Molar Volume of a Gas at STP: Formula and Calculator

This calculator finds the volume occupied by one mole of an ideal gas at standard temperature and pressure (STP), using the molar gas constant and the stated STP convention. Enter the temperature and pressure you are using; the result is molar volume in liters per mole, with a worked example and the assumptions explained below.

Formula

For an ideal gas, molar volume is the gas constant multiplied by absolute temperature, divided by pressure:

V_m = RT / P

• V_m is molar volume, in L/mol.
• R is the gas constant, 8.31446261815324 L·kPa/(mol·K). This is numerically equivalent to 8.31446261815324 J/(mol·K), since 1 J = 1 kPa·L.
• T is absolute temperature, in kelvins. Convert Celsius to kelvins with T = t + 273.15.
• t is the entered temperature, in °C.
• P is absolute pressure, in kPa.

The calculator uses the expression 8.31446261815324 × (t + 273.15) / p. Its second result converts liters to cubic centimeters using 1 L = 1000 cm³. Pressure must be absolute pressure, measured from a vacuum—not gauge pressure relative to the surrounding air.

Worked Example

Use the calculator’s default values: t = 0 °C and p = 101.325 kPa. These represent one common definition of STP: 0 °C and 1 atmosphere.

1. Convert the temperature to kelvins: T = 0 + 273.15 = 273.15 K.
2. Substitute into the ideal-gas formula: V_m = (8.31446261815324 × 273.15) / 101.325.
3. Evaluate: V_m = 22.41396954 L/mol, which rounds to 22.4140 L/mol at four decimal places.
4. Convert to cubic centimeters: 22.41396954 × 1000 = 22413.96954 cm³/mol, which rounds to 22414.0 cm³/mol.

So, at these conditions, one mole of an ideal gas occupies about 22.414 L. The value is not universal for every definition of STP: different reference temperatures or pressures produce different molar volumes.

Assumptions

• The gas behaves ideally. Real gases can deviate, particularly at high pressure or low temperature.
• Temperature is uniform and entered in Celsius; the calculation converts it to kelvins.
• Pressure is absolute and entered in kPa.
• STP is not a single universally used convention. The example uses 0 °C and 101.325 kPa (1 atm). The calculator lets you enter another reference condition.

Step-by-Step

1. Check which STP convention applies. A common textbook convention is 273.15 K (0 °C) and 101.325 kPa (1 atm). Some standards and references use 100 kPa instead. Use the temperature and pressure specified by your class, lab method, or reference source rather than assuming every source means the same thing.
2. Set the temperature. Enter the reference temperature in degrees Celsius. For 0 °C STP, leave the default at 0. For a different reference temperature, enter that value. The calculator adds 273.15 to convert it to kelvins, the absolute scale required by the gas law.
3. Enter absolute pressure. Enter the pressure in kPa. For 1 atm, use 101.325 kPa; for 1 bar, use 100 kPa. If a source gives pressure in atmospheres, multiply by 101.325 to convert atm to kPa. If it gives bar, multiply by 100 to convert bar to kPa.
4. Calculate the molar volume. Apply V_m = RT/P. The first result, in L/mol, is the volume per mole under the entered conditions. It is not the total volume of a particular gas sample unless the sample amount is exactly one mole.
5. Check the second unit. The calculator also reports cm³/mol. Since 1 L equals 1000 cm³, this is the same volume expressed in a smaller unit, not a different answer.
6. Use the result for a sample only if needed. For an ideal gas amount n, total volume is V = nV_m. For example, multiply the molar volume by 0.50 mol to estimate the volume of half a mole at the same temperature and pressure. Keep units consistent and do not confuse molar volume with sample volume.

Common Mistakes

• Mixing STP conventions: 0 °C and 100 kPa do not give exactly the same molar volume as 0 °C and 101.325 kPa. State the convention when reporting an answer.
• Using Celsius directly: The gas-law equation requires kelvins. Substituting 0 for 0 °C would incorrectly make the calculated volume zero.
• Entering gauge pressure: A gauge reading of zero does not mean zero absolute pressure; it usually means pressure equals the local atmosphere. Convert gauge pressure to absolute pressure before using the formula.
• Using mismatched units for R and pressure: The calculator uses R in L·kPa/(mol·K), so pressure must be in kPa. Do not enter 1.01325 as though it were kPa; that number is a pressure in bar.
• Calling the result an exact real-gas volume: 22.414 L/mol is an ideal-gas calculation for the stated conditions. Real-gas behavior may make an actual measured value differ.
• Rounding too early: Keep the full calculator result through intermediate steps, then round the reported answer to match the precision of the pressure and temperature data.

Tips

• Write the chosen STP temperature and pressure beside your result, such as “22.414 L/mol at 273.15 K and 101.325 kPa.” This makes the convention clear.
• For a quick reasonableness check near 0 °C and 1 atm, expect an ideal-gas result close to 22.4 L/mol.
• Use absolute temperature and absolute pressure consistently. Both are measured from zero on their respective scales.
• If you need a volume at conditions other than the reference state, enter those conditions directly. The same ideal-gas equation works for any positive absolute pressure and temperature, subject to the ideal-gas limitation.
• When bench work is implied, follow your lab method, the safety data sheet (SDS) and your supervisor.

Troubleshooting

The answer is far from 22.4 L/mol. Check that the temperature is near 0 °C, pressure is near 101.325 kPa, and the pressure field contains kPa rather than atm or bar. A different valid STP convention or reference condition will change the result.

The answer is negative or the temperature is rejected. Celsius temperatures below −273.15 °C are not physically possible. Confirm the temperature unit and decimal placement; do not enter a Kelvin value in the Celsius field.

The answer seems too small or too large by a factor of about 1000. Check whether you are reading L/mol or cm³/mol. The displayed outputs differ by exactly 1000 because 1 L = 1000 cm³.

A measured gas volume does not match the calculation. Verify the sample’s actual temperature and absolute pressure, and consider whether the gas is sufficiently close to ideal under those conditions. The formula predicts an ideal-gas value; measurement conditions and real-gas effects can cause a difference.

Frequently Asked Questions

What is the molar volume of an ideal gas at STP?
At 0 °C and 101.325 kPa (1 atm), it is about 22.414 L/mol. The precise value depends on the STP convention used.

Is STP 1 atm or 100 kPa?
Both conventions appear in educational and technical references. One common textbook definition is 0 °C and 1 atm; another standard reference pressure is 100 kPa. Always check the source’s definition.

Why does molar volume change with temperature and pressure?
From V_m = RT/P, increasing absolute temperature increases molar volume, while increasing absolute pressure decreases it, assuming ideal-gas behavior.

Can I use this formula for a real gas?
You can use it as an ideal-gas estimate. At conditions where intermolecular forces or molecular volume matter, a real-gas equation or experimental data may be needed.

How do I find the volume of more or less than one mole?
Multiply the molar volume by the amount in moles: V = nV_m. The amount and the molar volume must refer to the same temperature and pressure.

Does molar volume mean the volume of one molecule?
No. It is the volume occupied by one mole of a substance, which contains Avogadro’s number of particles. It is usually reported in L/mol.

Related

• Van der Waals Gas Pressure Calculator: Real Gas Pressure
• The Ideal Gas Law Calculator: Pressure From PV = nRT
• Molar Volume Calculation: Ideal Gas Vm = RT ÷ P

in t | Temperature | °C | 0 | -273.15
in p | Pressure | kPa | 101.325 | 0
out vm | Molar volume at STP | L/mol | 8.31446261815324 * (t + 273.15) / p | 4
out vcm | Molar volume | cm³/mol | vm * 1000 | 1