Charles's Law Calculator
Why a Balloon Shrinks in the Cold
Leave a helium balloon in a warm car and it strains against its knot; carry it out into winter air and it goes noticeably slack. That's Charles's law in action: at constant pressure, a gas's volume is directly proportional to its absolute temperature. Discovered by Jacques Charles in the 1780s, it's the temperature counterpart to Boyle's pressure-volume relationship, and it depends critically on measuring temperature on an absolute scale.
The Formula
Volume and temperature (in kelvin) rise and fall together in fixed proportion, provided pressure and the amount of gas stay constant. Temperatures entered in Celsius are converted to kelvin internally before the ratio is applied, since the relationship only holds on an absolute temperature scale.
Where This Comes Into Play
- Hot air ballooning — heating the air inside the envelope increases its volume relative to the surrounding cooler air, reducing density enough to generate lift.
- Tire pressure warnings — while tires are a closed volume rather than a free-expanding one, the same temperature-volume coupling is why cold mornings trigger low-pressure alerts.
- Engine and industrial gas systems — predicting how heated gas will expand is essential for safely sizing containment and venting.
- Laboratory gas-law demonstrations — Charles's law is a standard way to introduce the concept of absolute zero, since a linear plot of volume against temperature extrapolates to zero volume at 0 K.
A Worked Example
A 1.0 L balloon at room temperature (20°C = 293.15 K) is heated to 90°C (363.15 K):
V2 = 1.0 L × (363.15 K / 293.15 K)
V2 = 1.2388 L
A 70°C temperature rise expands the balloon's volume by roughly 24%, even though pressure never changes.
How to Use This Calculator
- Choose what to solve for: Find Final Volume (V2) or Find Final Temperature (T2).
- Enter Initial Volume (V1) and Initial Temperature (T1), selecting Celsius or Kelvin.
- Enter the remaining known value — Final Temperature (T2) or Final Volume (V2).
- Select Calculate to see the result along with the worked formula, with temperature results shown in both kelvin and Celsius.
Related Calculations
For the pressure-driven version of this same family of gas laws, see the Boyle's Law Calculator, or work with pressure, volume, and temperature together using the Ideal Gas Law Calculator.