What is the gas constant R?

R = 8.314 J/(mol·K) or 0.0821 L·atm/(mol·K). The value depends on the units used for pressure and volume. Always ensure consistent units throughout your calculation.

What is STP (Standard Temperature and Pressure)?

STP is 0°C (273.15 K) and 1 atm (101,325 Pa). At STP, one mole of an ideal gas occupies 22.4 liters. This is a common reference condition for gas calculations.

When does the ideal gas law not apply?

The ideal gas law is less accurate at high pressures, low temperatures, or for gases with strong intermolecular forces. Real gases deviate from ideal behavior; use the van der Waals equation for more accuracy.

How do I convert temperature for gas law calculations?

Always use absolute temperature (Kelvin). Convert Celsius to Kelvin: K = °C + 273.15. Never use Celsius or Fahrenheit directly in PV = nRT.

Ideal Gas Law Calculator - Solve PV=nRT Equations

Ideal Gas Law Formula

The fundamental equation relating pressure, volume, temperature, and amount of gas

PV = nRT

Solve for P

P = \frac{nRT}{V}

Solve for V

V = \frac{nRT}{P}

Solve for T

T = \frac{PV}{nR}

Solve for n

n = \frac{PV}{RT}

PV = nRT Calculator

Enter three variables to solve for the fourth

Solve For

Volume (m³)

Temperature (°C)

Amount (mol)

Gas Container Visualization

A closed container with gas molecules exerting pressure on all walls.

Pressure arrows on all wallsCyan dots = gas moleculesCenter marker = amount n

Pressure (P) arises from gas molecules colliding with container walls. Higher temperature or more moles increases collision frequency and thus pressure.

PV = nRT Relationship Diagrams

Three quick plots for the pairwise relationships when other variables are fixed.

Left plot: P decreases as V increases (inverse relation).

Middle plot: V increases linearly with T.

Right plot: P increases linearly with T.

Understanding the Ideal Gas Law

What Is the Ideal Gas Law?

The ideal gas law is one of the most fundamental equations in chemistry and physics. Written as $PV = nRT$ , it describes the state of a hypothetical “ideal gas” — a gas whose molecules occupy no volume and exert no intermolecular forces on one another. Despite being a simplification, the ideal gas law is remarkably accurate for most common gases at moderate temperatures and pressures.

The equation was first stated in its complete form in 1834 by Benoît Paul Émile Clapeyron, who unified earlier empirical gas laws into a single relationship. Each variable in the equation has a specific physical meaning:

P — Absolute pressure of the gas (in Pascals, Pa)
V — Volume of the gas sample (in cubic metres, m³)
n — Amount of substance of gas (in moles, mol)
R — The universal gas constant
T — Absolute temperature (in Kelvin, K)

The law tells us that if you know any three of these four variables (P, V, n, T), you can calculate the fourth. This makes it an indispensable tool for chemists, physicists, engineers, and students across many disciplines.

The Gas Constant R and Its Units

The universal gas constant $R$ is a physical constant that relates energy to temperature and amount of substance. Its value is precisely defined as:

R = 8.314\,462\,618\ldots\ \text{J mol}^{-1}\text{K}^{-1}

Depending on the units you use for pressure and volume, R takes different numerical values:

Value of R	Units	Common use
8.314	J/(mol·K)	SI standard, physics, engineering
0.08206	L·atm/(mol·K)	General chemistry courses
62.36	L·mmHg/(mol·K)	Lab settings using mmHg/torr
8314	L·Pa/(mol·K)	SI with litres for volume

Always match your choice of R to the units you use for P and V. Using mismatched units is one of the most common sources of error in gas law calculations.

Boyle’s, Charles’s, and Gay-Lussac’s Laws as Special Cases

The ideal gas law unifies three earlier empirical laws. Each one describes what happens when two variables are held constant:

Boyle’s Law (constant T and n)

At constant temperature and amount, pressure and volume are inversely proportional. Compressing a gas increases its pressure.

P_1 V_1 = P_2 V_2

Derived from PV = nRT by holding n, R, T constant.

Charles’s Law (constant P and n)

At constant pressure and amount, volume is directly proportional to absolute temperature. Heating a gas causes it to expand.

\frac{V_1}{T_1} = \frac{V_2}{T_2}

Derived from PV = nRT by holding n, R, P constant.

Gay-Lussac’s Law (constant V and n)

At constant volume and amount, pressure is directly proportional to absolute temperature. This is why pressure cookers build up pressure when heated.

\frac{P_1}{T_1} = \frac{P_2}{T_2}

Derived from PV = nRT by holding n, R, V constant.

Avogadro’s Law (constant P and T)

At constant pressure and temperature, volume is directly proportional to amount. Equal volumes of gases at the same conditions contain equal numbers of molecules.

\frac{V_1}{n_1} = \frac{V_2}{n_2}

Derived from PV = nRT by holding P, R, T constant.

STP and SATP Standard Conditions

Chemists often quote gas properties at defined standard conditions to allow fair comparison. Three reference conditions are commonly used:

STP

Standard Temperature & Pressure

0 °C (273.15 K)

1 atm (101,325 Pa)

22.4 L/mol

NTP

Normal Temperature & Pressure

20 °C (293.15 K)

1 atm (101,325 Pa)

24.0 L/mol

SATP

Standard Ambient T & P

25 °C (298.15 K)

1 bar (100,000 Pa)

24.8 L/mol

Note that IUPAC redefined STP in 1982 to use 1 bar (100,000 Pa) rather than 1 atm. Some older textbooks still use the pre-1982 definition. Always check which standard your source is using.

Limitations: Real Gases vs. Ideal Gases

The ideal gas law assumes two things that are never exactly true: (1) gas molecules have zero volume, and (2) there are no intermolecular attractions or repulsions. Real gases deviate from this model most noticeably under:

High pressure — molecules are forced close together; their finite size becomes significant.
Low temperature — kinetic energy decreases, allowing intermolecular forces to matter more.
Polar or large molecules — gases like NH₃, CO₂, and SO₂ have stronger interactions.

For more accurate results in these regimes, chemists use the van der Waals equation:

\left(P + \frac{an^2}{V^2}\right)(V - nb) = nRT

where $a$ corrects for intermolecular attractions and $b$ corrects for molecular volume. However, for most introductory chemistry and engineering problems, the ideal gas law gives results accurate to within a few percent.

Ideal Gas Law Calculator

What Is the Ideal Gas Law?

The Gas Constant R and Its Units

Boyle’s, Charles’s, and Gay-Lussac’s Laws as Special Cases

Boyle’s Law (constant T and n)

Charles’s Law (constant P and n)

Gay-Lussac’s Law (constant V and n)

Avogadro’s Law (constant P and T)

STP and SATP Standard Conditions

STP

NTP

SATP

Limitations: Real Gases vs. Ideal Gases

External Resources

NIST WebBook

Khan Academy

Chem LibreTexts

Boyle’s Law (Constant T, n)

Charles’s Law (Constant P, n)

Gay-Lussac’s Law (Constant V, n)

Avogadro’s Law (Constant P, T)

Laboratory Applications

Industrial Applications

Environmental Science

Frequently Asked Questions

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Significant Figures