Last updated: June 2026
Use this ideal gas calculator to solve gas law questions involving pressure, volume, amount of gas and temperature. This page also includes molar mass of gas and molar gas volume because both are applications of the ideal gas equation.
What is an ideal gas?
An ideal gas is a simplified model of a gas. In this model, gas particles are assumed to have negligible volume and no intermolecular forces between them. They move randomly and collide elastically with the walls of the container.
Real gases do not behave perfectly like ideal gases, but many gases behave approximately ideally at low pressure and high temperature. This makes the ideal gas equation very useful for school chemistry calculations.
Ideal gas equation
The ideal gas equation is:
pV = nRT
where p is pressure, V is volume, n is amount of gas in mol, R is the gas constant, and T is temperature in kelvin.
In most A-Level Chemistry calculations, the safest unit set is:
p in Pa, V in m3, n in mol, R = 8.314 J mol−1 K−1, and T in K.
Important unit conversions
Many mistakes in ideal gas calculations come from using the wrong units. The formula pV = nRT is simple, but the units must match.
1 dm3 = 1000 cm3
1 dm3 = 1.00 × 10−3 m3
1 atm = 101325 Pa
temperature in K = temperature in °C + 273.15
How to use the ideal gas equation
First identify which quantity is unknown. Then rearrange pV = nRT.
n = pV / RT
p = nRT / V
V = nRT / p
T = pV / nR
Molar Gas Volume Calculator
Molar gas volume is the volume occupied by one mole of gas under a stated set of conditions.
From the ideal gas equation:
pV = nRT
If n = 1 mol, then:
Vm = RT / p
where Vm is the molar gas volume.
At room temperature and pressure, many school chemistry questions use:
1 mol of gas = 24.0 dm3
At standard temperature and pressure, some questions use:
1 mol of gas = 22.4 dm3
Always check the conditions stated in the question before choosing the molar gas volume.
Molar Mass of Gas Calculator
The molar mass of a gas can be found by combining the ideal gas equation with the relationship between mass and moles.
From the mole formula:
n = m / M
where m is mass and M is molar mass.
Substitute n = m / M into pV = nRT:
pV = (m / M)RT
Rearranging gives:
M = mRT / pV
This is why a molar mass of gas calculation is really an ideal gas calculation in disguise.
Gas density and molar mass
Another common form connects gas density with molar mass. Since density is mass divided by volume, the ideal gas equation can be rearranged to:
M = dRT / p
where d is gas density. This form is useful when the question gives gas density instead of separate mass and volume.
Worked examples
Example 1: Finding moles of gas
A gas occupies 24.0 dm3 at 298 K and 101000 Pa. Find the amount of gas in mol.
n = pV / RT
24.0 dm3 = 0.0240 m3
n = (101000 × 0.0240) / (8.314 × 298)
n = 0.978 mol
Example 2: Finding molar gas volume
Find the molar gas volume at 298 K and 100000 Pa.
Vm = RT / p
Vm = (8.314 × 298) / 100000
Vm = 0.0248 m3 mol−1
Since 1 m3 = 1000 dm3:
Vm = 24.8 dm3 mol−1
Example 3: Using molar gas volume shortcut
Calculate the volume occupied by 0.250 mol of gas at room temperature and pressure, assuming 1 mol of gas occupies 24.0 dm3.
volume = 0.250 × 24.0
volume = 6.00 dm3
Example 4: Finding molar mass of a gas
A gas has mass 0.720 g and occupies 300 cm3 at 298 K and 100000 Pa. Find its molar mass.
M = mRT / pV
0.720 g = 0.000720 kg
300 cm3 = 0.000300 m3
M = (0.000720 × 8.314 × 298) / (100000 × 0.000300)
M = 0.0595 kg mol−1 = 59.5 g mol−1
Common exam traps
Frequently Asked Questions
What does an ideal gas calculator calculate?
An ideal gas calculator can calculate pressure, volume, amount of gas or temperature using pV = nRT.
What value of R should I use?
For A-Level and Singapore H2 Chemistry, the most common value is R = 8.314 J mol−1 K−1. With this value, pressure should be in Pa and volume should be in m3.
What is molar gas volume?
Molar gas volume is the volume occupied by one mole of gas under stated conditions. At room temperature and pressure, many school questions use 24.0 dm3 mol−1.
How do I calculate molar mass of a gas?
Use M = mRT / pV. This comes from combining pV = nRT with n = m / M.
Why group gas molar mass and molar gas volume with ideal gas?
Both are direct applications of the ideal gas equation. Grouping them together helps students see that the same core equation is being used in different forms.