This Charles’s law calculator solves V₁/T₁ = V₂/T₂ — how a gas’s volume changes with temperature at constant pressure. Enter any three values (temperatures in kelvin) to find the fourth.
What Is Charles’s Law?
Charles’s law says that at constant pressure, a gas’s volume is directly proportional to its absolute temperature: heat a gas and it expands in exact proportion to its kelvin temperature. It is the constant-pressure slice of the Ideal Gas Law, the sibling of Boyle’s Law (constant temperature), and part of our Physics Calculators collection.
Worked Example (Verified)
A balloon holds 3.0 L at 300 K (27 °C). Heat it to 450 K (177 °C) at constant pressure:
V₂ = V₁ × T₂/T₁ = 3.0 × 450/300 = 4.5 L. Temperature rose by a factor of 1.5, so the volume did too — direct proportionality doing exactly what it promises.
The Kelvin Rule (the Only Way This Law Breaks)
- Charles’s law works only in kelvin. Plugging in Celsius gives nonsense: 3 L at “27 °C” heated to “177 °C” would falsely predict 19.7 L.
- Convert first: K = °C + 273.15. The calculator displays °C alongside for intuition, but computes in kelvin.
- The proportionality extrapolates to zero volume at 0 K — the reasoning that first revealed absolute zero’s existence.
Charles’s Law in Real Life
- Hot-air balloons: heating the envelope’s air expands it (and spills some out), making the remaining air less dense than the surroundings — lift, via Charles’s law.
- A balloon in a freezer shrivels and re-inflates on warming — the classic demo.
- Tire pressure gauges on cold mornings: mostly Gay-Lussac territory (fixed volume), but a tire’s slight volume change is Charles quietly at work too.
Related Tools
- Boyle’s Law Calculator — pressure ↔ volume
- Ideal Gas Law Calculator — the parent law
- Gay-Lussac’s Law Calculator — pressure ↔ temperature
Frequently Asked Questions
What is the formula for Charles’s law?
V₁/T₁ = V₂/T₂, at constant pressure and amount of gas, with temperatures in kelvin.
Why must I use kelvin?
Because the proportionality is to absolute temperature. Celsius has an arbitrary zero (the freezing point of water), which breaks ratios; kelvin’s zero is absolute.
What happens to a gas heated from 300 K to 600 K?
Its volume doubles, at constant pressure — temperature factor 2, volume factor 2.
How is Charles’s law different from Boyle’s law?
Charles holds pressure constant and links volume to temperature; Boyle holds temperature constant and links pressure to volume. Both are special cases of PV = nRT.
Does Charles’s law work for liquids?
No — it is a gas law. Liquids expand with temperature too, but weakly and not by this proportionality.
Is this Charles’s law calculator free?
Yes — free, instant, no sign-up.