Answer first
What this calculator tells you
Calculate the pressure of a gas from its amount, temperature and volume. Estimate the pressure in a sealed container as the temperature or volume changes. Formula: P = n × R × T ÷ V, with R = 0.082057 L·atm ÷ (mol·K). At the worked-example inputs, the pressure (atm) is 1. Holding every other input steady, moving amount of gas (mol) from 0.8 to 1.2 moves the result from 0.801 to 1.2.
Transparent method
The formula
Estimate the pressure in a sealed container as the temperature or volume changes.
Worked example
Example inputs
How to interpret the result
Pressure, volume and temperature of a gas are tied together by the amount of gas. One mole at 300 kelvin in 24.6 liters presses at about 1 atmosphere, or 101 kilopascals. Squeeze the same gas into half the space and the pressure doubles. Heat it and the pressure climbs in step with the kelvin temperature, which is why a sealed can is dangerous when it is heated.
At the worked-example inputs the pressure (atm) is 1. It rises with temperature (k) and amount of gas (mol) and falls as volume (l) increases.
These are textbook formulas for ideal conditions: no air resistance, no friction, gravity of 9.81 meters per second squared and gases that behave ideally. Real results differ, so treat them as first estimates and use the units the formulas expect (meters, kilograms, seconds).
Before you rely on it
What to check
Use kelvin, not Celsius. Adding 273.15 to a Celsius reading is the step people skip, and it changes the answer by a large factor.
The common error
Where people go wrong with ideal gas law calculator
Applying the law to a gas near condensing or at very high pressure. Real gases depart from the ideal formula there, and the result can be well off.
Sensitivity evidence
How amount of gas (mol) changes the pressure (atm)
Holding every other input at the worked-example value, moving amount of gas (mol) from 0.8 to 1.2 moves the pressure (atm) from 0.801 to 1.2: a spread of 0.4, or 40% of the worked-example result.
| Amount of gas (mol) | Pressure (atm) | Pressure (kPa) |
|---|---|---|
| 0.8 | 0.801 | 81.1 |
| 0.9 | 0.901 | 91.3 |
| 1worked example | 1 | 101.4 |
| 1.1 | 1.1 | 111.5 |
| 1.2 | 1.2 | 121.7 |
Every input, tested
Which input moves the pressure (atm) most
Of the 3 inputs, volume (l) moves the pressure (atm) most (0.207 across the range tested) and amount of gas (mol) moves it least (0.2).
| Input | Tested from | To | Pressure (atm) at each end | Swing |
|---|---|---|---|---|
| Volume (L) | 22 | 27 | 1.1 to 0.912 | 0.207 (21%) |
| Temperature (K) | 270 | 330 | 0.901 to 1.1 | 0.2 (20%) |
| Amount of gas (mol) | 0.9 | 1.1 | 0.901 to 1.1 | 0.2 (20%) |
Two variables at once
Pressure (atm) by amount of gas (mol) and temperature (k)
Across the grid the pressure (atm) runs from 0.64 to 1.4. Moving amount of gas (mol) from 0.8 to 1.2 shifts it by 0.4 at the middle column, and moving temperature (k) from 240 to 360 shifts it by 0.4 at the middle row, so neither is the bigger lever here.
| Amount of gas (mol) \ Temperature (K) | 240 | 300 | 360 |
|---|---|---|---|
| 0.8 | 0.64 | 0.801 | 0.961 |
| 0.9 | 0.721 | 0.901 | 1.1 |
| 1 | 0.801 | 1 | 1.2 |
| 1.1 | 0.881 | 1.1 | 1.3 |
| 1.2 | 0.961 | 1.2 | 1.4 |
The highlighted cell is the worked example: 1.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Amount of gas (mol) | 1 | Enter the amount of gas (mol) used in this calculation. |
| Temperature (K) | 300 | Kelvin: add 273.15 to a Celsius reading. |
| Volume (L) | 24.6 | Enter the volume (l) used in this calculation. |
| Pressure (atm) | 1 | |
| Pressure (kPa) | 101.4 | |
Inputs, definitions and assumptions
Amount of gas (mol)
Enter the amount of gas (mol) used in this calculation. The prefilled worked-example value is 1.
Temperature (K)
Kelvin: add 273.15 to a Celsius reading. The prefilled worked-example value is 300.
Volume (L)
Enter the volume (l) used in this calculation. The prefilled worked-example value is 24.6.
How to use this calculator
- 1Verify the inputs. Gather amount of gas (mol), temperature (k) and volume (l) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the pressure (atm) at 1. Store your own version of it as Scenario A.
- 3Test one change. Start with volume (l), the input with the biggest effect here: moving volume (l) from 22 to 27 takes the pressure (atm) from 1.1 to 0.912, a swing of 21% of the worked-example figure.
- 4Check the extremes. At half the example volume (l) (12.3) the pressure (atm) is 2; at double (49.2) it is 0.5.
People also ask
Frequently asked questions
How do you calculate ideal gas law?
P = n × R × T ÷ V, with R = 0.082057 L·atm ÷ (mol·K). At the worked-example inputs the pressure (atm) is 1.
What does the ideal gas law result mean?
Estimate the pressure in a sealed container as the temperature or volume changes. At the worked-example inputs the pressure (atm) is 1. It rises with temperature (k) and amount of gas (mol) and falls as volume (l) increases.
How much does amount of gas (mol) change the pressure (atm)?
Holding every other input at the worked-example value, moving amount of gas (mol) from 0.8 to 1.2 moves the pressure (atm) from 0.801 to 1.2, a spread of 0.4.
What are the limits of this ideal gas law calculator?
These are textbook formulas for ideal conditions: no air resistance, no friction, gravity of 9.81 meters per second squared and gases that behave ideally. Real results differ, so treat them as first estimates and use the units the formulas expect (meters, kilograms, seconds). The tables on this page test amount of gas (mol) only from 0.8 to 1.2; a value outside that range is not tabulated here.
Which input moves the pressure (atm) most in the ideal gas law calculator?
Ranked by how far each moves the pressure (atm) across the range tested: volume (l) (0.207, 21%), temperature (k) (0.2, 20%) and amount of gas (mol) (0.2, 20%).
If I double volume (l) in the ideal gas law calculator, does the pressure (atm) double?
Doubling it from 24.6 to 49.2 takes the pressure (atm) from 1 to 0.5, which is 0.50 times the worked-example figure. So it falls instead of rising. Halving it to 12.3 gives 2.
How much does temperature (k) matter in the ideal gas law calculator?
The worked example uses 300. With the other inputs left at the worked example, moving temperature (k) from 270 to 330 takes the pressure (atm) from 0.901 to 1.1, a swing of 20% of the worked-example figure.
How much does volume (l) matter in the ideal gas law calculator?
The worked example uses 24.6. With the other inputs left at the worked example, moving volume (l) from 22 to 27 takes the pressure (atm) from 1.1 to 0.912, a swing of 21% of the worked-example figure.
Which inputs change the pressure (kpa) in the ideal gas law calculator?
At the worked-example inputs it is 101.4. Amount of gas (mol) takes it from 91.3 to 111.5, temperature (k) takes it from 91.3 to 111.5 and volume (l) takes it from 113.4 to 92.4.
Which units do the formulas expect?
Meters, kilograms and seconds, which give newtons, joules and watts. A speed in miles per hour or a mass in pounds needs converting first, or the result will be wrong by a fixed factor.
Sources and evidence
Free Calculators Online is independent and is not affiliated with or endorsed by the source organizations. Educational estimates only.