Answer first
What this calculator tells you
Find the final volume of a gas after its pressure and temperature change. Predict how a gas changes volume when both its pressure and its temperature shift. Formula: P₁ × V₁ ÷ T₁ = P₂ × V₂ ÷ T₂, so V₂ = P₁ × V₁ × T₂ ÷ (T₁ × P₂), with temperatures in kelvin. At the worked-example inputs, the final volume (l) is 5.8. Holding every other input steady, moving initial pressure (any unit) from 0.8 to 1.2 moves the result from 4.7 to 7.
Transparent method
The formula
Predict how a gas changes volume when both its pressure and its temperature shift.
Worked example
Example inputs
How to interpret the result
The combined gas law joins Boyle's, Charles's and Gay-Lussac's laws: pressure times volume divided by temperature stays constant for a fixed amount of gas. Raise the pressure from 1 to 2 and the temperature from 300 to 350 kelvin, and 10 liters shrink to about 5.83. Pressure pushes the volume down, and the temperature pushes it up, and the two effects multiply.
At the worked-example inputs the final volume (l) is 5.8. It rises with initial pressure (any unit), initial volume (l) and final temperature (k) and falls as initial temperature (k) and final pressure (same unit) increase.
These are exact physics and chemistry formulas. Real-world results add tolerances from component quality, temperature and measurement error that this calculator does not model.
Before you rely on it
What to check
Use kelvin for both temperatures and the same pressure unit on both sides. A Celsius reading in the formula gives a result that is far off.
The common error
Where people go wrong with combined gas law calculator
Applying it when gas is added or leaks out. The law holds only for a fixed amount of gas, and a changing amount needs the ideal gas law instead.
Sensitivity evidence
How initial pressure (any unit) changes the final volume (l)
Holding every other input at the worked-example value, moving initial pressure (any unit) from 0.8 to 1.2 moves the final volume (l) from 4.7 to 7: a spread of 2.3, or 40% of the worked-example result.
| Initial pressure (any unit) | Final volume (L) | P × V ÷ T (constant) |
|---|---|---|
| 0.8 | 4.7 | 0.0267 |
| 0.9 | 5.3 | 0.0300 |
| 1worked example | 5.8 | 0.0333 |
| 1.1 | 6.4 | 0.0367 |
| 1.2 | 7 | 0.0400 |
Every input, tested
Which input moves the final volume (l) most
Of the 5 inputs, initial temperature (k) moves the final volume (l) most (1.2 across the range tested) and final temperature (k) moves it least (1.2).
| Input | Tested from | To | Final volume (L) at each end | Swing |
|---|---|---|---|---|
| Initial temperature (K) | 270 | 330 | 6.5 to 5.3 | 1.2 (20%) |
| Final pressure (same unit) | 1.8 | 2.2 | 6.5 to 5.3 | 1.2 (20%) |
| Initial pressure (any unit) | 0.9 | 1.1 | 5.3 to 6.4 | 1.2 (20%) |
| Initial volume (L) | 9 | 11 | 5.3 to 6.4 | 1.2 (20%) |
| Final temperature (K) | 315 | 385 | 5.3 to 6.4 | 1.2 (20%) |
Two variables at once
Final volume (L) by initial pressure (any unit) and initial volume (l)
Across the grid the final volume (l) runs from 3.7 to 8.4. Moving initial pressure (any unit) from 0.8 to 1.2 shifts it by 2.3 at the middle column, and moving initial volume (l) from 8 to 12 shifts it by 2.3 at the middle row, so neither is the bigger lever here.
| Initial pressure (any unit) \ Initial volume (L) | 8 | 10 | 12 |
|---|---|---|---|
| 0.8 | 3.7 | 4.7 | 5.6 |
| 0.9 | 4.2 | 5.3 | 6.3 |
| 1 | 4.7 | 5.8 | 7 |
| 1.1 | 5.1 | 6.4 | 7.7 |
| 1.2 | 5.6 | 7 | 8.4 |
The highlighted cell is the worked example: 5.8.
Step by step
The worked example, input by input
| Input | Value used | What it means |
|---|---|---|
| Initial pressure (any unit) | 1 | Enter the initial pressure (any unit) used in this calculation. |
| Initial volume (L) | 10 | Enter the initial volume (l) used in this calculation. |
| Initial temperature (K) | 300 | Kelvin: add 273.15 to a Celsius reading. |
| Final pressure (same unit) | 2 | Enter the final pressure (same unit) used in this calculation. |
| Final temperature (K) | 350 | Enter the final temperature (k) used in this calculation. |
| Final volume (L) | 5.8 | |
| P × V ÷ T (constant) | 0.0333 | |
Inputs, definitions and assumptions
Initial pressure (any unit)
Enter the initial pressure (any unit) used in this calculation. The prefilled worked-example value is 1.
