# How do I use the combined gas law?

Solves the combined gas law P₁V₁/T₁ = P₂V₂/T₂ for any one of pressure, volume or temperature before or after a change, in atm, kPa, mmHg, L, °C or K.

- Page: https://www.acalculator.org/chemistry/combined-gas-law-calculator
- JSON spec: https://www.acalculator.org/chemistry/combined-gas-law-calculator.json
- Version: 212825213a5b

## Default answer

Example with the default inputs (Pressure P₁ 153 atm, Volume V₁ 13.2 L, Temperature T₁ 27 °C, Pressure P₂ 3.13 atm, Temperature T₂ 37 °C): A gas at 153 atm, 13.2 L and 27 °C is at 3.13 atm, 666.7 L and 37 °C after the change.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| p1 | Pressure P₁ | The gas pressure before the change (absolute, not gauge). |
| v1 | Volume V₁ | The gas volume before the change. |
| t1 | Temperature T₁ | The gas temperature before the change; above absolute zero. |
| p2 | Pressure P₂ | The gas pressure after the change (absolute, not gauge). |
| v2 | Volume V₂ | The gas volume after the change. |
| t2 | Temperature T₂ | The gas temperature after the change; above absolute zero. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| p1 | Pressure P₁ | The gas pressure before the change (absolute, not gauge). |
| v1 | Volume V₁ | The gas volume before the change. |
| t1 | Temperature T₁ | The gas temperature before the change; above absolute zero. |
| p2 | Pressure P₂ | The gas pressure after the change (absolute, not gauge). |
| v2 | Volume V₂ | The gas volume after the change. |
| t2 | Temperature T₂ | The gas temperature after the change; above absolute zero. |

## Method

P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂, with T in kelvins. For example V₂ = P₁V₁T₂ ÷ (T₁P₂).

## Assumptions

- The gas is ideal and its amount does not change (no gas leaks in or out).
- Temperatures are absolute: °C + 273.15 = K, and (°F + 459.67) × 5/9 = K.
- Pressures are absolute pressures, not gauge readings.

## Worked examples

1. p1 = 15,502,725, v1 = 0.0132, t1 = 300.15, p2 = 317,147.25, t2 = 310.15 gives v2 = 0.666737. Source: OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law, https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Example 9.10 Using the Combined Gas Law: about 667 L (the book rounds to 300 K and 310 K).
2. p1 = 360,000, v1 = 0.00035, t1 = 297.15, v2 = 0.00035, t2 = 323.15 gives p2 = 391,499.242807. Source: OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law, https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Example 9.5 Predicting Change in Pressure with Temperature: about 390 kPa.
3. p1 = 101,325, v1 = 0.00015, t1 = 273.15, p2 = 101,325, v2 = 0.000132 gives t2 = 239.8257. Source: OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law, https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Example 9.7 Measuring Temperature with a Volume Change: 239.8 K (−33.4 °C).
4. p1 = 99,991.776316, v1 = 0.0003, t1 = 283.15, p2 = 99,991.776316, t2 = 303.15 gives v2 = 0.000321. Source: OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law, https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Example 9.6 Predicting Change in Volume with Temperature: 0.321 L.

## FAQ

### What is the combined gas law?

For a fixed amount of gas, pressure × volume ÷ temperature stays the same: P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂. It joins Boyle’s law (P and V), Charles’s law (V and T) and Gay-Lussac’s law (P and T) in one equation.

### Why must the temperature be in kelvins?

The law works with absolute temperature, which starts at absolute zero. 27 °C is 300.15 K. You can type °C or °F here; the calculator turns every temperature into kelvins before it divides.

### How do I solve for the final volume?

Rearrange to V₂ = P₁V₁T₂ ÷ (T₁P₂). A 13.2 L scuba tank at 153 atm and 27 °C gives about 667 L of air at 3.13 atm and 37 °C.

### How do I use it when one value stays the same?

Type the same value before and after. With equal volumes it becomes Gay-Lussac’s law: a can at 360 kPa and 24 °C reaches about 391 kPa at 50 °C.

### Do the units have to match?

No. Each value can be in its own unit (atm, kPa, mmHg, psi, L, mL, °C, K, °F). The calculator converts everything to pascals, cubic meters and kelvins, and shows the answer in the unit you pick.

### Should I use gauge pressure from a tire or tank gauge?

No. The law needs absolute pressure. Add the air pressure around you (about 1 atm, 101.325 kPa or 14.7 psi) to a gauge reading first.

## Sources

- OpenStax, Chemistry 2e, section 9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law: P₁V₁/T₁ = P₂V₂/T₂; Examples 9.5, 9.6, 9.7 and 9.10. CC BY 4.0, retrieved 2026-10-02. https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law
- NIST Special Publication 811, Appendix B.9: 1 standard atmosphere = 101,325 Pa exactly; 1 psi = 6,894.757 Pa. Retrieved 2026-10-02. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b9