Charles's Law Calculator

Charles's Law states that at constant pressure the volume of a fixed amount of gas is directly proportional to its absolute temperature:

$\frac{V_1}{T_1} = \frac{V_2}{T_2} \qquad \text{equivalently} \qquad V = kT$

• $V_1$, $V_2$ — the initial and final volume. Any unit works (L, mL, m³) as long as both sides use the same one, because the units cancel in the ratio.
• $T_1$, $T_2$ — the initial and final temperature, which must be in kelvin: $T(\mathrm{K}) = T(^\circ\mathrm{C}) + 273.15$.
• $k$ — a proportionality constant fixed by the pressure and the amount of gas.

What the law assumes. The gas is treated as ideal, the pressure is held constant, and the amount of gas is constant — nothing escapes, dissolves or reacts. Real gases follow the law closely at ordinary pressures and well above their boiling points, and deviate when they are cold or compressed enough that molecular volume and intermolecular attraction stop being negligible.

Why kelvin. A plot of $V$ against temperature in °C is a straight line that extrapolates to $V = 0$ at $-273.15$ °C, not at 0 °C. Only on the kelvin scale, whose zero sits at that intercept, is the ratio $V/T$ actually constant.

Step by step

1. List the four quantities $V_1, T_1, V_2, T_2$ and mark which one is unknown. Three must be given.
2. Convert every temperature to kelvin. This is the step that decides whether the answer is right.
3. Match the volume units. Convert one so that $V_1$ and $V_2$ share a unit; no conversion is needed for temperature beyond kelvin.
4. Rearrange, then substitute.

$V_2 = V_1 \times \frac{T_2}{T_1} \qquad\qquad T_2 = T_1 \times \frac{V_2}{V_1}$

5. Sanity-check the direction. Heating at constant pressure must increase the volume; cooling must decrease it. If your answer moves the other way, the ratio is upside down.

Significant figures

The answer carries as many significant figures as the least precise measurement. Adding 273.15 is an exact conversion, so it never removes digits — but it does change how many you have: 25 °C (2 s.f.) becomes 298.15 K, and the precision of the original reading, ±1 °C, is what limits the result. Quote a volume found from 3-significant-figure data to 3 significant figures.

Reading it as a graph

Because $V = kT$, a $V$-versus-$T$(K) plot is a straight line through the origin with slope $k$. The slope is $nR/P$, so the same data set also tells you the amount of gas if the pressure is known.

• Using Celsius or Fahrenheit. Substituting 25 and 75 instead of 298.15 K and 348.15 K gives a volume ratio of 3.0 instead of 1.17 — a threefold error. Charles's Law is only linear on an absolute scale.
• Mixing volume units. $V_1$ in mL and $V_2$ in L silently rescales the answer by 1000.
• Forgetting the constant-pressure condition. If the pressure also changes, Charles's Law alone is not enough — use the combined gas law $P_1V_1/T_1 = P_2V_2/T_2$.
• Applying it across a phase change. Once the gas condenses, there is no longer a fixed amount of gas and the proportionality breaks down.
• Inverting the ratio. $V_2 = V_1 (T_2/T_1)$, not $V_1 (T_1/T_2)$. Checking that heating enlarges the volume catches this instantly.