Charles Law Calculator

Charles’ law, sometimes called the law of volumes, states that the volume of a fixed mass of gas is directly proportional to its absolute temperature when pressure remains constant. In equation form: V ∝ T, or equivalently V/T = constant. For two states of the same gas at constant pressure, this gives the two-point form V₁/T₁ = V₂/T₂.

The law was discovered experimentally by Jacques Charles around 1787 during balloon experiments, though Charles never published his findings. Guillaume Amontons had conducted similar studies a century earlier. Joseph Gay-Lussac published the generalised results for gases in 1808, which is why some textbooks credit the law to Gay-Lussac instead.

Charles’ law applies to an ideal gas undergoing an isobaric process — a process in which pressure stays constant throughout. Air is a real gas, but under everyday conditions of moderate temperature and pressure it behaves close enough to ideal that Charles’ law gives accurate, practical results, a consequence of the same kinetic molecular theory that describes how gas molecules move and collide.

Temperature must always be expressed in Kelvin, never Celsius or Fahrenheit, because the relationship V ∝ T only holds for an absolute temperature scale — one whose zero corresponds to a true physical zero of thermal energy. The Kelvin scale starts at absolute zero (0 K = −273.15 °C), the temperature at which molecular motion theoretically ceases and an ideal gas’s volume would shrink to zero. Substituting Celsius or Fahrenheit directly into the formula gives physically meaningless answers.

Charles’ law is a foundational result in thermodynamics and a building block of the broader Combined Gas Law and the Ideal Gas Law (PV = nRT).

The Charles law formula is V₁/T₁ = V₂/T₂, where the subscripts 1 and 2 indicate the initial and final states of the gas at constant pressure. Volumes may be expressed in litres, millilitres, cubic metres, or cubic feet — the formula works in any unit as long as both volumes use the same one. Temperatures, however, must be converted to Kelvin before calculating. To convert Celsius to Kelvin, add 273.15. To convert Fahrenheit to Kelvin, use K = (°F − 32) × 5/9 + 273.15.

The formula is valid only when pressure and the amount of gas (moles) remain constant. If pressure also changes, use the combined gas law equation. If temperature is fixed and pressure changes instead, use Boyle’s Law. If volume is fixed, use Gay-Lussac’s Law. The rearranged form needed depends on which value is unknown — see the breakdown for each variable below.

The equation V₁/T₁ = V₂/T₂ comes from the proportionality statement V ∝ T. Writing this as an equality with a constant k gives V = kT, or V/T = k. Because k depends only on the fixed amount of gas and the fixed pressure, it is the same at any state of the gas — so V₁/T₁ and V₂/T₂ must equal the same constant, giving the two-point form directly.

“Directly proportional” has a precise meaning here: doubling the absolute temperature exactly doubles the volume; tripling it triples the volume. This fixed ratio is the thermal expansion ratio of the gas, and the relationship is linear, passing through the origin.

Charles’ law connects to the Ideal Gas Law, PV = nRT. Solving for V gives V = (nR/P) × T. When n, the gas constant R, and P are held constant, the bracketed quantity is itself a constant — equal to the Charles law constant k = nR/P. Charles’ law is the special case of the Ideal Gas Law for an isobaric process. Likewise, the Combined Gas Law P₁V₁/T₁ = P₂V₂/T₂ reduces to Charles’ law when P₁ = P₂.

The graph shows a perfectly straight line through the origin at constant pressure. The slope of the line equals V/T = k, the Charles law constant. As temperature increases, volume increases proportionally. At absolute zero, the line theoretically reaches zero volume — real gases liquefy or solidify before reaching this point.

Each line in the second diagram represents Charles’ law at a different constant pressure: the gas law constant k = V/T changes with pressure, but the linear, origin-through relationship never does. Because k = nR/P, the lowest pressure P₁ produces the steepest line, P₂ sits between the other two, and the highest pressure P₃ produces the shallowest line, which is why the three lines fan out from a shared origin rather than running side by side. The graph holds only for ideal gases; real gas deviations appear at high pressures or very low temperatures.

Spelled out, the table separates the six laws by what each one freezes. Charles’ law holds pressure and moles fixed, Boyle’s holds temperature and moles, Gay-Lussac’s holds volume and moles, and Avogadro’s holds pressure and temperature. The combined form fixes only the amount of gas, and the ideal form fixes nothing at all.

Need to solve for pressure changes alongside volume and temperature? Our combined gas law calculator merges Charles’, Boyle’s, and Gay-Lussac’s laws into one solver.

The three single-variable gas laws describe special cases of a more general relationship. Combining all three yields the Combined Gas Law, which still assumes a fixed amount of gas. Adding the role of moles via the universal gas constant R = 8.314 J/(mol·K) produces the Ideal Gas Law — the most general statement of ideal gas behaviour.

The diagram reads as a chain of five boxes that wraps onto a second row. Boyle’s law comes first, pairing pressure with volume at fixed temperature. Charles’ law follows, pairing volume with temperature at fixed pressure. Gay-Lussac’s law completes the trio, pairing pressure with temperature at fixed volume. The fourth box merges all three into one equation, and the fifth generalises it once more by letting the amount of gas enter the calculation. Each step along the chain removes a restriction rather than replacing the law before it.