Charles's Law Calculator
Solve V₁/T₁ = V₂/T₂ for any of the four variables — temperature is always converted to kelvin automatically. A live 3D balloon expands and changes color with temperature, alongside charts of the classic V–T line through absolute zero.
Reviewed by the ToolNestr Editorial Team — July 2026
Important: Charles's law requires absolute temperature. Enter °C or K below — °C is converted to kelvin automatically before solving.
Two ideas that trip students up
1. Hotter gas takes up more room
A cold, small, blue balloon next to a hot, large, red one — the same gas at two different absolute temperatures, expanding at constant pressure.
2. Every line points to absolute zero
Straight V-vs-T lines for different gas samples all extrapolate back to the same point: V = 0 at 0 K. That shared intercept is exactly how absolute zero was discovered.
Charles's law graphs
How it works
The core idea in one line: heat a gas at constant pressure and it expands in direct proportion to its absolute temperature — but that proportion only works in kelvin, never Celsius.
V₁/T₁ = V₂/T₂
volume ÷ absolute temperature is constant at fixed P and n
K = °C + 273.15
convert to kelvin before using the formula — always
V₂ = V₁ × T₂ / T₁
solve for the new volume
Rearranged, V₁/T₁ = V₂/T₂ solves any of the four variables: V₂ = V₁T₂/T₁ and T₂ = T₁V₂/V₁. It only holds when pressure and the amount of gas (moles) stay fixed — and temperature must be absolute (kelvin), since the direct proportionality breaks down completely if you use Celsius, whose zero point is arbitrary rather than physical.
Worked example 1 — heating a gas sample
Given: A gas occupies 2.00 L at 20°C. It is heated at constant pressure to 80°C. Find the new volume.
Using Celsius directly (80 ÷ 20 = 4×) would badly overstate the expansion — the correct kelvin ratio gives only about a 20% increase.
Worked example 2 — a weather balloon cooling as it rises
Given: A weather balloon holds 5.00 L of gas at 25°C at launch. As it rises, the surrounding air cools it to -40°C, while pressure inside stays effectively constant. Find the new volume.
The gas contracts as it cools, exactly as Charles's law predicts — this is one reason balloon envelopes are launched under-inflated, with room to change size in either direction.
Charles's law vs Boyle's law vs Gay-Lussac's law
Each law holds one variable fixed and relates the other two — easy to mix up unless you track what stays constant.
| Law | Held constant | Relationship |
|---|---|---|
| Charles's law | Pressure, moles | V and T — directly proportional (V₁/T₁ = V₂/T₂) |
| Boyle's law | Temperature, moles | P and V — inversely proportional (P₁V₁ = P₂V₂) |
| Gay-Lussac's law | Volume, moles | P and T — directly proportional (P₁/T₁ = P₂/T₂) |
All three are special cases of the combined/ideal gas law PV = nRT, each freezing one variable to isolate the other two.
Where Charles's law actually matters
🎈 Hot air balloons
Heating the air inside a balloon envelope makes it expand and become less dense than the surrounding cool air, generating lift. This is the single most direct, visible demonstration of Charles's law in everyday life.
🌤️ Weather balloons
As a weather balloon climbs into the cold upper atmosphere, the gas inside contracts as temperature falls, then re-expands as ambient pressure drops with altitude — a combination of Charles's and Boyle's effects that engineers must plan for.
🔧 Engine cylinders
Combustion rapidly heats gas inside an engine cylinder at roughly constant pressure during parts of the cycle, driving the dramatic volume expansion that pushes the piston — Charles's law in a very compressed timescale.
🧴 Aerosol can warnings
Aerosol cans warn against storage near heat because warming the gas inside raises its volume (and pressure) sharply, risking rupture — the same underlying physics as the balloon, just in a rigid container instead.
Common misconceptions
"You can plug Celsius values straight into Charles's law."
False — this is the single most common student error. The V ∝ T proportionality only holds for absolute temperature. You must convert every temperature to kelvin (K = °C + 273.15) before using V₁/T₁ = V₂/T₂, or the answer will be badly wrong.
"Charles's law means volume and temperature are equal."
False — they are proportional, not equal. V/T is a constant ratio, not V = T. Doubling the absolute temperature doubles the volume; it does not make the volume numerically equal to the temperature.
"Charles's law works even if pressure changes too."
False — pressure (and the amount of gas) must be held constant. That constraint is the entire premise of the law. If pressure changes as well, you need the combined gas law, P₁V₁/T₁ = P₂V₂/T₂, instead.
"A gas's volume can actually reach zero at absolute zero."
Not physically — real gases liquefy or solidify long before 0 K, so the straight-line V–T relationship breaks down at low temperatures. The V = 0 extrapolation is a theoretical idealization, but it is precisely what led scientists to locate absolute zero at -273.15°C.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, Chemistry 2e — gas laws and Charles's law (free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 10, Gases.
- • Zumdahl & Zumdahl, Chemistry — the gas laws and kinetic molecular theory.
Charles's law assumes constant pressure and a fixed amount of gas (n). Temperatures are converted to kelvin internally. Results are rounded for display.
How to use this calculator
Enter three values
Fill any three of V₁, T₁, V₂, T₂; the fourth solves live.
Mind the units
Toggle °C or K for each temperature field — conversion to kelvin happens automatically before solving.
See it in the balloon
Drag the temperature slider and watch the 3D balloon expand and shift color from blue to red.
Related tools
Frequently asked questions
What is Charles's law?
Charles's law states that at constant pressure and a fixed amount of gas, volume and absolute temperature are directly proportional: V₁/T₁ = V₂/T₂. Heat a gas and it expands; cool it and it contracts, in direct proportion to its temperature in kelvin.
Why must temperature be in kelvin, not Celsius, for Charles's law?
The proportionality V ∝ T only holds for absolute temperature. Celsius has an arbitrary zero point (the freezing point of water), so ratios of Celsius values are meaningless for this law — 40°C is not "twice as hot" as 20°C. Kelvin starts at absolute zero, where a gas's volume would theoretically reach zero, so ratios of kelvin temperatures correctly track ratios of volume. Always convert with K = °C + 273.15 before using the formula.
What has to stay constant for Charles's law to apply?
Pressure and the amount of gas (moles) must both stay fixed. Charles's law isolates the volume–temperature relationship only when those two are held constant — if pressure also changes, you need the combined gas law instead.
How did Charles's law lead to the discovery of absolute zero?
Plotting volume against Celsius temperature for a gas at constant pressure gives a straight line. Extrapolating that line backward, it crosses V = 0 at almost exactly -273.15°C for every gas, regardless of what gas it is. That universal x-intercept is what led scientists to define absolute zero (0 K) as the coldest possible temperature — the point where an ideal gas's volume would vanish.
Can Charles's law volume actually reach zero?
No — real gases liquefy or solidify long before reaching absolute zero, so the straight-line V–T relationship breaks down at low temperatures. The V = 0 extrapolation is a theoretical construct of the ideal gas model, not something you can observe directly, but it correctly predicts where absolute zero sits on the temperature scale.