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Use this free Ideal Gas Law Calculator to instantly solve any unknown variable in the fundamental Ideal Gas Law equation: PV = nRT — where P is the gas pressure in atm, kPa, or mmHg, V is the gas volume in litres (L) or m³, n is the number of moles of gas (mol), R is the universal gas constant (8.314 J/mol·K or 0.08206 L·atm/mol·K), and T is the absolute temperature in Kelvin (K). Enter any three known gas parameters to automatically solve the fourth — computing: gas pressure (P) in atm, kPa, bar, or mmHg · gas volume (V) in litres or m³ · number of moles (n) from mass & molar mass · temperature (T) in Kelvin, Celsius & Fahrenheit — with automatic unit conversion across all standard pressure, volume, and temperature units.
The PV = nRT Ideal Gas Law is the single most important equation in gas chemistry and physical chemistry, applied extensively across science and engineering disciplines: chemistry stoichiometry — moles, mass & gas volume problems · STP & NTP gas volume calculations (22.4 L/mol at STP) · molar mass and gas density determination · partial pressure & Dalton's Law of partial pressures · thermodynamic cycle & heat engine analysis · atmospheric science & meteorology pressure calculations · industrial gas cylinder pressure & storage volume sizing. Trusted by A-Level and AP Chemistry students, undergraduate chemistry and chemical engineering learners, physics researchers, thermodynamics engineers, and science educators for precise ideal gas behavior calculations grounded in Boyle's Law, Charles' Law, Gay-Lussac's Law, and Avogadro's Law.
⚠ Chemistry Disclaimer: This Ideal Gas Law calculator assumes ideal gas behavior — where gas molecules have no intermolecular attractive or repulsive forces and negligible molecular volume relative to the container. These assumptions break down for real gases at high pressure (above 10 atm), low temperature (near condensation or liquefaction point), and for polar molecules (NH₃, H₂O vapor) and heavy gases. For real gas calculations, apply the van der Waals equation: (P + a/V²)(V − b) = nRT. Always use absolute temperature in Kelvin (K = °C + 273.15) — never Celsius or Fahrenheit — to avoid calculation errors. Verify results with a qualified chemistry or chemical engineering professional for safety-critical industrial gas applications.
The Ideal Gas Law is one of the most important equations inchemistry and thermodynamics. It describes the relationship between the pressure, volume, temperature, and quantity of a gas.
Scientists use the ideal gas law to predict how gases behave under different conditions. By combining several earlier gas laws, the equation provides a powerful way to analyze gas systems in laboratories, industrial processes, and scientific research.
The ideal gas model assumes that gas particles move randomly, collide elastically, and occupy negligible volume compared to the space in which they move. While this model simplifies real-world behavior, it provides very accurate predictions under many standard conditions.
Students, engineers, and scientists frequently use anideal gas law calculator to determine unknown variables such as pressure, volume, temperature, or the number of moles of gas.
Understanding the ideal gas equation helps explain many physical phenomena including gas expansion, compression, heating, cooling, and atmospheric behavior.
The mathematical expression of the Ideal Gas Law is:
This equation links the four key properties of gases: pressure, volume, temperature, and amount of substance.
The universal gas constant R ensures that all units in the equation remain consistent. Depending on the measurement units used, different values of the gas constant may be applied.
The ideal gas law combines several classic gas laws, including Boyle's Law, Charles's Law, and Avogadro's Law, into one unified equation.
The ideal gas equation can be rearranged to solve for any unknown variable depending on the available information.
This flexibility makes the equation extremely useful in chemistry calculations, physics experiments, and engineering applications.
| Variable | Rearranged Formula |
|---|---|
| Pressure | P = (nRT) / V |
| Volume | V = (nRT) / P |
| Moles | n = (PV) / (RT) |
| Temperature | T = (PV) / (nR) |
When performing calculations, temperature must always be converted to Kelvin. This is because the ideal gas equation requires an absolute temperature scale.
The ideal gas law plays a crucial role in many scientific and industrial fields. It helps researchers understand how gases behave under varying pressure, temperature, and volume conditions.
Some of the most common applications include:
For example, meteorologists use gas law equations to study atmospheric pressure and temperature changes. Similarly, chemical engineers apply the ideal gas equation when designing industrial reactors and gas processing equipment.
| Field | Application |
|---|---|
| Chemistry | Predicting reaction gas volumes |
| Meteorology | Understanding atmospheric pressure |
| Engineering | Designing gas storage and compressors |
| Physics | Studying thermodynamic systems |
Although the ideal gas law provides accurate predictions in many situations, it relies on several simplifying assumptions.
The equation assumes that gas particles haveno volume and that there areno intermolecular forces between them. In reality, real gases do have particle size and experience attractive forces.
Because of these assumptions, gases may deviate from ideal behavior under certain conditions.
When these deviations become significant, scientists use more advanced equations such as theVan der Waals equation to better describe real gas behavior.
Despite these limitations, the ideal gas law remains one of the most widely used equations in chemistry, physics, and engineering education.
The Ideal Gas Law is a fundamental equation in chemistry and physics that describes the relationship between pressure, volume, temperature, and amount of gas.
An Ideal Gas Law calculator helps determine pressure, volume, temperature, or moles using the PV = nRT equation.
The Ideal Gas Law formula is PV = nRT.
P represents the pressure exerted by gas molecules on the walls of a container.
V represents the volume occupied by the gas.
n represents the amount of gas in moles.
T represents the absolute temperature of the gas measured in Kelvin.
R is the universal gas constant that links energy, temperature, and amount of gas.
A commonly used value is 0.0821 L·atm/(mol·K).
Gas law equations require absolute temperature to maintain proportional relationships.
No. Temperature must be converted to Kelvin before using the equation.
Pressure in atmospheres, volume in liters, temperature in Kelvin, and moles in mol.
Pressure can be calculated using P = (nRT) ÷ V.
Volume can be calculated using V = (nRT) ÷ P.
Temperature can be calculated using T = PV ÷ (nR).
An ideal gas is a theoretical gas that follows gas laws perfectly without intermolecular interactions.
Real gases may deviate from the equation at high pressure or low temperature.
Strong intermolecular forces and molecular volume can cause deviations.
Boyle’s Law states that pressure and volume are inversely proportional when temperature is constant.
Charles’ Law states that volume increases proportionally with temperature when pressure is constant.
Gay-Lussac’s Law states that pressure increases with temperature when volume is constant.
The Combined Gas Law relates pressure, volume, and temperature when the amount of gas remains constant.
It combines Boyle’s Law, Charles’ Law, and Avogadro’s Law into one equation.
It is used in chemistry, physics, meteorology, engineering, and environmental science.
Meteorologists use it to analyze atmospheric pressure and temperature relationships.
Engineers use it to model gas behavior in engines, pipelines, and industrial systems.
Yes. Chemistry and physics students commonly use them to solve gas law problems.
Yes. It helps visualize how pressure, temperature, volume, and moles interact.
It assumes molecules have negligible volume and no intermolecular forces.
Students, teachers, scientists, and engineers frequently use gas law calculators.