Skip to main content

Calculators

Ideal Gas Law Calculator

Solve PV = nRT for pressure, volume, moles, or temperature.

Ideal Gas Law Calculator tool

Loading tool…

Jump to a section

About This Tool

The ideal gas law connects four state variables of a gas: absolute pressure P, volume V, amount n, and absolute temperature T. This calculator rearranges PV = nRT to solve any one of those variables from the other three. Choose among common pressure, volume, and temperature units; the calculator converts them to compatible SI quantities before applying the universal gas constant. The result is useful for classroom problems and first-pass estimates when ideal-gas behavior is a reasonable approximation.

How To Use It

  1. Choose the variable you want to solve for.
  2. Choose the result unit, then enter the other three quantities in the units shown. Pressure must be absolute pressure, not gauge pressure.
  3. Temperature can be entered in Celsius, Fahrenheit, or kelvins; the calculator converts it to kelvins before using the gas equation.
  4. Review the rearranged formula, SI-unit substitution, SI result, and selected-unit result before applying the ideal-gas assumptions to a real system.

Examples

One mole near room temperature

At 25 °C, one mole occupying about 24.465 L corresponds to approximately 101.325 kPa absolute pressure under the ideal model.

Molar volume near 0 °C

At 0 °C and 101.325 kPa, one ideal mole occupies about 22.414 L.

Find amount of gas

For 10 L at 100 kPa and 26.85 °C (300 K), n = PV/(RT) ≈ 0.401 mol.

Useful Notes

The ideal gas equation

PV = nRT. Solving for each variable gives P = nRT/V, V = nRT/P, n = PV/(RT), and T = PV/(nR). This tool uses R = 8.31446261815324 Pa·m³/(mol·K).

Temperature must be absolute

Gas-law ratios require absolute temperature. Celsius values are converted with T(K) = T(°C) + 273.15. A non-positive kelvin temperature is physically invalid for this model.

Use absolute pressure

PV = nRT uses absolute pressure measured relative to vacuum. A gauge pressure reading must be converted to absolute pressure by accounting for the surrounding atmospheric pressure before it is used.

Unit consistency

The calculation converts the selected pressure unit to pascals, volume to cubic meters, and temperature to kelvins so the SI gas constant can be used consistently. Results are converted back to your selected result unit for readability.

Following the calculation steps

The result first shows the formula rearranged for the unknown, then substitutes pressure in pascals, volume in cubic meters, temperature in kelvins, amount in moles, and the SI gas constant. The final line converts the SI answer to the result unit you selected.

When the ideal model works best

Ideal-gas behavior is generally a better approximation at relatively low pressure and sufficiently high temperature, away from condensation and critical regions. The acceptable error depends on the gas and purpose.

Real-gas limitations

Real molecules occupy space and interact. At high pressure, low temperature, or near phase transitions, an equation of state or compressibility-factor method may be needed. This calculator does not model gas identity, humidity, reactions, mixtures, phase equilibrium, or measurement uncertainty.

FAQ

What does R mean in PV = nRT?

R is the universal gas constant. This calculator uses 8.31446261815324 Pa·m³/(mol·K), which is equivalent to 8.31446261815324 J/(mol·K).

How do I solve PV = nRT for volume?

Divide both sides by pressure P to isolate volume: V = nRT/P. Enter absolute pressure, moles, and temperature in the calculator, then choose Volume (V).

Can I use gauge pressure?

Not directly. The ideal gas law requires absolute pressure. Convert gauge pressure to absolute pressure first.

Why is Celsius converted to kelvins?

The gas law requires an absolute temperature scale. Celsius has an arbitrary zero and cannot be used directly in PV = nRT.

Is the ideal gas law exact?

No. It is an idealized model. Real-gas deviations can become important depending on pressure, temperature, gas identity, and proximity to a phase change.

Can I use this for air?

It can provide an ideal-gas approximation for air when conditions are appropriate, but it does not account for humidity, changing composition, or non-ideal effects.