Ideal Gas Law Calculator
PV = nRT, with the units kept honest.
Ideal Gas Law Calculator
P = nRT / V with R = 8.314 kPa L / (mol K) and T in kelvin.
Calculated instantly
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What This Calculator Does
The Ideal Gas Law Calculator solves PV = nRT for pressure using moles, temperature, and volume, then reports density and molar volume. It uses the gas constant that matches kilopascals and litres, so the units stay consistent.
How It Works
Temperature in Celsius is converted to kelvin. Pressure is moles times the gas constant 8.314 times temperature, divided by volume in litres, giving kilopascals. Dividing by 101.325 converts to atmospheres. Density is the mass of gas, moles times molar mass, divided by volume. Molar volume is volume divided by moles and is about 24.5 L/mol at 25 C and one atmosphere for an ideal gas.
Example
One mole of air at 25 C in 24.47 L gives P = 1 x 8.314 x 298.15 / 24.47 = 101.3 kPa, or about 1.000 atm. With a molar mass of 28.97 g/mol the density is 28.97 / 24.47 = 1.184 g/L, and the molar volume is 24.47 L/mol.
Formula
P = nRT / VT (K) = temperature in C + 273.15mass / volume = n x molar mass / VV / nReading the Results
Pressure
Absolute pressure in kilopascals from the ideal gas law. It is not gauge pressure; add atmospheric pressure if you need a gauge reading.
Density
Mass per litre at the stated temperature and volume. It assumes the gas behaves ideally, which is close enough for air at ordinary conditions.
Molar volume
Volume per mole. At 0 C and one atmosphere it is about 22.4 L/mol; at 25 C it is about 24.5 L/mol.
Sources and References
NIST - Ideal Gas Law and the Gas Constant
Gas constant values and units
Reference values for R and the conditions under which the ideal approximation is reasonable.
OpenStax Chemistry - The Ideal Gas Law
PV = nRT and its applications
Textbook derivation and worked examples, including unit conversion.
References identify the method or data behind this calculator. Where a standard or tariff changes, the current edition applies, and the assumptions stated above take precedence over a remembered figure.
Frequently Asked Questions
Why do I have to add 273.15 to the temperature?
The gas laws are based on absolute temperature, where zero means the particles have minimum thermal energy. Celsius starts at the freezing point of water, not absolute zero. Using 25 instead of 298.15 understates the pressure by a factor of about 12.
Which value of R should I use?
Use 8.314 when pressure is in kPa and volume in litres. Use 0.08206 when pressure is in atmospheres and volume in litres. The numerical value changes with the units, but the physical relationship does not. This calculator uses the kPa form.
When does the ideal gas law break down?
At high pressure, low temperature, or near the boiling point, intermolecular forces and molecular volume matter. Real gas equations such as van der Waals add corrections. For air at room temperature and near atmospheric pressure, the ideal approximation is usually adequate.
Is the pressure absolute or gauge?
The ideal gas law uses absolute pressure. Gauge pressure measures the difference from the surrounding atmosphere. If a gauge reads 200 kPa, the absolute pressure is about 301 kPa at sea level, and the ideal gas calculation needs the absolute value.
Can I solve for volume or moles instead?
Yes, by rearranging: V = nRT/P and n = PV/RT. This calculator is set up to solve for pressure from the other three. Use the same unit discipline, and convert temperature to kelvin before substituting.