Ideal Gas Law Calculator

Free Ideal Gas Law Calculator

This Ideal Gas Law Calculator solves PV = nRT for pressure, volume, temperature or amount of gas. Enter pressure in kilopascals, volume in cubic metres, temperature in Celsius and amount in moles; the calculator performs the essential kelvin conversion and displays all substitution steps. The labelled container diagram shows your live P, V, T and n values beside moving gas particles.

It is useful for chemistry and physics homework, gas-cylinder estimates, laboratory exercises and thermodynamics revision. The formula models an ideal gas, which is most accurate at relatively low pressure and high temperature. Real gases can deviate due to molecular attraction and finite molecular size.

Ideal Gas Law Formula: PV = nRT

The ideal gas equation is PV = nRT. P is absolute pressure in pascals, V is volume in cubic metres, n is amount in moles, R is the universal gas constant 8.314 J/(mol·K), and T is absolute temperature in kelvin. This calculator accepts kPa and converts it to Pa internally.

Temperature must be in kelvin, not Celsius. Convert with T(K) = T(°C) + 273.15. Using Celsius directly can create meaningless or inaccurate results because the ideal gas law uses temperature measured from absolute zero.

Worked Ideal Gas Law Example

One mole of an ideal gas at 25°C in 0.024465 m³ has pressure P = nRT/V. Convert 25°C to 298.15 K. Then P = 1 × 8.314 × 298.15 / 0.024465 ≈ 101,325 Pa, or 101.325 kPa. This is approximately one atmosphere.

If temperature rises while volume and moles are fixed, pressure rises. If volume increases at fixed temperature and moles, pressure falls. These relationships explain gas behaviour in containers, balloons and engines.

Gas Law Units and Rearrangements

Use P = nRT/V for pressure, V = nRT/P for volume, T = PV/(nR) for temperature and n = PV/(RT) for amount. Ensure compatible SI units: Pa, m³, K and mol. One atmosphere equals 101.325 kPa, and one litre equals 0.001 m³.

For simple questions where moles remain constant, Boyle's law, Charles's law or the combined gas law may be more convenient. PV = nRT combines those relationships and includes amount of gas explicitly.

When Gases Are Not Ideal

A gas acts most ideally when particles are far apart: low pressure and high temperature. At high pressure or near condensation, attractive forces and molecular volume become important. Carbon dioxide, steam and refrigerants can differ noticeably from the ideal model under practical conditions.

Engineers may use compressibility factors or real-gas equations such as van der Waals for accurate system calculations. Do not use an ideal gas result as the sole basis for pressurized equipment, storage or safety decisions.

Practical Applications and Safety

The ideal gas law supports calculations in weather balloons, respiratory systems, laboratory reactions, scuba gases, combustion, pneumatic systems and chemical processes. It connects microscopic particle motion to measurable pressure and temperature.

Pressurized gas containers can be hazardous. Temperature increases can raise pressure sharply in sealed vessels. Use rated cylinders, regulators and relief devices, and follow local safety procedures. This educational calculator does not replace pressure-vessel engineering or material compatibility checks.

Ideal Gas Law FAQ Summary

PV = nRT uses absolute pressure and kelvin temperature. Rearrange the formula for the unknown and keep SI units consistent. The model is a strong approximation for many classroom conditions but less accurate at high pressure and low temperature.