About

Charles' Law describes the linear relationship between the volume V of a confined gas and its absolute temperature T at constant pressure. Formally, V ∝ T when pressure P and amount of substance n are held fixed. The law breaks down near condensation points and at extreme pressures where intermolecular forces dominate. Miscalculating temperature in Celsius instead of Kelvin is the most common source of error. It produces nonsensical negative volumes. This calculator enforces Kelvin conversion internally, preventing that class of mistake.

The relationship was first documented by Jacques Charles in 1787 and later confirmed by Joseph Louis Gay-Lussac in 1802. It applies strictly to ideal gases. Real gases deviate significantly below their Boyle temperature or above roughly 10 MPa. For those regimes, the van der Waals equation or Peng-Robinson EOS is required. This tool approximates behavior assuming ideal gas conditions and constant pressure throughout the process.

Formulas

Charles' Law states that for a fixed mass of gas at constant pressure, the ratio of volume to absolute temperature is constant.

V₁T₁ = V₂T₂

Solving for each variable:

V₂ = V₁ × T₂T₁

T₂ = T₁ × V₂V₁

Temperature conversion to Kelvin:

T_K = T_°C + 273.15

T_K = (T_°F − 32) × 59 + 273.15

T_K = T_°R × 59

Where V₁ = initial volume, T₁ = initial absolute temperature, V₂ = final volume, T₂ = final absolute temperature. All temperatures must be in Kelvin (K) for the law to hold. Using Celsius or Fahrenheit directly produces incorrect results because these scales have arbitrary zero points that do not represent the absence of thermal energy.

Reference Data

Gas	Molar Mass g/mol	Boiling Point K	Critical Temp K	Critical Pressure MPa	Ideal Gas Validity Range
Helium (He)	4.003	4.22	5.19	0.227	Excellent above 10 K
Hydrogen (H₂)	2.016	20.28	33.14	1.296	Good above 50 K
Neon (Ne)	20.180	27.07	44.49	2.760	Good above 60 K
Nitrogen (N₂)	28.014	77.36	126.19	3.390	Good above 150 K
Oxygen (O₂)	31.998	90.20	154.58	5.043	Good above 180 K
Argon (Ar)	39.948	87.30	150.86	4.898	Good above 180 K
Carbon Dioxide (CO₂)	44.009	194.65	304.13	7.375	Fair above 350 K
Methane (CH₄)	16.043	111.66	190.56	4.599	Good above 220 K
Ammonia (NH₃)	17.031	239.81	405.56	11.357	Fair above 450 K
Water Vapor (H₂O)	18.015	373.15	647.10	22.064	Fair above 700 K
Sulfur Dioxide (SO₂)	64.066	263.05	430.64	7.884	Fair above 480 K
Chlorine (Cl₂)	70.906	239.11	416.90	7.991	Fair above 460 K
Propane (C₃H₈)	44.096	231.04	369.83	4.248	Fair above 400 K
Ethane (C₂H₆)	30.069	184.57	305.32	4.872	Good above 340 K
Xenon (Xe)	131.293	165.03	289.73	5.841	Good above 320 K

Frequently Asked Questions

Charles' Law requires an absolute temperature scale because the proportionality V ∝ T only holds when T = 0 represents zero molecular kinetic energy. Celsius and Fahrenheit have arbitrary zero points. Using °C directly would predict that gas at 0 °C has zero volume, which is physically meaningless. Kelvin starts at absolute zero (−273.15 °C), ensuring the linear relationship between volume and temperature remains mathematically valid across all positive values.

A result below 0 K is physically impossible and indicates invalid input conditions. This calculator will flag such results as errors. In practice, a negative Kelvin result means the assumed constant-pressure process cannot occur - the gas would condense into a liquid or solid before reaching that state. Always verify that your initial conditions are within the gas phase region for the substance in question.

Charles' Law is derived from the ideal gas model, which assumes no intermolecular forces and zero molecular volume. Real gases follow it closely at high temperatures and low pressures - specifically, when the temperature is well above the gas's critical temperature and pressure is below roughly 1 MPa. Gases like helium and hydrogen approximate ideal behavior across wide ranges. Polar molecules like water vapor or ammonia deviate substantially near their condensation points. For high-accuracy work with real gases, use the van der Waals equation or the Peng-Robinson equation of state.

Yes. Charles' Law applies to gas mixtures as long as no component condenses during the temperature change. Dalton's Law of Partial Pressures ensures each component behaves independently at constant total pressure. The total volume of the mixture follows V₁/T₁ = V₂/T₂ identically to a pure gas. However, if any component reaches its dew point during heating or cooling, that fraction will undergo a phase transition and the law no longer applies to the system.

Charles' Law strictly requires constant pressure throughout the process. If pressure changes simultaneously with temperature, you need the Combined Gas Law: (P₁V₁)/T₁ = (P₂V₂)/T₂. Even small pressure fluctuations - for example, from altitude changes during an experiment - introduce systematic error. At sea level, atmospheric pressure varies by roughly ±3 kPa day to day, which translates to approximately ±3% volume error for sensitive measurements.

The calculator accepts any consistent volume unit for both V₁ and V₂ - liters, milliliters, cubic meters, cubic feet, or gallons. Because Charles' Law is a ratio (V₁/T₁ = V₂/T₂), the units cancel as long as both volumes use the same unit. The calculator does not convert between volume units; it solves the proportionality. Enter both volumes in the same unit and interpret the result in that same unit.