absolute zero (0 K = −273.15 °C), ensuring no negative or zero temperature values that would break the proportionality. This calculator automatically converts °C, °F, and °R to Kelvin internally.
The Ideal Gas Law assumes that gas molecules have negligible volume, experience no intermolecular forces, and undergo perfectly elastic collisions. These assumptions hold well at low pressures and high temperatures. Real gases deviate from ideal behavior at high pressures or low temperatures, where the van der Waals equation is more accurate.
1 atm = 101,325 Pa = 101.325 kPa = 760 mmHg = 760 torr. This calculator handles all unit conversions automatically — just select your preferred unit from the dropdown, and the conversion to SI base units (Pa) is performed before applying PV = nRT.
1 m³ = 1,000 L = 1,000 dm³ = 1,000,000 cm³ = 1,000,000 mL. The calculator converts your selected volume unit to m³ internally before computing. For reference, 1 mole of an ideal gas at 0°C and 1 atm occupies 22.414 liters (Standard Temperature and Pressure, STP).
The number of moles (n) represents the quantity of gas, where 1 mole contains approximately 6.022 × 10²³ molecules (Avogadro's number). You can calculate moles from mass using n = mass / molar mass. For example, 2 grams of hydrogen gas (H₂, molar mass = 2 g/mol) equals 1 mole.
The Ideal Gas Law is an approximation that works best for real gases at low pressures (below a few atmospheres) and high temperatures (well above the gas's boiling point). For more accurate results with real gases under extreme conditions, use the van der Waals equation, which accounts for molecular volume and intermolecular attractions.