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Ideal Gas Law (PV = nRT) Calculator

The Ideal Gas Law relates the macroscopic state variables of a hypothetical ideal gas: absolute pressure, volume, substance amount in moles, and absolute temperature.

Select which state parameter to compute.

Absolute pressure in kilopascals (101.325 kPa = 1 atm = 1.01325 bar = 14.7 PSI).

Gas container volume in Liters (1000 L = 1 m³).

Chemical amount of substance in moles.

Temperature in Celsius (converted internally to Kelvin: T_K = T_C + 273.15).

Calculated Result
101.325 kPa

Solved Pressure (P)

Pressure

101.32 kPa (1.000 atm)

Volume

22.41 L

Moles

1.000 mol

Temperature

0.0°C (273.1 K)

Calculation Breakdown

  1. Equation of State & Universal Gas ConstantAbsolute Temperature T = 273.15 KP⋅V=n⋅R⋅T,R=8.31446 kPa⋅L/(mol⋅K)P \cdot V = n \cdot R \cdot T, \quad R = 8.31446 \text{ kPa}\cdot\text{L}/(\text{mol}\cdot\text{K})
  2. Algebraic Solution for PP = 101.325 kPaP=nRTVP = \frac{n R T}{V}
  3. Equivalent Pressure & Volume Conversions1.000 atm, 0.0224 m³1 atm=101.325 kPa=1.01325 bar=14.696 PSI1 \text{ atm} = 101.325 \text{ kPa} = 1.01325 \text{ bar} = 14.696 \text{ PSI}

Pressure vs Volume (Boyle’s Law Isotherm at 0°C, 1 mol)

Interactive visualization based on your current inputs

Pressure (kPa)
0.05711417022710 L15 L20 L25 L30 LVolume (L)Pressure (kPa)

What Is the Ideal Gas Law (PV = nRT) Calculator?

The Ideal Gas Law is the equation of state governing hypothetical gases consisting of randomly moving point particles that undergo perfectly elastic collisions.

It is one of the most fundamental equations in chemistry, thermodynamics, and atmospheric physics.

How Does the Ideal Gas Law (PV = nRT) Calculator Work?

The law combines Boyle’s Law (P ∝ 1/V), Charles’s Law (V ∝ T), and Avogadro’s Law (V ∝ n).

By selecting any target variable, the calculator algebraically isolates and solves it using consistent SI/metric units.

Ideal Gas Law (PV = nRT) Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

PV=nRT  ⟺  P=nRTVP V = n R T \iff P = \frac{n R T}{V}

Universal gas constant R links thermal kinetic energy per mole to thermodynamic pressure and volume.

How to Use the Ideal Gas Law (PV = nRT) Calculator

  1. Choose the parameter you want to solve for (P, V, n, or T).
  2. Fill in the other three known state variables.

Step-by-Step Example Calculation

Standard Temperature and Pressure (STP)

Input Values:

targetVariable:V
pressure:101.325
volume:1
moles:1
temperature:0
Worked Steps: At standard atmospheric pressure (101.325 kPa) and 0°C (273.15 K), exactly 1.0 mole of ideal gas occupies 22.41 Liters.

Understanding Your Result

Solved Value: Computed physical parameter in standard scientific units.

Equivalents: Pressure converted to atmospheres, bar, and PSI; Volume in Liters and cubic meters.

Factors That Affect the Result

  • Temperature: Heating a sealed rigid container raises pressure directly.
  • Molar Mass: Moles relate to mass via molecular weight (m = n · M).

When Should You Use This Calculator?

  • Gas stoichiometry and chemical reactor pressure design.
  • HVAC expansion tanks, compressed air cylinders, and diving tank calculations.

Assumptions & Limitations

  • Assumes zero molecular volume and zero intermolecular attractive forces.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Exact analytical solution to the ideal gas equation of state.

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