# How does Charles law work?

Solves Charles’s law V₁/T₁ = V₂/T₂ for a gas at constant pressure: the new volume after a temperature change, or the temperature for a new volume, in liters, mL, °C, °F or kelvins.

- Page: https://www.acalculator.org/chemistry/charles-law-calculator
- JSON spec: https://www.acalculator.org/chemistry/charles-law-calculator.json
- Version: a1c25d6a32da

## Default answer

Example with the default inputs (Find V₂, Volume V₁ 0.3 L, Temperature T₁ 49.9999999999999 °F, Temperature T₂ 85.9999999999999 °F): The answer is V₂ = 0.32119 L.

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| find | Find | Which of the four values to work out from the other three. |
| v1 | Volume V₁ | The gas volume before the change. |
| t1 | Temperature T₁ | The gas temperature before the change; above absolute zero. |
| 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 |
| --- | --- | --- |
| result | Answer | The value worked out, to 6 significant figures. |
| v1L | V₁ (L) | The volume before the change, in liters. |
| t1K | T₁ (K) | The temperature before the change, in kelvins. |
| v2L | V₂ (L) | The volume after the change, in liters. |
| t2K | T₂ (K) | The temperature after the change, in kelvins. |

## Method

V₁ ÷ T₁ = V₂ ÷ T₂ with T in kelvins: V₂ = V₁T₂ ÷ T₁; T₂ = T₁V₂ ÷ V₁; V₁ = V₂T₁ ÷ T₂; T₁ = T₂V₁ ÷ V₂.

## Assumptions

- The pressure and the amount of gas stay the same, and the gas is ideal.
- Temperatures are absolute: K = °C + 273.15; K = (°F + 459.67) × 5/9.

## Worked examples

1. find = v2, v1 = 0.0003, t1 = 283.15, t2 = 303.15 gives v2L = 0.32119, result = V₂ = 0.32119 L. Source: OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law (Charles’s law, V ÷ T constant), 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.
2. find = t2, v1 = 0.00015, t1 = 273.15, v2 = 0.000132 gives t2K = 239.8257, result = T₂ = 239.826 K (−33.3243 °C). Source: OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law (Charles’s law, V ÷ T constant), 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).
3. find = v2, v1 = 0.000405, t1 = 298, t2 = 467 gives v2L = 0.634681. Source: OpenStax, Chemistry 2e, §9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law (Charles’s law, V ÷ T constant), https://openstax.org/books/chemistry-2e/pages/9-2-relating-pressure-volume-amount-and-temperature-the-ideal-gas-law, Check Your Learning after Example 9.6: 635 mL.

## FAQ

### What is Charles’s law?

At constant pressure, the volume of a fixed amount of gas is proportional to its absolute temperature: V ÷ T stays the same, so V₁ ÷ T₁ = V₂ ÷ T₂. Double the kelvin temperature and the volume doubles.

### Why must I use kelvins?

The law holds for absolute temperature, which starts at absolute zero. Doubling 10 °C to 20 °C does not double the volume; 283.15 K to 293.15 K raises it by only about 3.5%. Type °C or °F and the page converts.

### How do I find the new volume?

V₂ = V₁ × T₂ ÷ T₁. 0.300 L of gas warmed from 10 °C (283.15 K) to 30 °C (303.15 K) grows to 0.300 × 303.15 ÷ 283.15 = 0.321 L.

### How do I find a temperature from a volume change?

T₂ = T₁ × V₂ ÷ V₁. Hydrogen that shrinks from 150.0 cm³ at 0 °C to 131.7 cm³ is at 273.15 × 131.7 ÷ 150.0 = 239.8 K, about −33.3 °C.

### How is Charles’s law related to the combined gas law?

The combined gas law P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂ becomes Charles’s law when the pressure does not change. Use the combined gas law calculator when the pressure changes too.

### Does it work for liquids or solids?

No. It describes ideal gases. Real gases follow it well at ordinary pressures and temperatures, but not close to the temperature where they condense.

## Sources

- OpenStax, Chemistry 2e, section 9.2 Relating Pressure, Volume, Amount, and Temperature: The Ideal Gas Law: Charles’s law, Examples 9.6 and 9.7 and the Check Your Learning after Example 9.6. CC BY 4.0, retrieved 2026-10-03. 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.8: 1 ft³ = 0.028316846592 m³; 1 gal = 0.003785411784 m³; °F and °C to kelvins. Retrieved 2026-10-03. https://www.nist.gov/pml/special-publication-811/nist-guide-si-appendix-b-conversion-factors/nist-guide-si-appendix-b8