Ideal Gas Law Calculator,
solve PV = nRT for any variable.

Field guide

PV = nRT: the equation that describes most gas behaviour.

What is the Ideal Gas Law?

The Ideal Gas Law is a fundamental equation of state that combines three earlier empirical laws — Boyle's Law, Charles's Law, and Avogadro's Law — into one unified relationship:

Where P is pressure, V is volume,n is the amount of substance in moles, R is the universal gas constant, and T is the absolute temperature in Kelvin. The equation describes the state of a hypothetical "ideal" gas — one in which gas molecules have no volume of their own and exert no attractive or repulsive forces on each other.

The four variables

Each of the four variables has a specific physical meaning:

• P — Pressure: The force the gas exerts per unit area of its container. Measured in atm, kPa, mmHg, bar, or psi. Standard atmospheric pressure is 1 atm = 101.325 kPa = 760 mmHg = 1.01325 bar.
• V — Volume: The space the gas occupies. In the Ideal Gas Law, this is the total volume of the container, not just the space between molecules. Measured in litres, millilitres, or cubic metres.
• n — Moles: The amount of substance — the number of gas molecules expressed in moles (1 mol = 6.022 × 10²³ molecules, Avogadro's number). It is not the mass in grams; to find moles from mass, divide by the molar mass (g/mol).
• T — Temperature: Must be in Kelvin for the Ideal Gas Law to work. Kelvin is an absolute scale with no negative values; 0 K (absolute zero) is the coldest possible temperature, equivalent to −273.15 °C. Convert: K = °C + 273.15; K = (°F − 32) × 5/9 + 273.15.

The gas constant R

R is the universal gas constant, a fundamental physical constant equal to 8.314 J/(mol·K). Its numerical value depends on which units are used for pressure and volume:

• 0.082057 L·atm/(mol·K) — most common in chemistry, used by this calculator when inputs are in atm and litres
• 8.314 J/(mol·K) = 8.314 Pa·m³/(mol·K) — SI units; used in thermodynamics and physics
• 8.314 L·kPa/(mol·K) = 8.314 cm³·MPa/(mol·K)
• 62.364 L·mmHg/(mol·K) — useful in medical and atmospheric contexts
• 83.14 cm³·bar/(mol·K)

This calculator converts all inputs to atm and litres internally, uses R = 0.082057 L·atm/(mol·K), then converts the result back to whatever unit you selected. This ensures the calculation is always internally consistent regardless of the units you choose.

Standard conditions: STP and SATP

Two standard reference conditions are widely used in chemistry:

• STP (Standard Temperature and Pressure): 0 °C (273.15 K) and 1 atm (101.325 kPa). At STP, one mole of an ideal gas occupies exactly 22.414 litres — the molar volume of an ideal gas at STP.
• SATP (Standard Ambient Temperature and Pressure):25 °C (298.15 K) and 100 kPa (not 101.325 kPa). At SATP, one mole of an ideal gas occupies 24.789 litres. This is the IUPAC-recommended standard since 1982 and is used in most modern chemistry references.

Note that older textbooks may define STP as 0 °C and 1 atm (the pre-1982 definition), while newer texts use 0 °C and 100 kPa. The two differ by about 1.3% in molar volume. Always check which definition applies in your context.

What is an ideal gas?

An ideal gas is a theoretical model that makes two simplifying assumptions: (1) gas molecules have no volume of their own — they are treated as point particles, and (2) there are no intermolecular forces between gas molecules. Real gases approximate ideal behaviour well at low pressures and high temperatures, where molecules are far apart and their volume and interactions are negligible compared to the space they occupy.

At high pressures, real gas molecules are crowded together and their own finite volume becomes significant, causing the real gas to occupy more volume than the ideal prediction. At low temperatures or high pressures, intermolecular attractions cause the gas to occupy less volume than predicted. The Van der Waals equation corrects for both effects: (P + a/V²)(V − b) = nRT, where a accounts for attractions and b accounts for molecular volume.

Using the Ideal Gas Law for real problems

Despite its simplifications, the Ideal Gas Law works well for:

• Lab gas calculations: How much oxygen is produced in a reaction? What pressure does a gas exert in a sealed vessel?
• Balloon and tyre problems: How does pressure change when temperature rises in a sealed container (Gay-Lussac's Law)?
• Stoichiometry with gases: Converting moles of a gas product to volume at a given temperature and pressure.
• Atmospheric science: Estimating air density and composition in the upper atmosphere where pressures are low.
• Industrial process design: A first approximation for gas storage tanks, pipelines, and reactor vessels.

Why temperature must be in Kelvin

The Ideal Gas Law requires absolute temperature because it is rooted in kinetic molecular theory — temperature is a measure of average molecular kinetic energy. At absolute zero (0 K), molecular motion theoretically stops and pressure would be zero. Celsius and Fahrenheit are relative scales with arbitrary zero points. If you used °C and plugged in 0 °C, you would get PV = 0 (since T = 0), which is physically incorrect. Always convert to Kelvin: K = °C + 273.15.

Disclaimer

Results assume ideal gas behaviour. For gases at high pressures, low temperatures, or near their boiling point, real-gas corrections (Van der Waals or other equations of state) will give more accurate results. This calculator is appropriate for introductory chemistry, laboratory estimates, and problems that state "assume ideal gas."