Initial volume (L)
Enter the initial volume (l) used in this calculation. The prefilled worked-example value is 10.
Initial temperature (K)
Kelvin: add 273.15 to a Celsius reading. The prefilled worked-example value is 300.
Final pressure (same unit)
Enter the final pressure (same unit) used in this calculation. The prefilled worked-example value is 2.
Final temperature (K)
Enter the final temperature (k) used in this calculation. The prefilled worked-example value is 350.
How to use this calculator
- 1Verify the inputs. Gather initial pressure (any unit), initial volume (l), initial temperature (k), final pressure (same unit) and final temperature (k) from your own documents; the prefilled values are examples.
- 2Save a baseline. The worked example puts the final volume (l) at 5.8. Store your own version of it as Scenario A.
- 3Test one change. Start with initial temperature (k), the input with the biggest effect here: moving initial temperature (k) from 270 to 330 takes the final volume (l) from 6.5 to 5.3, a swing of 20% of the worked-example figure.
- 4Check the extremes. At half the example initial temperature (k) (150) the final volume (l) is 11.7; at double (600) it is 2.9.
People also ask
Frequently asked questions
How do you calculate combined gas law?
P₁ × V₁ ÷ T₁ = P₂ × V₂ ÷ T₂, so V₂ = P₁ × V₁ × T₂ ÷ (T₁ × P₂), with temperatures in kelvin. At the worked-example inputs the final volume (l) is 5.8.
What does the combined gas law result mean?
Predict how a gas changes volume when both its pressure and its temperature shift. At the worked-example inputs the final volume (l) is 5.8. It rises with initial pressure (any unit), initial volume (l) and final temperature (k) and falls as initial temperature (k) and final pressure (same unit) increase.
How much does initial pressure (any unit) change the final volume (l)?
Holding every other input at the worked-example value, moving initial pressure (any unit) from 0.8 to 1.2 moves the final volume (l) from 4.7 to 7, a spread of 2.3.
What are the limits of this combined gas law calculator?
These are exact physics and chemistry formulas. Real-world results add tolerances from component quality, temperature and measurement error that this calculator does not model. The tables on this page test initial pressure (any unit) only from 0.8 to 1.2; a value outside that range is not tabulated here.
Which input moves the final volume (l) most in the combined gas law calculator?
Ranked by how far each moves the final volume (l) across the range tested: initial temperature (k) (1.2, 20%), final pressure (same unit) (1.2, 20%), initial pressure (any unit) (1.2, 20%) and initial volume (l) (1.2, 20%).
If I double initial temperature (k) in the combined gas law calculator, does the final volume (l) double?
Doubling it from 300 to 600 takes the final volume (l) from 5.8 to 2.9, which is 0.50 times the worked-example figure. So it falls instead of rising. Halving it to 150 gives 11.7.
How much does initial volume (l) matter in the combined gas law calculator?
The worked example uses 10. Holding every other input at its worked-example value, moving initial volume (l) from 9 to 11 takes the final volume (l) from 5.3 to 6.4, a swing of 20% of the worked-example figure.
How much does initial temperature (k) matter in the combined gas law calculator?
The worked example uses 300. Holding every other input at its worked-example value, moving initial temperature (k) from 270 to 330 takes the final volume (l) from 6.5 to 5.3, a swing of 20% of the worked-example figure.
How much does final pressure (same unit) matter in the combined gas law calculator?
The worked example uses 2. With the other inputs left at the worked example, moving final pressure (same unit) from 1.8 to 2.2 takes the final volume (l) from 6.5 to 5.3, a swing of 20% of the worked-example figure.
How much does final temperature (k) matter in the combined gas law calculator?
The worked example uses 350. With the other inputs left at the worked example, moving final temperature (k) from 315 to 385 takes the final volume (l) from 5.3 to 6.4, a swing of 20% of the worked-example figure.
Which inputs change the p × v ÷ t (constant) in the combined gas law calculator?
At the worked-example inputs it is 0.0333. Initial pressure (any unit) takes it from 0.0300 to 0.0367, initial volume (l) takes it from 0.0300 to 0.0367 and initial temperature (k) takes it from 0.0370 to 0.0303.
Does Ohm's law apply to every electrical component?
Only to purely resistive, linear components: a plain resistor, for instance. Components like diodes, transistors and many real-world loads have a voltage-current relationship that isn't a straight line, so Ohm's law doesn't directly describe them.
Why does wire gauge affect voltage drop?
A thinner wire (higher AWG number) has more electrical resistance per foot than a thicker one. So it dissipates more voltage as heat over the same run length and current. Long runs or high currents need a thicker gauge to keep voltage drop within an acceptable range.
Sources and evidence
Free Calculators Online is independent and is not affiliated with or endorsed by the source organizations. Educational estimates only.