How does Charles law work?
Type the volume and temperature of a gas before a change, and one of them after it. The Charles law calculator finds the missing value, with the pressure held constant.
- Answer
- V₂ = 0.32119 L
The answer is V₂ = 0.32119 L.
- V₁ (L)
- 0.3
- T₁ (K)
- 283.15
- V₂ (L)
- 0.32119
- T₂ (K)
- 303.15
Answer: V₂ = 0.32119 L. The answer is V₂ = 0.32119 L.
How to calculate
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.
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.
Method: V₁ ÷ T₁ = V₂ ÷ T₂ with T in kelvins: V₂ = V₁T₂ ÷ T₁; T₂ = T₁V₂ ÷ V₁; V₁ = V₂T₁ ÷ T₂; T₁ = T₂V₁ ÷ V₂.
- 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
Each example is checked against the calculator on every build.
- Find V₂, Volume V₁ 0.3 L, Temperature T₁ 50 °F, Temperature T₂ 86 °F gives V₂ (L) 0.32119, Answer 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
- Find T₂, Volume V₁ 0.15 L, Temperature T₁ 32 °F, Volume V₂ 0.1317 L gives T₂ (K) 239.8257, Answer 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)
- Find V₂, Volume V₁ 0.405 L, Temperature T₁ 76.73 °F, Temperature T₂ 380.9 °F gives V₂ (L) 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
How it works
Pick the value to find and type the other three. With the pressure and the amount of gas held constant,
V₁ ÷ T₁ = V₂ ÷ T₂
so V₂ = V₁T₂ ÷ T₁, T₂ = T₁V₂ ÷ V₁, V₁ = V₂T₁ ÷ T₂ and T₁ = T₂V₁ ÷ V₂. Temperatures are absolute: K = °C + 273.15, and K = (°F + 459.67) × 5/9. Volumes are in cubic meters inside the page: 1 L = 0.001 m³; 1 mL = 1 cm³ = 10⁻⁶ m³; 1 ft³ = 0.028316846592 m³; 1 gal = 0.003785411784 m³.
Exact arithmetic. Each value is read as the exact decimal you typed, in its unit, and every unit size is exact, so each result is an exact fraction until it is rounded for display.
Output format. The answer line shows the solved value to 6 significant figures with no thousands separators: a volume in liters (V₂ = 0.32119 L), or a temperature in kelvins with degrees Celsius (T₂ = 239.826 K (−33.3243 °C)), with the true minus sign. The rows show V₁ and V₂ in liters and T₁ and T₂ in kelvins, to 6 significant figures.
When there is no answer. A solved volume outside 10⁻¹² to 10⁹ m³, or a solved temperature outside 10⁻⁶ to 10⁹ K.
Assumptions
- The gas is ideal; its pressure and amount stay the same.
Worked examples by hand
Warming carbon dioxide (OpenStax Example 9.6). V₂ = 0.300 × 303.15 ÷ 283.15 = 0.32119 L (the book: 0.321 L).
A gas thermometer (OpenStax Example 9.7). T₂ = 273.15 × 131.7 ÷ 150.0 = 239.8257 K, which is 239.8257 − 273.15 = −33.3243 °C (the book: 239.8 K).
Heating ethane (OpenStax Check Your Learning). V₂ = 405 × 467 ÷ 298 = 634.681 mL (the book: 635 mL).
Other questions people ask
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.