Ideal Gas Law Calculator
Solves PV = nRT for pressure, volume, moles or temperature — leave one blank.
Last updated
Your details
Leave exactly one of the four boxes above blank — that is the one this solves for.
Result
- Pressure
- 101,325 Pa
- Volume
- 0.02241397 m³
- Amount
- 1 mol
- Temperature
- 273.15 K
- Molar volume
- 22.414 L/mol
1 atm
22.41397 litres
0 °C
22.414 L/mol at 0 °C and 1 atm
Solving for volume…
P × V = n × R × T
R = 8.314463 J/(mol·K)
T = 273.15 K
n × R × T = 2,271.0955
V = 0.02241397 m³
Formula — written step by step
One mole at 0 °C and one atmosphere…
P × V = n × R × T
T = 0 °C = 273.15 K
R = 8.314463 J/(mol·K)
V = nRT ÷ P
V = 1 × 8.314463 × 273.15 ÷ 101,325
V = 0.0224140 m³ = 22.414 L
P is absolute pressure in pascals, V volume in cubic metres, n the amount in moles, R the molar gas constant and T absolute temperature in kelvin. 22.414 litres per mole at 0 °C and one atmosphere is the molar volume every chemistry course begins with.
A worked example
A tyre on a cold morning
- Inflated at
- 25 °C — 298.15 K
- Gauge pressure
- 220 kPa, so 321 kPa absolute
- Morning temperature
- −5 °C — 268.15 K
- Volume and amount are fixed, so P ÷ T is constant
- P₂ = P₁ × T₂ ÷ T₁
- P₂ = 321 × 268.15 ÷ 298.15
- P₂ = 288.7 kPa absolute
Gauge pressure falls to about 187 kPa — a drop of 33 kPa
That is roughly 5 psi lost to temperature alone, with no leak at all. The calculation only works in absolute terms: using gauge pressure and Celsius would give a drop several times too large. This is why tyre pressures should be checked cold and why warning lights appear on the first frost.
How to use this calculator
- Fill in three of the four boxes — pressure, volume, amount and temperature — and leave the fourth blank.
- Pressure must be absolute, not gauge. Add 101,325 Pa to a gauge reading before entering it.
- Choose your temperature unit; the calculator converts to kelvin, which is what the law requires.
- The molar volume row is a quick sanity check: near 0 °C and one atmosphere it should sit close to 22.4 L/mol.
One equation, four quantities
The ideal gas law states that pressure times volume equals the amount of gas times the gas constant times absolute temperature. It ties together every property of a gas sample in a single relationship, and knowing any three fixes the fourth.
It also absorbs the historical gas laws. Boyle’s, Charles’s, Gay-Lussac’s and Avogadro’s laws are each PV = nRT with two quantities held constant, which is why the same equation answers questions that were once considered separate.
Temperature must be absolute
The law requires kelvin, and this is where most errors happen. Celsius has an arbitrary zero — the freezing point of water — while the law needs a scale whose zero means no thermal motion at all.
The consequence of getting it wrong is not a small inaccuracy. Substituting 0 °C directly would predict that the gas occupies no volume whatsoever, and a Celsius value anywhere near room temperature produces an error of several hundred percent. This calculator converts for you, but the same trap waits in any spreadsheet.
Where the ideal model breaks down
The law assumes gas molecules have no volume of their own and no attraction between them. Both assumptions are good at ordinary pressures and temperatures well above the boiling point, where molecules are far apart and interact rarely.
They fail at high pressure, where the molecules’ own volume becomes a significant fraction of the container, and near condensation, where intermolecular attraction pulls the real volume below the prediction. The van der Waals equation corrects for both with two substance-specific constants, at the cost of the simplicity that makes this form so useful.
Formula & methodology
What this calculator assumes
- Assumes molecules occupy no volume and do not attract each other. Both hold well at ordinary pressures and well above the boiling point, and fail at high pressure or near condensation.
- Temperature must be absolute. A Celsius value would predict zero volume at 0 °C.
- Pressure must be absolute, not gauge. Adding atmospheric pressure to a gauge reading is required.
- Accurate to roughly 1% for common gases at everyday conditions. The van der Waals equation does better where it matters.
Sources
The gas laws as special cases
| Law | Held constant | Relationship |
|---|---|---|
| Boyle’s | n, T | P × V is constant |
| Charles’s | n, P | V ÷ T is constant |
| Gay-Lussac’s | n, V | P ÷ T is constant |
| Avogadro’s | P, T | V ÷ n is constant |
| Combined | n | PV ÷ T is constant |
Each historical gas law is PV = nRT with two quantities held fixed. They were discovered separately over 150 years and only later recognised as one relationship.
Frequently asked questions
Why must temperature be in kelvin?
Because the law needs a scale whose zero is absolute. Using Celsius would predict zero volume at 0 °C and gives errors of hundreds of percent near room temperature.
Should I use gauge or absolute pressure?
Absolute. Add atmospheric pressure — about 101,325 Pa — to any gauge reading before entering it. This is the second most common source of error after the temperature scale.
What is a mole?
An amount of substance containing 6.02214076 × 10²³ particles. For a gas at 0 °C and one atmosphere, one mole occupies 22.414 litres regardless of which gas it is.
How accurate is the ideal gas law?
Within about 1% for most gases at ordinary temperatures and pressures. It degrades at high pressure and near the condensation point, where the van der Waals equation does better.