Ideal Gas Law Calculator
Solve for pressure, volume, moles, or temperature of an ideal gas — pick which one to solve for below.
Calculator verified • Last updated: August 2026
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Pressure vs. Volume (at Constant n, T)
Holding moles and temperature fixed at your current values, this curve shows how pressure and volume trade off — squeeze the volume down and pressure rises, exactly following the inverse relationship built into PV = nRT. Hover (or tap) any point on the line to read its exact pressure and volume.
The Ideal Gas Law Explained
The ideal gas law ties together the four measurable properties of a gas — pressure, volume, amount, and temperature — into a single equation that describes how they relate.
P: pressure, in atmospheres (atm).
V: volume, in liters (L).
n: amount of gas, in moles (mol).
R: the gas constant, 0.08206 L·atm/(mol·K).
T: temperature, in kelvin (K).
Since it relates all four quantities in one equation, knowing any three lets you solve for the fourth.
Worked Example: Standard Temperature and Pressure
Using the calculator's defaults — 1 mole of gas at 0°C (273.15 K) — solving for pressure with a volume of 22.4 L gives almost exactly 1 atm, which is precisely the definition of "standard temperature and pressure" (STP) in chemistry: the conditions under which one mole of any ideal gas occupies 22.4 liters. This is a foundational reference point used throughout gas stoichiometry.
The Individual Gas Laws Hiding Inside PV = nRT
The ideal gas law is really a combination of simpler relationships discovered separately, each named after the chemist who found it: Boyle's law (pressure and volume are inversely related, at constant n and T), Charles's law (volume and temperature are directly related, at constant n and P), and Avogadro's law (volume and moles are directly related, at constant P and T). PV = nRT unifies all three into one equation, which is why it's such a powerful, general tool.
A Brief History of the Ideal Gas Law
The combined law took its modern form in the work of French engineer Émile Clapeyron in 1834, who unified the previously separate empirical gas laws of Boyle, Charles, and Gay-Lussac into a single equation. The theoretical justification came later from the kinetic theory of gases, developed through the mid-to-late 19th century by physicists including James Clerk Maxwell and Ludwig Boltzmann, which explained why an idealized model of colliding particles would obey exactly this relationship.
Common Ideal Gas Law Mistakes
Using Celsius instead of Kelvin for temperature is by far the most common error, since the law's proportionality only works on an absolute temperature scale. Forgetting to match pressure and volume units to the value of R being used (mixing atm with a version of R meant for pascals, for instance) is another frequent slip. Applying the ideal gas law to conditions where real gas behavior deviates significantly — very high pressure or very low temperature, near a gas's condensation point — is a third common mistake, since the "ideal" approximation breaks down there.
Gas Law Terms You Should Know
STP (Standard Temperature and Pressure) — 0°C (273.15 K) and 1 atm, a common reference condition.
Molar Volume — the volume one mole of an ideal gas occupies at STP, 22.4 L.
Gas Constant (R) — the proportionality constant in PV = nRT, with a value that depends on the units chosen.
Kinetic Theory of Gases — the model explaining gas behavior as the statistical result of many particles in constant motion.
This calculator assumes ideal gas behavior; real gases deviate somewhat at high pressure or low temperature, requiring more complex equations of state.
Frequently Asked Questions
Why does temperature have to be in Kelvin for this formula?
Because the ideal gas law describes a direct proportional relationship with temperature, and that only works on a scale where zero actually means zero — no molecular motion at all. Celsius and Fahrenheit have arbitrary zero points, so plugging in a Celsius value would give a physically meaningless result; Kelvin's zero point (absolute zero) is what makes the proportionality in PV = nRT correct.
What makes a gas "ideal" — do real gases actually follow this law?
An ideal gas is a simplified model that assumes gas particles have no volume themselves and no attractive or repulsive forces between them — an approximation that works remarkably well for most real gases at ordinary temperatures and pressures. It breaks down at very high pressure or very low temperature, where real molecular size and intermolecular forces start to matter, which is why more complex equations of state exist for those conditions.
Why does R have different numeric values in different textbooks?
R is the same physical constant everywhere, but its numeric value depends entirely on which units you're using for pressure, volume, and energy — 0.0821 L·atm/(mol·K) and 8.314 J/(mol·K) describe exactly the same constant, just expressed in different unit systems. This calculator uses the L·atm/(mol·K) form since it pairs naturally with the atm and L units typically used in general chemistry.