Solve Charles's Law (V1/T1 = V2/T2) for any unknown gas volume or temperature at constant pressure. Enter three known values and select which variable to solve for. Supports Kelvin, Celsius, and Fahrenheit for temperature, and litres, millilitres, or cubic metres for volume.
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Standard Formula
Charles's Law: V1/T1 = V2/T2 at constant pressure and fixed amount of gas. Temperature must be in Kelvin for the ratio to be valid.
V₁ / T₁ = V₂ / T₂
V = volume | T = absolute temperature (Kelvin) | pressure and amount of gas constant
1. Initial State
2. Final State
Result
Unknown
V2
Variable being solved
Calculated Value
4.00 L
In selected unit
Kelvin Equivalent
4.00 L
Always shown in K or L
Initial State
V1 (initial volume)-
T1 (initial temperature)-
T1 in Kelvin-
Final State
T2 (final temperature)-
T2 in Kelvin-
V2 (final volume)-
V1/T1 = V2/T2-
Worked Example (default values)
Known: V1 = 2 L at T1 = 0 °C (273.15 K)
Known: T2 = 273.15 °C (546.30 K)
Formula: V2 = V1 x T2 / T1
V2 = 2 x 546.30 / 273.15= 4.00 L
What is Charles's Law?
Charles's Law describes the relationship between the volume and temperature of a gas at constant pressure. It was formulated by French physicist Jacques Charles around 1787, and later confirmed and published by Joseph Louis Gay-Lussac in 1802. The law states that the volume of a fixed amount of gas is directly proportional to its absolute temperature when pressure is held constant.
This means that if you heat a gas, it expands. If you cool it, it contracts. The proportion is exact for ideal gases: doubling the Kelvin temperature exactly doubles the volume. This behaviour underpins many everyday phenomena, from why a balloon shrivels in cold weather to how hot air balloons rise.
The Formula
Charles's Law is written as:
V1 / T1 = V2 / T2
Where:
V1 is the initial volume of the gas
T1 is the initial temperature in Kelvin
V2 is the final volume of the gas
T2 is the final temperature in Kelvin
The formula can be rearranged to solve for any one unknown:
Solving For
Rearranged Formula
Final volume (V2)
V2 = V1 x T2 / T1
Final temperature (T2)
T2 = T1 x V2 / V1
Initial volume (V1)
V1 = V2 x T1 / T2
Initial temperature (T1)
T1 = T2 x V1 / V2
Temperature Conversion for Charles's Law
Because Charles's Law requires absolute temperature, you must convert Celsius or Fahrenheit to Kelvin before applying the formula. This calculator handles the conversion automatically, but the equations are:
Celsius to Kelvin: K = °C + 273.15
Fahrenheit to Kelvin: K = (°F + 459.67) x 5/9
A common mistake is to use Celsius directly. For example, if T1 = 20 °C and T2 = 40 °C, the correct Kelvin values are 293.15 K and 313.15 K. The ratio T2/T1 is 313.15/293.15 = 1.068, not 40/20 = 2.0. Using Celsius gives a significantly wrong answer.
Real-World Examples
Charles's Law explains many observable phenomena:
Hot air balloons: Air inside the balloon is heated, which increases its volume and reduces its density, causing the balloon to rise.
Tyres in cold weather: Cold temperatures decrease the volume (and therefore pressure) of air inside tyres, which is why tyre pressure drops in winter.
Bread rising in an oven: Carbon dioxide gas produced by yeast expands as the oven heats up, causing the dough to rise.
Aerosol cans: These carry warnings against exposure to heat because increasing temperature increases pressure and volume in a fixed container, which can cause the can to burst.
Breathing: The diaphragm increases lung volume, which reduces pressure and draws in air. Temperature changes also slightly affect lung volume.
Limitations of Charles's Law
Charles's Law applies precisely only to ideal gases. Real gases deviate from ideal behaviour under high pressures or at temperatures close to their boiling point. For example, carbon dioxide near its critical point, or any gas when it starts to condense into a liquid, will not follow Charles's Law accurately. For most laboratory conditions involving common gases at moderate pressures and temperatures, the law is an excellent approximation.
Sources and method: Charles's Law as formulated by Jacques Charles (c. 1787) and published by Gay-Lussac (1802). Formula V1/T1 = V2/T2 derived from the direct proportionality of volume and absolute temperature at constant pressure, per NIST and standard physical chemistry references (Atkins' Physical Chemistry).
This calculator applies Charles's Law for ideal gases at constant pressure. Real gases may deviate at extreme temperatures or pressures. For precision work, consult appropriate thermodynamic data for the specific gas involved.
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