Free Ideal Gas Law Calculator

The Ideal Gas Law Calculator serves as a comprehensive PV nRT calculator that lets you compute any unknown gas property—pressure, volume, temperature, or amount—by entering the other three values. It combines the functions of a gas pressure calculator, gas volume calculator, gas temperature calculator, and moles of gas calculator into a single ideal gas equation solver. By using the universal gas constant R, the tool delivers accurate results for a broad range of input units.

Understanding Ideal Gases

An ideal gas is a theoretical model in which the constituent molecules are treated as point masses that move randomly, undergo perfectly elastic collisions, and exert no forces on one another aside from the collision moment. The molecules themselves occupy negligible volume. Despite being an approximation, this model works remarkably well for real gases at low density and high temperature, where intermolecular forces become insignificant.

The Ideal Gas Equation

The core relationship linking pressure, volume, amount, and temperature is expressed as:

$$PV = nRT$$

where:

• $P$ – gas pressure, measured in pascals (Pa)
• $V$ – gas volume, in cubic meters (m³)
• $n$ – number of moles (mol)
• $R$ – universal gas constant, $8.31446261815324\ \text{J}\cdot\text{mol}^{-1}\cdot\text{K}^{-1}$
• $T$ – absolute temperature, in kelvins (K)

By rearranging the formula, you can solve for any variable. For example, to compute the volume occupied by 40 moles at 1013 hPa (101300 Pa) and 250 K:

$$V = \frac{nRT}{P} = \frac{40 \times 8.31446261815324 \times 250}{101300} \approx 0.82\ \text{m}^{3}$$

The Universal Gas Constant

The constant $R$ (8.31446261815324 J·mol⁻¹·K⁻¹) is also known as the molar gas constant. It links the energy scale (joules) to the amount of substance and temperature. Physically, $R = k_B N_A$, where $k_B$ is Boltzmann’s constant and $N_A$ is Avogadro’s number. This constant appears not only in the ideal gas law but also in many other fundamental thermodynamic relations.

Derived Gas Laws

Fixing one variable in the ideal gas law yields three classic relationships:

Law	Fixed variable	Relationship
Boyle’s (isothermal)	Temperature ($T$)	$PV = \text{constant}$
Charles’s (isochoric)	Volume ($V$)	$\dfrac{P}{T} = \text{constant}$
Gay‑Lussac’s (isobaric)	Pressure ($P$)	$\dfrac{V}{T} = \text{constant}$

These laws describe common thermodynamic processes and are essential for interpreting gas behavior under changing conditions.

Example: Calculating Pressure or Temperature

Suppose you have 0.1 mol of gas inside a 1 m³ container at 50 °C. First convert the temperature to kelvin: $T = 50 + 273.15 = 323.15\ \text{K}$. Then compute $nRT = 0.1 \times 8.3145 \times 323.15 \approx 268.7\ \text{J}$. Because $P = nRT / V$, the pressure is $268.7\ \text{Pa}$ (about 0.00265 atm). Alternatively, if you know pressure, volume, and moles, you can use the calculator to find temperature directly from $T = \frac{PV}{nR}$.

When To Use the Ideal Gas Law

The equation is most accurate when the gas is sparse—low pressure and high temperature—so that intermolecular forces and particle volume are negligible. In such conditions, the ideal gas law gives a reliable approximation, making it a staple in physics, chemistry, and engineering thermodynamics. This tool also works well alongside other thermodynamic calculators, such as those for air pressure at altitude or combined gas law problems.