What is Charles's Law?

Charles's Law states that, for a fixed amount of an ideal gas held at constant pressure, the volume is directly proportional to the absolute temperature: V / T = constant, or equivalently V1/T1 = V2/T2. It was formulated by Jacques Charles in 1787 and later formalised by Joseph Louis Gay-Lussac.

Why must temperature be in Kelvin?

Charles's Law requires absolute temperature because the relationship V proportional to T only holds on a scale that starts at absolute zero. Celsius and Fahrenheit have arbitrary zero points, so using them directly would give wrong answers. This calculator converts Celsius and Fahrenheit to Kelvin automatically before computing.

What does 'constant pressure' mean in practice?

It means the gas is free to expand or contract in response to temperature changes without the surrounding pressure changing — like a balloon exposed to the atmosphere, or a gas in a frictionless piston at ambient pressure. If pressure also changes, you need the Combined Gas Law (P1V1/T1 = P2V2/T2) instead.

Can I use this for real gases or only ideal gases?

Strictly, Charles's Law applies to ideal gases. Real gases deviate at high pressures or near their liquefaction points. For everyday conditions — atmospheric pressure, temperatures well above the boiling point of the gas — the ideal approximation is accurate to within a fraction of a percent, so this calculator is perfectly suitable.

What volume units does the calculator support?

Litres (L), millilitres (mL) and cubic metres (m3). All three convert to m3 internally; the result is then converted back to whichever unit you selected for the unknown.

How can I verify the answer manually?

After computing, click 'Show working'. The last step prints V1/T1 and V2/T2 in m3/K side by side. For a correct answer the two ratios will be equal (they match to six decimal places, subject to floating-point rounding).

Charles's Law Calculator

Charles’s Law describes one of the most intuitive behaviours of gases: heat a gas and it expands; cool it and it contracts. Provided the pressure stays constant and the amount of gas is fixed, the relationship between volume and temperature is perfectly linear when temperature is measured in Kelvin. This calculator solves the law in any direction — find a missing volume or a missing temperature — and shows every conversion step so you can follow the maths.

The law and its formula

Jacques Charles observed in 1787 that equal volumes of different gases expand by the same fraction for a given rise in temperature. The modern statement is:

V / T = constant (at constant pressure, fixed amount of gas)

For comparing two states of the same gas:

V₁ / T₁ = V₂ / T₂

Rearranged to solve for each variable:

V2 = V1 × T2 / T1
V1 = V2 × T1 / T2
T2 = T1 × V2 / V1
T1 = T2 × V1 / V2

Temperature must be in Kelvin (K). The conversion is simple: K = °C + 273.15. This calculator handles the conversion automatically if you enter Celsius or Fahrenheit.

How the calculator works

You select which of the four variables to solve for.
You enter the three known values with their units (volume in L/mL/m³; temperature in K/°C/°F).
The calculator converts every input to SI base units (m³ and K), applies the appropriate rearrangement, and converts the answer back to your preferred output unit.
A verification step confirms V₁/T₁ = V₂/T₂ (both ratios shown in m³/K) so you can spot any input error instantly.
Click Copy result + working to paste the full step-by-step solution into a document or lab report.

Worked example

A sample of nitrogen gas occupies 3.00 L at 27 °C (300 K). The gas is heated at constant pressure to 127 °C (400 K). What is the new volume?

Using V₂ = V₁ × T₂ / T₁:

V₁ = 3.00 L = 0.003 m³
T₁ = 300 K
T₂ = 400 K
V₂ = 0.003 × 400 / 300 = 0.004 m³ = 4.00 L

The volume increases by one-third, exactly in proportion to the absolute-temperature rise. You can verify: V₁/T₁ = 0.003/300 = 1×10⁻⁵ m³/K, and V₂/T₂ = 0.004/400 = 1×10⁻⁵ m³/K. The ratios match.

V₁	T₁	T₂	V₂
2.00 L	273 K (0 °C)	546 K (273 °C)	4.00 L
500 mL	300 K	450 K	750 mL
1.00 m³	250 K	500 K	2.00 m³
10.0 L	200 K	300 K	15.0 L

Real-world applications

Charles’s Law governs many everyday phenomena: hot-air balloons rise because heated air at constant (atmospheric) pressure expands, becoming less dense than the surrounding cooler air; bread dough rises in a warm oven as gas bubbles expand; car tyre pressure increases slightly in summer because air in the tyre warms up. In the laboratory, knowing how volume scales with temperature is essential for calibrating gas syringes, designing reaction vessels, and interpreting gas-collection-over-water experiments.

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